4.2: Theoretical Probability
It is not always feasible to conduct an experiment over and over again, so it would be better to be able to find the probabilities without conducting the experiment. These probabilities are called Theoretical Probabilities .
To be able to do theoretical probabilities, there is an assumption that you need to consider. It is that all of the outcomes in the sample space need to be equally likely outcomes . This means that every outcome of the experiment needs to have the same chance of happening.
Example \(\PageIndex{1}\) Equally likely outcomes
Which of the following experiments have equally likely outcomes?
- Rolling a fair die.
- Flip a coin that is weighted so one side comes up more often than the other.
- Pull a ball out of a can containing 6 red balls and 8 green balls.
- Picking a card from a deck.
- Rolling a die to see if it is fair.
 The outcomes are the different sides, so each outcome is equally likely.
- Since the coin is weighted, one side is more likely to come up than the other side. The outcomes are the different sides, so each outcome is not equally likely.
- Since each ball is the same size, then each ball has the same chance of being chosen. The outcomes of this experiment are the individual balls, so each outcome is equally likely. Don’t assume that because the chances of pulling a red ball are less than pulling a green ball that the outcomes are not equally likely.
- If you assume that the deck is fair, then each card has the same chance of being chosen. Thus the outcomes are equally likely outcomes. You do have to make this assumption. For many of the experiments you will do, you do have to make this kind of assumption.
- In this case you are not sure the die is fair. The only way to determine if it is fair is to actually conduct the experiment, since you don’t know if the outcomes are equally likely. If the experimental probabilities are fairly close to the theoretical probabilities, then the die is fair.
If the outcomes are not equally likely, then you must do experimental probabilities. If the outcomes are equally likely, then you can do theoretical probabilities.
Definition \(\PageIndex{1}\): Theoretical Probabilities
If the outcomes of an experiment are equally likely, then the probability of event A happening is
\(P(A)=\dfrac{\# \text { of outcomes in event space }}{\# \text { of outcomes in sample space }}\)
Example \(\PageIndex{2}\) calculating theoretical probabilities
Suppose you conduct an experiment where you flip a fair coin twice.
- What is the sample space?
- What is the probability of getting exactly one head?
- What is the probability of getting at least one head?
- What is the probability of getting a head and a tail?
- What is the probability of getting a head or a tail?
- What is the probability of getting a foot?
- What is the probability of each outcome? What is the sum of these probabilities?
Solution
a. There are several different sample spaces you can do. One is SS={0, 1, 2} where you are counting the number of heads. However, the outcomes are not equally likely since you can get one head by getting a head on the first flip and a tail on the second or a tail on the first flip and a head on the second. There are 2 ways to get that outcome and only one way to get the other outcomes. Instead it might be better to give the sample space as listing what can happen on each flip. Let H = head and T = tail, and list which can happen on each flip.
SS={HH, HT, TH, TT}
b. Let A = getting exactly one head. The event space is A = {HT, TH}. So
\(P(A)=\dfrac{2}{4} \text { or } \dfrac{1}{2}\)
It may not be advantageous to reduce the fractions to lowest terms, since it is easier to compare fractions if they have the same denominator.
c. Let B = getting at least one head. At least one head means get one or more. The event space is B = {HT, TH, HH} and
\(P(B)=\dfrac{3}{4}\)
Since P(B) is greater than the P(A), then event B is more likely to happen than event A.
d. Let C = getting a head and a tail = {HT, TH} and
\(P(C)=\dfrac{2}{4}\)
This is the same event space as event A, but it is a different event. Sometimes two different events can give the same event space.
e. Let D = getting a head or a tail. Since or means one or the other or both and it doesn’t specify the number of heads or tails, then D = {HH, HT, TH, TT} and
\(P(D)=\dfrac{4}{4}=1\)
f. Let E = getting a foot. Since you can’t get a foot, E = {} or the empty set and
\(P(E)=\dfrac{0}{4}=0\)
g. \(P(H H)=P(H T)=P(T H)=P(T T)=\dfrac{1}{4}\). If you add all of these probabilities together you get 1.
This example had some results in it that are important concepts. They are summarized below:
Probability Properties
- \(0 \leq P(\text { event }) \leq 1\)
- If the P(event)=1, then it will happen and is called the certain event.
- If the P(event)=0, then it cannot happen and is called the impossible event.
- \(\sum P(\text { outcome })=1\)
Example \(\PageIndex{3}\) calculating theoretical probabilities
Suppose you conduct an experiment where you pull a card from a standard deck.
- What is the sample space?
- What is the probability of getting a Spade?
- What is the probability of getting a Jack?
- What is the probability of getting an Ace?
- What is the probability of not getting an Ace?
- What is the probability of getting a Spade and an Ace?
- What is the probability of getting a Spade or an Ace?
- What is the probability of getting a Jack and an Ace?
- What is the probability of getting a Jack or an Ace?
Solution
a. SS = {2S, 3S, 4S, 5S, 6S, 7S, 8S, 9S, 10S, JS, QS, KS, AS, 2C, 3C, 4C, 5C, 6C, 7C, 8C, 9C, 10C, JC, QC, KC, AC, 2D, 3D, 4D, 5D, 6D, 7D, 8D, 9D, 10D, JD, QD, KD, AD, 2H, 3H, 4H, 5H, 6H, 7H, 8H, 9H, 10H, JH, QH, KH, AH}
b. Let A = getting a spade = {2S, 3S, 4S, 5S, 6S, 7S, 8S, 9S, 10S, JS, QS, KS, AS} so
\(P(A)=\dfrac{13}{52}\)
c. Let B = getting a Jack = {JS, JC, JH, JD} so
\(P(B)=\dfrac{4}{52}\)
d. Let C = getting an Ace = {AS, AC, AH, AD} so
\(P(C)=\dfrac{4}{52}\)
e. Let D = not getting an Ace = {2S, 3S, 4S, 5S, 6S, 7S, 8S, 9S, 10S, JS, QS, KS, 2C, 3C, 4C, 5C, 6C, 7C, 8C, 9C, 10C, JC, QC, KC, 2D, 3D, 4D, 5D, 6D, 7D, 8D, 9D, 10D, JD, QD, KD, 2H, 3H, 4H, 5H, 6H, 7H, 8H, 9H, 10H, JH, QH, KH} so
\(P(D)=\dfrac{48}{52}\)
Notice, \(P(D)+P(C)=\dfrac{48}{52}+\dfrac{4}{52}=1\), so you could have found the probability of D by doing 1 minus the probability of C \(P(D)=1-P(C)=1-\dfrac{4}{52}=\dfrac{48}{52}\).
f. Let E = getting a Spade and an Ace = {AS} so
\(P(E)=\dfrac{1}{52}\)
g. Let F = getting a Spade and an Ace ={2S, 3S, 4S, 5S, 6S, 7S, 8S, 9S, 10S, JS, QS, KS, AS, AC, AD, AH} so
\(P(F)=\dfrac{16}{52}\)
h. Let G = getting a Jack and an Ace = { } since you can’t do that with one card. So
\(P(G)=0\)
i. Let H = getting a Jack or an Ace = {JS, JC, JD, JH, AS, AC, AD, AH} so
\(P(H)=\dfrac{8}{52}\)
Example \(\PageIndex{4}\) calculating theoretical probabilities
Suppose you have an iPod Shuffle with the following songs on it: 5 Rolling Stones songs, 7 Beatles songs, 9 Bob Dylan songs, 4 Faith Hill songs, 2 Taylor Swift songs, 7 U2 songs, 4 Mariah Carey songs, 7 Bob Marley songs, 6 Bunny Wailer songs, 7 Elton John songs, 5 Led Zeppelin songs, and 4 Dave Mathews Band songs. The different genre that you have are rock from the 60s which includes Rolling Stones, Beatles, and Bob Dylan; country includes Faith Hill and Taylor Swift; rock of the 90s includes U2 and Mariah Carey; Reggae includes Bob Marley and Bunny Wailer; rock of the 70s includes Elton John and Led Zeppelin; and bluegrasss/rock includes Dave Mathews Band.
The way an iPod Shuffle works, is it randomly picks the next song so you have no idea what the next song will be. Now you would like to calculate the probability that you will hear the type of music or the artist that you are interested in. The sample set is too difficult to write out, but you can figure it from looking at the number in each set and the total number. The total number of songs you have is 67.
- What is the probability that you will hear a Faith Hill song?
- What is the probability that you will hear a Bunny Wailer song?
- What is the probability that you will hear a song from the 60s?
- What is the probability that you will hear a Reggae song?
- What is the probability that you will hear a song from the 90s or a bluegrass/rock song?
- What is the probability that you will hear an Elton John or a Taylor Swift song?
- What is the probability that you will hear a country song or a U2 song?
Solution
a. There are 4 Faith Hill songs out of the 67 songs, so
\(P(\text { Faith Hill song })=\dfrac{4}{67}\)
b. There are 6 Bunny Wailer songs, so
\(P(\text { Bunny Wailer })=\dfrac{6}{67}\)
c. There are 5, 7, and 9 songs that are classified as rock from the 60s, which is 21 total, so
\(P(\text { rock from the } 60 \mathrm{s})=\dfrac{21}{67}\)
d. There are 6 and 7 songs that are classified as Reggae, which is 13 total, so
\(P(\text { Reggae })=\dfrac{13}{67}\)
e. There are 7 and 4 songs that are songs from the 90s and 4 songs that are bluegrass/rock, for a total of 15, so
\(P(\text { rock from the } 90 \text { s or bluegrass/rock })=\dfrac{15}{67}\)
f. There are 7 Elton John songs and 2 Taylor Swift songs, for a total of 9, so
\(P(\text { Elton John or Taylor Swift song })=\dfrac{9}{67}\)
g. There are 6 country songs and 7 U2 songs, for a total of 13, so
\(P(\text { country or } \mathrm{U} 2 \text { song })=\dfrac{13}{67}\)
Of course you can do any other combinations you would like.
Notice in Example \(\PageIndex{3}\) part e, it was mentioned that the probability of event D plus the probability of event C was 1. This is because these two events have no outcomes in common, and together they make up the entire sample space. Events that have this property are called complementary events .
Definition \(\PageIndex{2}\): complementary events
If two events are complementary events then to find the probability of one just subtract the probability of the other from one. Notation used for complement of A is not A or \(A^{c}\).
\(P(A)+P\left(A^{c}\right)=1, \text { or } P(A)=1-P\left(A^{c}\right)\)
Example \(\PageIndex{5}\) complementary events
- Suppose you know that the probability of it raining today is 0.45. What is the probability of it not raining?
- Suppose you know the probability of not getting the flu is 0.24. What is the probability of getting the flu?
- In an experiment of picking a card from a deck, what is the probability of not getting a card that is a Queen?
Solution
a. Since not raining is the complement of raining, then
\(P(\text { not raining })=1-P(\text { raining })=1-0.45=0.55\)
b. Since getting the flu is the complement of not getting the flu, then
\(P(\text { getting the flu })=1-P(\text { not getting the flu })=1-0.24=0.76\)
c. You could do this problem by listing all the ways to not get a queen, but that set is fairly large. One advantage of the complement is that it reduces the workload. You use the complement in many situations to make the work shorter and easier. In this case it is easier to list all the ways to get a Queen, find the probability of the Queen, and then subtract from one. Queen = {QS, QC, QD, QH} so
\(P(\text { Queen })=\dfrac{4}{52}\) and
\(P(\text { not Queen })=1-P(\text { Queen })=1-\dfrac{4}{52}=\dfrac{48}{52}\)
The complement is useful when you are trying to find the probability of an event that involves the words at least or an event that involves the words at most. As an example of an at least event is suppose you want to find the probability of making at least $50,000 when you graduate from college. That means you want the probability of your salary being greater than or equal to $50,000. An example of an at most event is suppose you want to find the probability of rolling a die and getting at most a 4. That means that you want to get less than or equal to a 4 on the die. The reason to use the complement is that sometimes it is easier to find the probability of the complement and then subtract from 1. Example \(\PageIndex{6}\) demonstrates how to do this.
Example \(\PageIndex{6}\) using the complement to find probabilities
- In an experiment of rolling a fair die one time, find the probability of rolling at most a 4 on the die.
- In an experiment of pulling a card from a fair deck, find the probability of pulling at least a 5 (ace is a high card in this example).
Solution
a. The sample space for this experiment is {1, 2, 3, 4, 5, 6}. You want the event of getting at most a 4, which is the same as thinking of getting 4 or less. The event space is {1, 2, 3, 4}. The probability is
\(P(\text { at most } 4)=\dfrac{4}{6}\)
Or you could have used the complement. The complement of rolling at most a 4 would be rolling number bigger than 4. The event space for the complement is {5, 6}. The probability of the complement is \(\dfrac{2}{6}\). The probability of at most 4 would be
\(P(\text { at most } 4)=1-P(\text { more than } 4)=1-\dfrac{2}{6}=\dfrac{4}{6}\)
Notice you have the same answer, but the event space was easier to write out. On this example it probability wasn’t that useful, but in the future there will be events where it is much easier to use the complement.
b. The sample space for this experiment is
SS = {2S, 3S, 4S, 5S, 6S, 7S, 8S, 9S, 10S, JS, QS, KS, AS, 2C, 3C, 4C, 5C, 6C, 7C, 8C, 9C, 10C, JC, QC, KC, AC, 2D, 3D, 4D, 5D, 6D, 7D, 8D, 9D, 10D, JD, QD, KD, AD, 2H, 3H, 4H, 5H, 6H, 7H, 8H, 9H, 10H, JH, QH, KH, AH}
Pulling a card that is at least a 5 would involve listing all of the cards that are a 5 or more. It would be much easier to list the outcomes that make up the complement. The complement of at least a 5 is less than a 5. That would be the event of 4 or less. The event space for the complement would be {2S, 3S, 4S, 2C, 3C, 4C, 2D, 3D, 4D, 2H, 3H, 4H}. The probability of the complement would be \(\dfrac{12}{52}\). The probability of at least a 5 would be
\(P(\text { at least } \mathbf{a} 5)=1-P(4 \text { or less })=1-\dfrac{12}{52}=\dfrac{40}{52}\)
Another concept was show in Example \(\PageIndex{3}\) parts g and i. The problems were looking for the probability of one event or another. In part g, it was looking for the probability of getting a Spade or an Ace. That was equal to \(\dfrac{16}{52}\). In part i, it was looking for the probability of getting a Jack or an Ace. That was equal to \(\dfrac{8}{52}\). If you look back at the parts b, c, and d, you might notice the following result:
\(P(\text { Jack })+P(\text { Ace })=P(\text { Jack or Ace }) \text { but } P(\text { Spade })+P(\text { Ace }) \neq P(\text { Spade or } \text { Ace })\)
Why does adding two individual probabilities together work in one situation to give the probability of one or another event and not give the correct probability in the other?
The reason this is true in the case of the Jack and the Ace is that these two events cannot happen together. There is no overlap between the two events, and in fact the \(P(\text { Jack and } \mathrm{Acc})=0\). However, in the case of the Spade and Ace, they can happen together. There is overlap, mainly the ace of spades. The \(P(\text { Spade and } \mathrm{Ace}) \neq 0\).
When two events cannot happen at the same time, they are called mutually exclusive . In the above situation, the events Jack and Ace are mutually exclusive, while the events Spade and Ace are not mutually exclusive.
Addition Rules:
If two events A and B are mutually exclusive, then
\(P(A \text { or } B)=P(A)+P(B) \text { and } P(A \text { and } B)=0\)
If two events A and B are not mutually exclusive, then
\(P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)\)
Example \(\PageIndex{7}\) using addition rules
Suppose your experiment is to roll two fair dice.
- What is the sample space?
- What is the probability of getting a sum of 5?
- What is the probability of getting the first die a 2?
- What is the probability of getting a sum of 7?
- What is the probability of getting a sum of 5 and the first die a 2?
- What is the probability of getting a sum of 5 or the first die a 2?
- What is the probability of getting a sum of 5 and sum of 7?
- What is the probability of getting a sum of 5 or sum of 7?
Solution
a. As with the other examples you need to come up with a sample space that has equally likely outcomes. One sample space is to list the sums possible on each roll. That sample space would look like: SS = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. However, there are more ways to get a sum of 7 then there are to get a sum of 2, so these outcomes are not equally likely. Another thought is to list the possibilities on each roll. As an example you could roll the dice and on the first die you could get a 1. The other die could be any number between 1 and 6, but say it is a 1 also. Then this outcome would look like (1,1). Similarly, you could get (1, 2), (1, 3), (1,4), (1, 5), or (1, 6). Also, you could get a 2, 3, 4, 5, or 6 on the first die instead. Putting this all together, you get the sample space:
\(\begin{array}{r}{\mathrm{SS}=\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)} \\ {(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)} \\ {(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)} \\ {(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)} \\ {(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)} \\ {(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) \}}\end{array}\)
Notice that a (2,3) is different from a (3,2), since the order that you roll the die is important and you can tell the difference between these two outcomes. You don’t need any of the doubles twice, since these are not distinguishable from each other in either order. This will always be the sample space for rolling two dice.
b. Let A = getting a sum of 5 = {(4,1), (3,2), (2,3), (1,4)} so
\(P(A)=\dfrac{4}{36}\)
c.  Let C = getting a sum of 7 = {(6,1), (5,2), (4,3), (3,4), (2,5), (1,6)} so
\(P(C)=\dfrac{6}{36}\)
e. This is events A and B which contains the outcome {(2,3)} so
\(P(A \text { and } B)=\dfrac{1}{36}\)
f. Notice from part e, that these two events are not mutually exclusive, so
\(P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)\)
\(=\dfrac{4}{36}+\dfrac{6}{36}-\dfrac{1}{36}\)
\(=\dfrac{9}{36}\)
g. These are the events A and C, which have no outcomes in common. Thus A and C = { } so
\(P(A \text { and } C)=0\)
h. From part g, these two events are mutually exclusive, so
\(P(A \text { or } C)=P(A)+P(C)\)
\(=\dfrac{4}{36}+\dfrac{6}{36}\)
\(=\dfrac{10}{36}\)
Odds
Many people like to talk about the odds of something happening or not happening. Mathematicians, statisticians, and scientists prefer to deal with probabilities since odds are difficult to work with, but gamblers prefer to work in odds for figuring out how much they are paid if they win.
Definition \(\PageIndex{3}\)
The actual odds against event A occurring are the ratio \(P\left(A^{c}\right) / P(A)\), usually expressed in the form a:b or a to b , where a and b are integers with no common factors.
Definition \(\PageIndex{4}\)
The actual odds in favor event A occurring are the ratio \(P(A) / P\left(A^{c}\right)\), which is the reciprocal of the odds against. If the odds against event A are a:b , then the odds in favor event A are b:a .
Definition \(\PageIndex{5}\)
The payoff odds against event A occurring are the ratio of the net profit (if you win) to the amount bet.
payoff odds against event A = (net profit) : (amount bet)
Example \(\PageIndex{8}\) odds against and payoff odds
In the game of Craps, if a shooter has a come-out roll of a 7 or an 11, it is called a natural and the pass line wins. The payoff odds are given by a casino as 1:1.
- Find the probability of a natural.
- Find the actual odds for a natural.
- Find the actual odds against a natural.
- If the casino pays 1:1, how much profit does the casino make on a $10 bet?
Solution
a. A natural is a 7 or 11. The sample space is
\(\begin{array}{r}{\mathrm{SS}=\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)} \\ {(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)} \\ {(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)} \\ {(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)} \\ {(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)} \\ {(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) \}}\end{array}\)
The event space is {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (5,6), (6,5)}
So \(P(7 \text { or } 11)=\dfrac{8}{36}\)
b.
odd for a natural \(=\dfrac{P(7 \text { or } 11)}{P(\text {not} 7 \text { or } 11)}\)
\(=\dfrac{8 / 36}{1-8 / 36}\)
\(=\dfrac{8 / 36}{28 / 36}\)
\(=\dfrac{8}{28}\)
\(=\dfrac{2}{7}\)
c.
odds against a natural \(=\dfrac{P(\text { not } 7 \text { or } 11)}{P(7 \text { or } 11)}=\dfrac{28}{8}=\dfrac{7}{2}=\dfrac{3.5}{1}\)
d. The actual odds are 3.5 to 1 while the payoff odds are 1 to 1. The casino pays you $10 for your $10 bet. If the casino paid you the actual odds, they would pay $3.50 on every $1 bet, and on $10, they pay \(3.5 * \$ 10=\$ 35\). Their profit is \(\$ 35-\$ 10=\$ 25\).
Homework
Exercise \(\PageIndex{1}\)
-
Example \(\PageIndex{1}\) contains the number of M&M’s of each color that were found in a case (Madison, 2013).
Blue Brown Green Orange Red Yellow Total 481 371 483 544<PHONE_NUMBER> Table \(\PageIndex{1}\) : M&M Distribution
a. Find the probability of choosing a green or red M&M.
b. Find the probability of choosing a blue, red, or yellow M&M.
c. Find the probability of not choosing a brown M&M.
d. Find the probability of not choosing a green M&M. -
Eyeglassomatic manufactures eyeglasses for different retailers. They test to see how many defective lenses they made in a time period. Example \(\PageIndex{2}\) gives the defect and the number of defects.
Defect type Number of defects Scratch 5865 Right shaped - small 4613 Flaked 1992 Wrong axis 1838 Chamfer wrong 1596 Crazing, cracks 1546 Wrong shape 1485 Wrong PD 1398 Spots and bubbles 1371 Wrong height 1130 Right shape - big 1105 Lost in lab 976 Spots/bubble 976 Table \(\PageIndex{2}\) : Number of Defective Lenses
a. Find the probability of picking a lens that is scratched or flaked.
b. Find the probability of picking a lens that is the wrong PD or was lost in lab.
c. Find the probability of picking a lens that is not scratched.
d. Find the probability of picking a lens that is not the wrong shape. -
An experiment is to flip a fair coin three times.
- State the sample space.
- Find the probability of getting exactly two heads. Make sure you state the event space.
- Find the probability of getting at least two heads. Make sure you state the event space.
- Find the probability of getting an odd number of heads. Make sure you state the event space.
- Find the probability of getting all heads or all tails. Make sure you state the event space.
- Find the probability of getting exactly two heads or exactly two tails.
- Find the probability of not getting an odd number of heads.

- State the sample space.
- Find the probability of getting a head. Make sure you state the event space.
- Find the probability of getting a 6. Make sure you state the event space.
- Find the probability of getting a 6 or a head.
- Find the probability of getting a 3 and a tail.
-
An experiment is rolling two fair dice.
- State the sample space.
- Find the probability of getting a sum of 3. Make sure you state the event space.
- Find the probability of getting the first die is a 4. Make sure you state the event space.
- Find the probability of getting a sum of 8. Make sure you state the event space.
- Find the probability of getting a sum of 3 or sum of 8.
- Find the probability of getting a sum of 3 or the first die is a 4.
- Find the probability of getting a sum of 8 or the first die is a 4.
- Find the probability of not getting a sum of 8.
-
An experiment is pulling one card from a fair deck.
- State the sample space.
- Find the probability of getting a Ten. Make sure you state the event space.
- Find the probability of getting a Diamond. Make sure you state the event space.
- Find the probability of getting a Club. Make sure you state the event space.
- Find the probability of getting a Diamond or a Club.
- Find the probability of getting a Ten or a Diamond.

- Find the probability of getting a red ball.
- Find the probability of getting a blue ball.
- Find the odds for getting a red ball.
- Find the odds for getting a blue ball.
-
In the game of roulette, there is a wheel with spaces marked 0 through 36 and a space marked 00.
- Find the probability of winning if you pick the number 7 and it comes up on the wheel.
- Find the odds against winning if you pick the number 7.
- The casino will pay you $20 for every dollar you bet if your number comes up. How much profit is the casino making on the bet?
- Answer
-
1. a. P(green or red) = 0.326, b. P(blue, red, or yellow) = 0.466, c. P(not brown) = 0.858, d. P(not green) = 0.816
3. a. See solutions, b. P(2 heads) = 0.375, c. P(at least 2 heads) = 0.50, d. P(odd number of heads) = 0.50, e. P(all heads or all tails) = 0.25, f. P(two heads or two tails) = 0.75, g. P(no an odd number of heads) = 0.50
5. a. See solutions, b.  P(sum of 8) = 0.139, e. P(sum of 3 or sum of 8) = 0.194, f.  P(sum of 8 or 1st die a 4) = 0.278, h. P(not getting a sum of 8) = 0.861
7. a. P(red ball) = 0.625, b. P(blue ball) = 0.375, c. 5 to 3 d. 3 to 5


12.1: Why It Matters- Managing Process
Why explain how operations management contributes to organizational success?
Operations management is just what it sounds like: managing the operations of the business. The role of an operations manager is broad and encompasses multiple operational areas. While other employees can focus on a specialized area of operation (for example, finance and marketing), an operations manager wears many hats and does a bit of everything. While the term may be unfamiliar, you have probably already seen operations management in action—it even played a role in creating the beautiful turkey dinner in the photo below.
What does it take to make Thanksgiving dinner happen? Planning, scheduling, technology, logistics, supply chain management, quality assurance—all the aspects of operations management. As an overview to this module, let’s take Turkey Day as an example:
- Planning . Turkey dinner for fifteen people doesn’t just happen. It takes careful planning and possibly the delegation of tasks and duties to others. Who sets the table? Who brings the green bean casserole? What time should everyone arrive?
- Scheduling . A turkey can take up to six hours to cook, and if you have only one oven, you’ll need to schedule what time the bird goes in and comes out so the rolls and sweet potatoes get a turn in the oven.
- Technology . Obviously you’ll need an oven (or maybe a high-tech turkey fryer) and any number of cooking gadgets. Even the humble thermometer counts as technology. Unless you’re preparing a raw, paleo Thanksgiving dinner, technology will be essential.
- Logistics . Fifteen people won’t all fit around your current table. What should you do? Seat the children at a card table? Rent a larger table?  Logistics, logistics.
- Supply Chain Management. Aunt Sue is bringing pies, Bob is responsible for rolls, Margaret is bringing the green beans. The host has to secure a fresh turkey before they sell out at the grocery store. If you live in the South, then you’ll want to call the local fisherman and reserve some oysters for the oyster dressing. All are important components of the supply chain—leave one out and you’ll miss a dish.
- Quality Assurance. Anyone who cooks knows you need to taste, season, and taste again to make sure the food is up to snuff. Quality assurance might also include asking Jean to bring drinks and flowers, since she’s a terrible cook.
Any undertaking that involves the coordination of effort, tasks, and resources can be considered operations management. In this module you’ll learn how operations management works in both manufacturing and service industries—in short, you’ll see how others get their turkey on the table.


5.3: Lab Report
Exercise A: Testing for Carbohydrates
Part 1: Benedict’s Test for Reducing Sugars
Record your results below:
|
Data Table for Carbohydrates |
Benedict’s Test (reducing sugars) |
Lugol’s Test (starch) |
||
|---|---|---|---|---|
|
Color before boiling |
Color after boiling |
Color before adding I 2 KI |
Color after adding I 2 KI |
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1) Distilled Water |
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2) Starch |
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3) Glucose |
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4) Maltose |
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5) Sucrose |
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6) Onion juice |
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7) Potato slice |
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8) Milk |
- Examine the carbohydrates data table. Create a hypothesis and a prediction for at least one of the samples you will be testing using Benedict’s test:
Hypothesis: ___________________________________________________________________
Prediction: ____________________________________________________________________
What is the independent variable? ________________________________________________
What is the dependent variable? __________________________________________________
Procedure
- Which samples tested positive for reducing sugars? ____________________________________
- Why did we test water with Benedict’s reagent? _______________________________________
- Did the results from your test support your hypothesis? Yes / No Explain: _________________ ______________________________________________________________________________
Part 2: Lugol’s Test for Starch
- Examine the previous data table. Create a hypothesis and a prediction for at least one of the samples you will be testing using Lugol’s test:
Hypothesis: ___________________________________________________________________
Prediction: ____________________________________________________________________
What is the independent variable? ________________________________________________
What is the dependent variable? __________________________________________________
- Which samples tested positive for starch? ____________________________________
- From the results of your tests, do you think that a potato stores its carbohydrates as sugars or as starch? ________________ Explain: ____________________________________________________________________________________________________
- How does an onion store its carbohydrates? ________________ How can you tell? ________________________________________________________________________________
- Did the results from your test support your hypothesis? Yes / No Explain: _______________________________________________________________________________________________
Exercise B: Testing for Lipids
Part 1: Grease Spot Test for Lipids
Describe the difference between the oil and water drop after drying: ___________________________________________________________________________________________________________________________
Data Table for Lipids
|
Substance |
Sudan IV Solubility Reaction (note the color and if + or – for lipids) |
|---|---|
|
1) Distilled Water |
|
|
2) Vegetable oil |
|
|
3) Onion juice |
|
|
4) Cola (regular) |
|
|
5) Hamburger juice |
Part 2: Sudan IV Test for Lipids
- Examine the data table for lipids. Create a hypothesis and a prediction for at least one of the samples you will be testing using the Sudan IV test:
Hypothesis: ___________________________________________________________________
Prediction: ____________________________________________________________________
What is the independent variable? ________________________________________________
What is the dependent variable? __________________________________________________
Procedure
- Which samples tested positive for lipids? ____________________________________________
- Why do the red droplets float? ____________________________________________________
- Did the results from your test support your hypothesis? Yes / No Explain: _________________ ______________________________________________________________________________
Exercise C: Testing for Proteins and Amino Acids
Part 1: Biuret Reagent Test for Proteins
- Examine the data table for proteins. Create a hypothesis and a prediction for at least one of the samples you will be testing using biuret reagent:
Hypothesis: ___________________________________________________________________
Prediction: ____________________________________________________________________
What is the independent variable? ________________________________________________
What is the dependent variable? __________________________________________________
Data Table for Proteins
|
Substance |
Color with Biuret Reagent after 2 Minutes |
Protein Present (+) or Absent (-) |
|---|---|---|
|
1) Distilled water |
||
|
2) Egg albumin |
||
|
3) Potato starch |
||
|
4) Glucose |
||
|
5) Amino acid |
- Which samples tested positive for proteins? __________________________________________
- What does this test tell you about the biochemical composition of starch or glucose? ________ ______________________________________________________________________________
- Did the results from your test support your hypothesis? Yes / No Explain: _______________________________________________________________________________________________
Part 2: Ninhydrin Test for Amino Acids
- Examine the data table for amino acids. Create a hypothesis and a prediction for at least one of the samples you will be testing using the ninhydrin test:
Hypothesis: ___________________________________________________________________
Prediction: ____________________________________________________________________
What is the independent variable? ________________________________________________
What is the dependent variable? __________________________________________________
Procedure
Complete the table, indicating the content of each solution.
Data Table for Amino Acids
|
Solution |
Final Color with Ninhydrin |
Type of Molecule in Solution |
|---|---|---|
|
A |
||
|
B |
||
|
C |
||
|
D |
Exercise D: Testing Unknowns (assigned unknowns: # _________ and # __________)
Data Table for Unknowns
|
Unknown Tested |
Positive (+) or Negative (-) Results |
||||
|---|---|---|---|---|---|
|
Benedict’s Test |
Lugol’s Test |
Biuret Test |
Ninhydrin Test |
Sudan IV Test |
|
|
1: |
|||||
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2: |
|||||
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3: |
|||||
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4: |
|||||
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5: |
|||||
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6: |
|||||
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7: |
|||||
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8: |
- Your instructor will provide you with a list of the possible unknown contents. Once you have completed the data table, match the names of the unknowns to the numbers in your table by writing the name of the unknown next to each respective


9.11: Why It Matters- Communicating Through Technology
Why learn to participate in meetings using phone and video conferencing tools?
Both personal and professional communications are becoming increasingly dependent on technology. Everything from ordering dinner from your favorite Thai place to showing samples to far-away colleagues to running a credit card transaction depends on internet and phone communication.
As with in-person communication, there are rules of etiquette for voice, video, and screen-sharing interactions. Some are specific to the technology you are using, but for the most part, there’s a simple set of guidelines that should see you through any interaction involving technology.
Technology can also generate strong emotion in people: fear, frustration, fascination. In this module, you will learn how to calm the emotion and refocus people on the work at hand.
There are, of course, also considerations about the technology itself: Which platform or application do you choose? How do you use it? How do you make sure the conversation goes smoothly and productively for all involved?
Throughout this module, we will assume that you are the host or originator of the communication, though we will talk about how to be an effective participant when someone else is hosting.
Contributors and Attributions
- Why It Matters: Communicating Through Technology. Authored by : Barbara Egel. Provided by : Lumen Learning. License : CC BY: Attribution
- Communication icon. Authored by : Josy Dom Alexis. Provided by : Noun Project. Located at : https://thenounproject.com/term/communication/1279839/ . License : CC BY: Attribution


23.6: Maxwell’s equations and electromagnetic waves
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This section is meant to be informative, as the material is beyond the scope of this textbook. Nonetheless, it is worth summarizing what we have learned about electricity and magnetism, as Maxwell did. We can summarize the main laws from electromagnetism as follows:
\[\begin{aligned} \oint \vec E\cdot d\vec A &= \frac{Q}{\epsilon_0}&\text{(Gauss' Law)}\\[4pt] \oint \vec B\cdot d\vec A &= 0 &\text{(No magnetic monopoles)}\\[4pt] \oint \vec B\cdot d\vec l &= \mu_0 I^{enc} &\text{(Ampere's Law)}\\[4pt] \oint \vec E\cdot d\vec l &= -\frac{d}{dt}\int \vec B\cdot d\vec A &\text{(Faraday's Law)}\\[4pt]\end{aligned}\]
where we wrote the magnetic flux in Faraday’s Law using the integral explicitly. As you recall, Gauss’ Law is equivalent to Coulomb’s Law, relating the electric field to electric charges that produce the electric field. Although we did not explicitly use the second equation, it is the equivalent to Gauss’ Law for the magnetic field. The flux of the magnetic field out of a closed surface must always be zero, since there are no magnetic monopoles, so that magnetic field lines never end.
When we covered ’s Law, we only considered a static current as the source of the magnetic field. However, if there is an electric field present, that is created by charges that are moving, then those can also contribute a current to ’s Law:
\[\begin{aligned} \oint \vec E\cdot d\vec A &= \frac{Q}{\epsilon_0}\quad \text{(Gauss' Law)}\\[4pt] \therefore Q &= \epsilon_0 \oint \vec E\cdot d\vec A\\[4pt] \therefore I &= \frac{dQ}{dt} = \epsilon_0\frac{d}{dt} \oint \vec E\cdot d\vec A\\[4pt]\end{aligned}\]
so that ’s Law, in its most general form, is written:
\[\begin{aligned} \oint \vec B\cdot d\vec l &= \mu_0 \left(I^{enc}+\epsilon_0\frac{d}{dt} \oint \vec E\cdot d\vec A\right)\quad \text{(Ampere's Law)}\end{aligned}\]
Writing out the four equations again:
\[\begin{aligned} \oint \vec E\cdot d\vec A &= \frac{Q}{\epsilon_0} &\text{(Gauss' Law)}\\[4pt] \oint \vec B\cdot d\vec A &= 0 &\text{(No magnetic monopoles)}\\[4pt] \oint \vec B\cdot d\vec l &= \mu_0 \left(I^{enc}+\epsilon_0\frac{d}{dt} \oint \vec E\cdot d\vec A\right) &\text{(Ampere's Law)}\\[4pt] \oint \vec E\cdot d\vec l &= -\frac{d}{dt}\int \vec B\cdot d\vec A &\text{(Faraday's Law)}\\[4pt]\end{aligned}\]
These four equations are known as Maxwell’s equation, and form our most complete theory of classical electromagnetism. It is quite interesting to note the similarities and relations between the electric and magnetic field. Maxwell’s equations contain equations for the circulation and the total flux out of a closed surface for both fields. ’s Law implies that a changing electric field will produce a magnetic field. Faraday’s Law implies that a changing magnetic field produces an electric field. If a point charge oscillates up and down, it will produce a changing electric field, which will produce a changing magnetic field, which will induce a changing magnetic field, etc. This is precisely what an electromagnetic wave is! The light that we see, the wifi signals for our precious phones, the highly penetrating radiation from nuclear reactors are all examples of electromagnetic waves (of different wavelengths).
In fact, as Maxwell did, we can obtain the wave equation (Section 14.2) from Maxwell’s equations. We sketch out the derivation here, but it is definitely beyond the scope of this textbook. However, you’re so close to seeing one of the most exciting revelations of physics that it would be a shame to skip!
We first write out Maxwell’s equations in differential form, as we have already shown for Gauss’ Law (Section 17.4) and ’s Law (Section 22.3)
\[\begin{aligned} \nabla \cdot \vec E &= \frac{\rho}{\epsilon_0} &\text{(Gauss' Law)}\\[4pt] \nabla \cdot \vec B&= 0 &\text{(No magnetic monopoles)}\\[4pt] \nabla \times \vec B &= \mu_0 \left(\vec j + \epsilon_0\frac{\partial \vec E}{\partial t}\right) &\text{(Ampere's Law)}\\[4pt] \nabla \times \vec E &= -\frac{\partial\vec B}{\partial t} &\text{(Faraday's Law)}\\[4pt]\end{aligned}\]
If we consider a vacuum region in space, with no charges and no currents, these equations reduce to:
\[\begin{aligned} \nabla \cdot \vec E &= 0 &\nabla \cdot \vec B&= 0\\[4pt] \nabla \times \vec B &= \mu_0 \epsilon_0\frac{\partial\vec E}{\partial t} & \nabla \times \vec E &= -\frac{\partial\vec B}{\partial t}\end{aligned}\]
We will make use of the following identity from vector calculus:
\[\begin{aligned} \nabla \times (\nabla \times \vec E)=\nabla(\nabla\cdot \vec E)-\nabla^2\vec E\end{aligned}\]
where:
\[\begin{aligned} \nabla^2\vec E &= \frac{\partial^2 \vec E}{\partial x^2}+\frac{\partial^2 \vec E}{\partial y^2} + \frac{\partial^2 \vec E}{\partial z^2}\\[4pt] &=\left(\frac{\partial^2 E_x}{\partial x^2}+\frac{\partial^2 E_x}{\partial y^2} + \frac{\partial^2 E_x}{\partial z^2} \right) \hat x+ \left( \frac{\partial^2 E_y}{\partial x^2}+\frac{\partial^2 E_y}{\partial y^2} + \frac{\partial^2 E_y}{\partial z^2} \right) \hat y \\[4pt] &+ \left(\frac{\partial^2 E_z}{\partial x^2}+\frac{\partial^2 E_z}{\partial y^2} + \frac{\partial^2 E_z}{\partial z^2} \right) \hat z\end{aligned}\]
is called the “vector Laplacian”.
Consider taking the curl ( \(\nabla \times\) ) of the equation that has the curl of the electric field (Faraday’s Law):
\[\begin{aligned} \nabla \times \bigg(\nabla \times \vec E &= -\frac{\partial\vec B}{\partial t}\bigg)\\[4pt] \nabla(\nabla\cdot \vec E)-\nabla^2\vec E &= -\nabla \times \frac{\partial\vec B}{\partial t}\\[4pt] -\nabla^2\vec E &= - \frac{\partial}{\partial t} \nabla \times \vec B\\[4pt] -\nabla^2\vec E &= - \frac{\partial}{\partial t} \mu_0 \epsilon_0\frac{\partial E}{\partial t}\\[4pt] -\nabla^2\vec E &= - \mu_0 \epsilon_0\frac{\partial^2\vec E}{\partial t^2} \end{aligned}\]
where, in the third line, we made use of Gauss’ Law ( \(\nabla \cdot \vec E=0\) ), and, in the fourth line, Ampere’s Law ( \(\nabla \times \vec B = \mu_0 \epsilon_0\frac{\partial E}{\partial t}\) ). The last equation that we obtained is a vector equation (the vector Laplacian has three components, as does the time-derivative of \(\vec E\) on the right-hand side). Consider the \(x\) component of this equation:
\[\begin{aligned} \frac{\partial^2 E_x}{\partial x^2}+\frac{\partial^2 E_x}{\partial y^2} + \frac{\partial^2 E_x}{\partial z^2} &= \mu_0 \epsilon_0\frac{\partial^2 E_x}{\partial t^2} \end{aligned}\]
If we define the quantity:
\[\begin{aligned} c = \frac{1}{\sqrt{\epsilon_0\mu_0}}\end{aligned}\]
then, the \(x\) component of the equation can be written as:
\[\begin{aligned} \frac{\partial^2 E_x}{\partial x^2}+\frac{\partial^2 E_x}{\partial y^2} + \frac{\partial^2 E_x}{\partial z^2} &= \frac{1}{c^2}\frac{\partial^2 E_x}{\partial t^2} \end{aligned}\]
which is exactly the wave equation for the component, \(E_x\) , of the electric field, propagating with a speed, \(c\) , the speed of light! Thus, the speed of light is directly related to the constant \(\epsilon_0\) , and \(\mu_0\) . You can write out similar equations for the \(y\) and \(z\) components of the electric field, and find the similar equations for the magnetic field if you start by taking the curl of ’s Law instead of Faraday’s Law.
We have just shown that electric and magnetic fields can behave as waves, which we now understand to be the waves that are responsible for light, radio waves, gamma rays, infra-red radiation, etc. All of these are types of electromagnetic waves, with different frequencies. Although we did not demonstrate this, the electromagnetic waves that propagate are such that the magnetic and electric field vectors are always perpendicular to each other. Electromagnetic waves also carry energy. Thus, a charge that is oscillating (say on a spring) and creating an electromagnetic wave must necessarily be losing energy (or work must be done to keep the charge oscillating with the same amplitude). Finally, it is worth noting that, according to Quantum Mechanics, light (and the other frequencies of radiation), are really carried by particles called “photons”. Those particles are strange, since their propagation is described by a wave equation.


3.4: The Nucleus
Diagram 3.14 : A cell with an enlarged chromosome
Diagram 3.15 : A full set of human chromosomes
The nucleus is the largest structure in a cell and can be seen with the light microscope. It is a spherical or oval body that contains the chromosomes . The nucleus controls the development and activity of the cell. Most cells contain a nucleus although mature red blood cells have lost theirs during development and some muscle cells have several nuclei.
A double membrane similar in structure to the plasma membrane surrounds the nucleus (now called the nuclear envelope). Pores in this nuclear membrane allow communication between the nucleus and the cytoplasm.
Within the nucleus one or more spherical bodies of darker material can be seen, even with the light microscope. These are called nucleoli and are made of RNA. Their role is to make new ribosomes.
Chromosomes
Inside the nucleus are the chromosomes which:
- contain DNA;
- control the activity of the cell;
- are transmitted from cell to cell when cells divide;
- are passed to a new individual when sex cells fuse together in sexual reproduction.
In cells that are not dividing the chromosomes are very long and thin and appear as dark grainy material. They become visible just before a cell divides when they shorten and thicken and can then be counted (see diagram 3.14).
The number of chromosomes in the cells of different species varies but is constant in the cells of any one species (e.g. horses have 64 chromosomes, cats have 38 and humans 46). Chromosomes occur in pairs (i.e. 32 pairs in the horse nucleus and 19 in that of the cat). Members of each pair are identical in length and shape and if you look carefully at diagram 3.15, you may be able to see some of the pairs in the human set of chromosomes.


23.6: The Small and Large Intestines
By the end of this section, you will be able to:
- Compare and contrast the location and gross anatomy of the small and large intestines
- Identify three main adaptations of the small intestine wall that increase its absorptive capacity
- Describe the mechanical and chemical digestion of chyme upon its release into the small intestine
- List three features unique to the wall of the large intestine and identify their contributions to its function
- Identify the beneficial roles of the bacterial flora in digestive system functioning
- Trace the pathway of food waste from its point of entry into the large intestine through its exit from the body as feces
The word intestine is derived from a Latin root meaning “internal,” and indeed, the two organs together nearly fill the interior of the abdominal cavity. In addition, called the small and large bowel, or colloquially the “guts,” they constitute the greatest mass and length of the alimentary canal and, with the exception of ingestion, perform all digestive system functions.
The Small Intestine
Chyme released from the stomach enters the small intestine , which is the primary digestive organ in the body. Not only is this where most digestion occurs, it is also where practically all absorption occurs. The longest part of the alimentary canal, the small intestine is about 3.05 meters (10 feet) long in a living person (but about twice as long in a cadaver due to the loss of muscle tone). Since this makes it about five times longer than the large intestine, you might wonder why it is called “small.” In fact, its name derives from its relatively smaller diameter of only about 2.54 cm (1 in), compared with 7.62 cm (3 in) for the large intestine. As we’ll see shortly, in addition to its length, the folds and projections of the lining of the small intestine work to give it an enormous surface area, which is approximately 200 m 2 , more than 100 times the surface area of your skin. This large surface area is necessary for complex processes of digestion and absorption that occur within it.
Structure
The coiled tube of the small intestine is subdivided into three regions. From proximal (at the stomach) to distal, these are the duodenum, jejunum, and ileum (Figure \(\PageIndex{1}\) ).
The shortest region is the 25.4-cm (10-in) duodenum , which begins at the pyloric sphincter. Just past the pyloric sphincter, it bends posteriorly behind the peritoneum, becoming retroperitoneal, and then makes a C-shaped curve around the head of the pancreas before ascending anteriorly again to return to the peritoneal cavity and join the jejunum. The duodenum can therefore be subdivided into four segments: the superior, descending, horizontal, and ascending duodenum.
Of particular interest is the hepatopancreatic ampulla (ampulla of Vater). Located in the duodenal wall, the ampulla marks the transition from the anterior portion of the alimentary canal to the mid-region, and is where the bile duct (through which bile passes from the liver) and the main pancreatic duct (through which pancreatic juice passes from the pancreas) join. This ampulla opens into the duodenum at a tiny volcano-shaped structure called the major duodenal papilla . The hepatopancreatic sphincter (sphincter of Oddi) regulates the flow of both bile and pancreatic juice from the ampulla into the duodenum.
The jejunum is about 0.9 meters (3 feet) long (in life) and runs from the duodenum to the ileum. Jejunum means “empty” in Latin and supposedly was so named by the ancient Greeks who noticed it was always empty at death. No clear demarcation exists between the jejunum and the final segment of the small intestine, the ileum.
The ileum is the longest part of the small intestine, measuring about 1.8 meters (6 feet) in length. It is thicker, more vascular, and has more developed mucosal folds than the jejunum. The ileum joins the cecum, the first portion of the large intestine, at the ileocecal sphincter (or valve). The jejunum and ileum are tethered to the posterior abdominal wall by the mesentery. The large intestine frames these three parts of the small intestine.
Parasympathetic nerve fibers from the vagus nerve and sympathetic nerve fibers from the thoracic splanchnic nerve provide extrinsic innervation to the small intestine. The superior mesenteric artery is its main arterial supply. Veins run parallel to the arteries and drain into the superior mesenteric vein. Nutrient-rich blood from the small intestine is then carried to the liver via the hepatic portal vein.
Histology
The wall of the small intestine is composed of the same four layers typically present in the alimentary system. However, three features of the mucosa and submucosa are unique. These features, which increase the absorptive surface area of the small intestine more than 600-fold, include circular folds, villi, and microvilli (Figure \(\PageIndex{2}\)). These adaptations are most abundant in the proximal two-thirds of the small intestine, where the majority of absorption occurs.
Circular folds
Also called a plica circulare, a circular fold is a deep ridge in the mucosa and submucosa. Beginning near the proximal part of the duodenum and ending near the middle of the ileum, these folds facilitate absorption. Their shape causes the chyme to spiral, rather than move in a straight line, through the small intestine. Spiraling slows the movement of chyme and provides the time needed for nutrients to be fully absorbed.
Villi
Within the circular folds are small (0.5–1 mm long) hairlike vascularized projections called villi (singular = villus) that give the mucosa a furry texture. There are about 20 to 40 villi per square millimeter, increasing the surface area of the epithelium tremendously. The mucosal epithelium, primarily composed of absorptive cells, covers the villi. In addition to muscle and connective tissue to support its structure, each villus contains a capillary bed composed of one arteriole and one venule, as well as a lymphatic capillary called a lacteal . The breakdown products of carbohydrates and proteins (sugars and amino acids) can enter the bloodstream directly, but lipid breakdown products are absorbed by the lacteals and transported to the bloodstream via the lymphatic system.
Microvilli
As their name suggests, microvilli (singular = microvillus) are much smaller (1 µ m) than villi. They are cylindrical apical surface extensions of the plasma membrane of the mucosa’s epithelial cells, and are supported by microfilaments within those cells. Although their small size makes it difficult to see each microvillus, their combined microscopic appearance suggests a mass of bristles, which is termed the brush border . Fixed to the surface of the microvilli membranes are enzymes that finish digesting carbohydrates and proteins. There are an estimated 200 million microvilli per square millimeter of small intestine, greatly expanding the surface area of the plasma membrane and thus greatly enhancing absorption.
Intestinal Glands
In addition to the three specialized absorptive features just discussed, the mucosa between the villi is dotted with deep crevices that each lead into a tubular intestinal gland (crypt of Lieberkühn), which is formed by cells that line the crevices (see Figure 23.19). These produce intestinal juice , a slightly alkaline (pH 7.4 to 7.8) mixture of water and mucus. Each day, about 0.95 to 1.9 liters (1 to 2 quarts) are secreted in response to the distention of the small intestine or the irritating effects of chyme on the intestinal mucosa.
The submucosa of the duodenum is the only site of the complex mucus-secreting duodenal glands (Brunner’s glands), which produce a bicarbonate-rich alkaline mucus that buffers the acidic chyme as it enters from the stomach.
The roles of the cells in the small intestinal mucosa are detailed in Table \(\PageIndex{1}\).
| Cell type | Location in the mucosa | Function |
|---|---|---|
| Absorptive | Epithelium/intestinal glands | Digestion and absorption of nutrients in chyme |
| Goblet | Epithelium/intestinal glands | Secretion of mucus |
| Paneth | Intestinal glands | Secretion of the bactericidal enzyme lysozyme; phagocytosis |
| G cells | Intestinal glands of duodenum | Secretion of the hormone intestinal gastrin |
| I cells | Intestinal glands of duodenum | Secretion of the hormone cholecystokinin, which stimulates release of pancreatic juices and bile |
| K cells | Intestinal glands | Secretion of the hormone glucose-dependent insulinotropic peptide, which stimulates the release of insulin |
| M cells | Intestinal glands of duodenum and jejunum | Secretion of the hormone motilin, which accelerates gastric emptying, stimulates intestinal peristalsis, and stimulates the production of pepsin |
| S cells | Intestinal glands | Secretion of the hormone secretin |
Intestinal MALT
The lamina propria of the small intestine mucosa is studded with quite a bit of MALT. In addition to solitary lymphatic nodules, aggregations of intestinal MALT, which are typically referred to as Peyer’s patches, are concentrated in the distal ileum, and serve to keep bacteria from entering the bloodstream. Peyer’s patches are most prominent in young people and become less distinct as you age, which coincides with the general activity of our immune system.
Interactive Link
Watch this animation that depicts the structure of the small intestine, and, in particular, the villi. Epithelial cells continue the digestion and absorption of nutrients and transport these nutrients to the lymphatic and circulatory systems. In the small intestine, the products of food digestion are absorbed by different structures in the villi. Which structure absorbs and transports fats?
Mechanical Digestion in the Small Intestine
The movement of intestinal smooth muscles includes both segmentation and a form of peristalsis called migrating motility complexes. The kind of peristaltic mixing waves seen in the stomach are not observed here.
If you could see into the small intestine when it was going through segmentation, it would look as if the contents were being shoved incrementally back and forth, as the rings of smooth muscle repeatedly contract and then relax. Segmentation in the small intestine does not force chyme through the tract. Instead, it combines the chyme with digestive juices and pushes food particles against the mucosa to be absorbed. The duodenum is where the most rapid segmentation occurs, at a rate of about 12 times per minute. In the ileum, segmentations are only about eight times per minute (Figure \(\PageIndex{4}\)).
When most of the chyme has been absorbed, the small intestinal wall becomes less distended. At this point, the localized segmentation process is replaced by transport movements. The duodenal mucosa secretes the hormone motilin , which initiates peristalsis in the form of a migrating motility complex . These complexes, which begin in the duodenum, force chyme through a short section of the small intestine and then stop. The next contraction begins a little bit farther down than the first, forces chyme a bit farther through the small intestine, then stops. These complexes move slowly down the small intestine, forcing chyme on the way, taking around 90 to 120 minutes to finally reach the end of the ileum. At this point, the process is repeated, starting in the duodenum.
The ileocecal valve, a sphincter, is usually in a constricted state, but when motility in the ileum increases, this sphincter relaxes, allowing food residue to enter the first portion of the large intestine, the cecum. Relaxation of the ileocecal sphincter is controlled by both nerves and hormones. First, digestive activity in the stomach provokes the gastroileal reflex , which increases the force of ileal segmentation. Second, the stomach releases the hormone gastrin, which enhances ileal motility, thus relaxing the ileocecal sphincter. After chyme passes through, backward pressure helps close the sphincter, preventing backflow into the ileum.  It takes about 3 to 5 hours for all chyme to leave the small intestine.
Chemical Digestion in the Small Intestine
The digestion of proteins and carbohydrates, which partially occurs in the stomach, is completed in the small intestine with the aid of intestinal and pancreatic juices. Lipids arrive in the intestine largely undigested, so much of the focus here is on lipid digestion, which is facilitated by bile and the enzyme pancreatic lipase.
Moreover, intestinal juice combines with pancreatic juice to provide a liquid medium that facilitates absorption. The intestine is also where most water is absorbed, via osmosis. The small intestine’s absorptive cells also synthesize digestive enzymes and then place them in the plasma membranes of the microvilli. This distinguishes the small intestine from the stomach; that is, enzymatic digestion occurs not only in the lumen, but also on the luminal surfaces of the mucosal cells.
For optimal chemical digestion, chyme must be delivered from the stomach slowly and in small amounts. This is because chyme from the stomach is typically hypertonic, and if large quantities were forced all at once into the small intestine, the resulting osmotic water loss from the blood into the intestinal lumen would result in potentially life-threatening low blood volume. In addition, continued digestion requires an upward adjustment of the low pH of stomach chyme, along with rigorous mixing of the chyme with bile and pancreatic juices. Both processes take time, so the pumping action of the pylorus must be carefully controlled to prevent the duodenum from being overwhelmed with chyme.
Disorders of the...
Small Intestine: Lactose Intolerance
Lactose intolerance is a condition characterized by indigestion caused by dairy products. It occurs when the absorptive cells of the small intestine do not produce enough lactase, the enzyme that digests the milk sugar lactose. In most mammals, lactose intolerance increases with age. In contrast, some human populations are able to maintain the ability to produce lactase as adults.
In people with lactose intolerance, the lactose in chyme is not digested. Bacteria in the large intestine ferment the undigested lactose, a process that produces gas. In addition to gas, symptoms include abdominal cramps, bloating, and diarrhea. Symptom severity ranges from mild discomfort to severe pain; however, symptoms resolve once the lactose is eliminated in feces.
The hydrogen breath test is used to help diagnose lactose intolerance. Lactose-tolerant people have very little hydrogen in their breath. Those with lactose intolerance exhale hydrogen, which is one of the gases produced by the bacterial fermentation of lactose in the colon. After the hydrogen is absorbed from the intestine, it is transported through blood vessels into the lungs. There are a number of lactose-free dairy products available in grocery stores. In addition, dietary supplements are available. Taken with food, they provide lactase to help digest lactose.
The Large Intestine
The large intestine is the terminal part of the alimentary canal. The primary function of this organ is to finish absorption of nutrients and water, synthesize certain vitamins, form feces, and eliminate feces from the body.
Structure
The large intestine runs from the appendix to the anus. It frames the small intestine on three sides. Despite its being about one-half as long as the small intestine, it is called large because it is more than twice the diameter of the small intestine, about 3 inches.
Subdivisions
The large intestine is subdivided into four main regions: the cecum, the colon, the rectum, and the anus. The ileocecal valve, located at the opening between the ileum and the large intestine, controls the flow of chyme from the small intestine to the large intestine.
Cecum
The first part of the large intestine is the cecum , a sac-like structure that is suspended inferior to the ileocecal valve. It is about 6 cm (2.4 in) long, receives the contents of the ileum, and continues the absorption of water and salts. The appendix (or vermiform appendix) is a winding tube that attaches to the cecum. Although the 7.6-cm (3-in) long appendix contains lymphoid tissue, suggesting an immunologic function, this organ is generally considered vestigial. However, at least one recent report postulates a survival advantage conferred by the appendix: In diarrheal illness, the appendix may serve as a bacterial reservoir to repopulate the enteric bacteria for those surviving the initial phases of the illness. Moreover, its twisted anatomy provides a haven for the accumulation and multiplication of enteric bacteria. The mesoappendix , the mesentery of the appendix, tethers it to the mesentery of the ileum.
Colon
The cecum blends seamlessly with the colon . Upon entering the colon, the food residue first travels up the ascending colon on the right side of the abdomen. At the inferior surface of the liver, the colon bends to form the right colic flexure (hepatic flexure) and becomes the transverse colon . The region defined as hindgut begins with the last third of the transverse colon and continues on. Food residue passing through the transverse colon travels across to the left side of the abdomen, where the colon angles sharply immediately inferior to the spleen, at the left colic flexure (splenic flexure). From there, food residue passes through the descending colon , which runs down the left side of the posterior abdominal wall. After entering the pelvis inferiorly, it becomes the s-shaped sigmoid colon , which extends medially to the midline (Figure \(\PageIndex{5}\)). The ascending and descending colon, and the rectum (discussed next) are located in the retroperitoneum. The transverse and sigmoid colon are tethered to the posterior abdominal wall by the mesocolon.
Homeostatic Imbalances
Colorectal Cancer
Each year, approximately 140,000 Americans are diagnosed with colorectal cancer, and another 49,000 die from it, making it one of the most deadly malignancies. People with a family history of colorectal cancer are at increased risk. Smoking, excessive alcohol consumption, and a diet high in animal fat and protein also increase the risk. Despite popular opinion to the contrary, studies support the conclusion that dietary fiber and calcium do not reduce the risk of colorectal cancer.
Colorectal cancer may be signaled by constipation or diarrhea, cramping, abdominal pain, and rectal bleeding. Bleeding from the rectum may be either obvious or occult (hidden in feces). Since most colon cancers arise from benign mucosal growths called polyps, cancer prevention is focused on identifying these polyps. The colonoscopy is both diagnostic and therapeutic. Colonoscopy not only allows identification of precancerous polyps, the procedure also enables them to be removed before they become malignant. Screening for fecal occult blood tests and colonoscopy is recommended for those over 50 years of age.
Rectum
Food residue leaving the sigmoid colon enters the rectum in the pelvis, near the third sacral vertebra. The final 20.3 cm (8 in) of the alimentary canal, the rectum extends anterior to the sacrum and coccyx. Even though rectum is Latin for “straight,” this structure follows the curved contour of the sacrum and has three lateral bends that create a trio of internal transverse folds called the rectal valves . These valves help separate the feces from gas to prevent the simultaneous passage of feces and gas.
Anal Canal
Finally, food residue reaches the last part of the large intestine, the anal canal , which is located in the perineum, completely outside of the abdominopelvic cavity. This 3.8–5 cm (1.5–2 in) long structure opens to the exterior of the body at the anus. The anal canal includes two sphincters. The internal anal sphincter is made of smooth muscle, and its contractions are involuntary. The external anal sphincter is made of skeletal muscle, which is under voluntary control. Except when defecating, both usually remain closed.
Histology
There are several notable differences between the walls of the large and small intestines (Figure \(\PageIndex{6}\)). For example, few enzyme-secreting cells are found in the wall of the large intestine, and there are no circular folds or villi. Other than in the anal canal, the mucosa of the colon is simple columnar epithelium made mostly of enterocytes (absorptive cells) and goblet cells. In addition, the wall of the large intestine has far more intestinal glands, which contain a vast population of enterocytes and goblet cells. These goblet cells secrete mucus that eases the movement of feces and protects the intestine from the effects of the acids and gases produced by enteric bacteria. The enterocytes absorb water and salts as well as vitamins produced by your intestinal bacteria.
Anatomy
Three features are unique to the large intestine: teniae coli, haustra, and epiploic appendages (Figure \(\PageIndex{7}\)). The teniae coli are three bands of smooth muscle that make up the longitudinal muscle layer of the muscularis of the large intestine, except at its terminal end. Tonic contractions of the teniae coli bunch up the colon into a succession of pouches called haustra (singular = haustrum), which are responsible for the wrinkled appearance of the colon. Attached to the teniae coli are small, fat-filled sacs of visceral peritoneum called epiploic appendages . The purpose of these is unknown. Although the rectum and anal canal have neither teniae coli nor haustra, they do have well-developed layers of muscularis that create the strong contractions needed for defecation.
 This mucosa varies considerably from that of the rest of the colon to accommodate the high level of abrasion as feces pass through.
 The pectinate line (or dentate line) is a horizontal, jagged band that runs circumferentially just below the level of the anal sinuses, and represents the junction between the hindgut and external skin. The mucosa above this line is fairly insensitive, whereas the area below is very sensitive. The resulting difference in pain threshold is due to the fact that the upper region is innervated by visceral sensory fibers, and the lower region is innervated by somatic sensory fibers.
Bacterial Flora
Most bacteria that enter the alimentary canal are killed by lysozyme, defensins, HCl, or protein-digesting enzymes. However, trillions of bacteria live within the large intestine and are referred to as the bacterial flora . Most of the more than 700 species of these bacteria are nonpathogenic commensal organisms that cause no harm as long as they stay in the gut lumen. In fact, many facilitate chemical digestion and absorption, and some synthesize certain vitamins, mainly biotin, pantothenic acid, and vitamin K. Some are linked to increased immune response. A refined system prevents these bacteria from crossing the mucosal barrier. First, peptidoglycan, a component of bacterial cell walls, activates the release of chemicals by the mucosa’s epithelial cells, which draft immune cells, especially dendritic cells, into the mucosa. Dendritic cells open the tight junctions between epithelial cells and extend probes into the lumen to evaluate the microbial antigens. The dendritic cells with antigens then travel to neighboring lymphoid follicles in the mucosa where T cells inspect for antigens. This process triggers an IgA-mediated response, if warranted, in the lumen that blocks the commensal organisms from infiltrating the mucosa and setting off a far greater, widespread systematic reaction.
Digestive Functions of the Large Intestine
The residue of chyme that enters the large intestine contains few nutrients except water, which is reabsorbed as the residue lingers in the large intestine, typically for 12 to 24 hours. Thus, it may not surprise you that the large intestine can be completely removed without significantly affecting digestive functioning. For example, in severe cases of inflammatory bowel disease, the large intestine can be removed by a procedure known as a colectomy. Often, a new fecal pouch can be crafted from the small intestine and sutured to the anus, but if not, an ileostomy can be created by bringing the distal ileum through the abdominal wall, allowing the watery chyme to be collected in a bag-like adhesive appliance.
Mechanical Digestion
In the large intestine, mechanical digestion begins when chyme moves from the ileum into the cecum, an activity regulated by the ileocecal sphincter. Right after you eat, peristalsis in the ileum forces chyme into the cecum. When the cecum is distended with chyme, contractions of the ileocecal sphincter strengthen. Once chyme enters the cecum, colon movements begin.
Mechanical digestion in the large intestine includes a combination of three types of movements. The presence of food residues in the colon stimulates a slow-moving haustral contraction . This type of movement involves sluggish segmentation, primarily in the transverse and descending colons. When a haustrum is distended with chyme, its muscle contracts, pushing the residue into the next haustrum. These contractions occur about every 30 minutes, and each last about 1 minute. These movements also mix the food residue, which helps the large intestine absorb water. The second type of movement is peristalsis, which, in the large intestine, is slower than in the more proximal portions of the alimentary canal. The third type is a mass movement . These strong waves start midway through the transverse colon and quickly force the contents toward the rectum.  Distension in the stomach and the breakdown products of digestion in the small intestine provoke the gastrocolic reflex , which increases motility, including mass movements, in the colon. Fiber in the diet both softens the stool and increases the power of colonic contractions, optimizing the activities of the colon.
Chemical Digestion
Although the glands of the large intestine secrete mucus, they do not secrete digestive enzymes. Therefore, chemical digestion in the large intestine occurs exclusively because of bacteria in the lumen of the colon. Through the process of saccharolytic fermentation , bacteria break down some of the remaining carbohydrates. This results in the discharge of hydrogen, carbon dioxide, and methane gases that create flatus (gas) in the colon; flatulence is excessive flatus. Each day, up to 1500 mL of flatus is produced in the colon. More is produced when you eat foods such as beans, which are rich in otherwise indigestible sugars and complex carbohydrates like soluble dietary fiber.
Absorption, Feces Formation, and Defecation
The small intestine absorbs about 90 percent of the water you ingest (either as liquid or within solid food). The large intestine absorbs most of the remaining water, a process that converts the liquid chyme residue into semisolid feces (“stool”). Feces is composed of undigested food residues, unabsorbed digested substances, millions of bacteria, old epithelial cells from the GI mucosa, inorganic salts, and enough water to let it pass smoothly out of the body. Of every 500 mL (17 ounces) of food residue that enters the cecum each day, about 150 mL (5 ounces) become feces.
Feces are eliminated through contractions of the rectal muscles. You help this process by a voluntary procedure called Valsalva’s maneuver , in which you increase intra-abdominal pressure by contracting your diaphragm and abdominal wall muscles, and closing your glottis.
The process of defecation begins when mass movements force feces from the colon into the rectum, stretching the rectal wall and provoking the defecation reflex, which eliminates feces from the rectum. This parasympathetic reflex is mediated by the spinal cord.   If you decide to delay defecation, it takes a few seconds for the reflex contractions to stop and the rectal walls to relax. The next mass movement will trigger additional defecation reflexes until you defecate.
If defecation is delayed for an extended time, additional water is absorbed, making the feces firmer and potentially leading to constipation. On the other hand, if the waste matter moves too quickly through the intestines, not enough water is absorbed, and diarrhea can result. This can be caused by the ingestion of foodborne pathogens. In general, diet, health, and stress determine the frequency of bowel movements. The number of bowel movements varies greatly between individuals, ranging from two or three per day to three or four per week.
Interactive Link
By watching this animation you will see that for the various food groups—proteins, fats, and carbohydrates—digestion begins in different parts of the digestion system, though all end in the same place. Of the three major food classes (carbohydrates, fats, and proteins), which is digested in the mouth, the stomach, and the small intestine?


3.8: The First Law of Thermodynamics (Summary)
Key Terms
| adiabatic process | process during which no heat is transferred to or from the system |
| boundary | imagined walls that separate the system and its surroundings |
| closed system | system that is mechanically and thermally isolated from its environment |
| cyclic process | process in which the state of the system at the end is same as the state at the beginning |
| environment | outside of the system being studied |
| equation of state | describes properties of matter under given physical conditions |
| equilibrium | thermal balance established between two objects or parts within a system |
| extensive variable | variable that is proportional to the amount of matter in the system |
| first law of thermodynamics | the change in internal energy for any transition between two equilibrium states is \(ΔE_{int}=Q−W\) |
| intensive variable | variable that is independent of the amount of matter in the system |
| internal energy | average of the total mechanical energy of all the molecules or entities in the system |
| isobaric process | process during which the system’s pressure does not change |
| isochoric process | process during which the system’s volume does not change |
| isothermal process | process during which the system’s temperature remains constant |
| molar heat capacity at constant pressure | quantifies the ratio of the amount of heat added removed to the temperature while measuring at constant pressure |
| molar heat capacity at constant volume | quantifies the ratio of the amount of heat added removed to the temperature while measuring at constant volume |
| open system | system that can exchange energy and/or matter with its surroundings |
| quasi-static process | evolution of a system that goes so slowly that the system involved is always in thermodynamic equilibrium |
| reversible process | process that can be reverted to restore both the system and its environment back to their original states together |
| surroundings | environment that interacts with an open system |
| thermodynamic process | manner in which a state of a system can change from initial state to final state |
| thermodynamic system | object and focus of thermodynamic study |
Key Equations
| Equation of state for a closed system | \(f(p,V,T)=0\) |
| Net work for a finite change in volume | \(W=∫^{V_2}_{V_1}pdV\) |
| Internal energy of a system (average total energy) | \(E_{int}=\sum_i(\bar{K_i}+\bar{U_i})\), |
| Internal energy of a monatomic ideal gas | \(E_{int}=nN_A(\frac{3}{2}k_BT)=\frac{3}{2}nRT\) |
| First law of thermodynamics | \(ΔE_{int}=Q−W\) |
| Molar heat capacity at constant pressure | \(C_p=C_V+R\) |
| Ratio of molar heat capacities | \(γ=C_p/C_V\) |
| Condition for an ideal gas in a quasi-static adiabatic process | \(pV^γ=constant\) |
Summary
3.2 Thermodynamic Systems
- A thermodynamic system, its boundary, and its surroundings must be defined with all the roles of the components fully explained before we can analyze a situation.
- Thermal equilibrium is reached with two objects if a third object is in thermal equilibrium with the other two separately.
- A general equation of state for a closed system has the form \(f(p,V,T)=0\), with an ideal gas as an illustrative example.
3.3 Work, Heat, and Internal Energy
- Positive (negative) work is done by a thermodynamic system when it expands (contracts) under an external pressure.
- Heat is the energy transferred between two objects (or two parts of a system) because of a temperature difference.
- Internal energy of a thermodynamic system is its total mechanical energy.
3.4 First Law of Thermodynamics
- The internal energy of a thermodynamic system is a function of state and thus is unique for every equilibrium state of the system.
- The increase in the internal energy of the thermodynamic system is given by the heat added to the system less the work done by the system in any thermodynamics process.
3.5 Thermodynamic Processes
- The thermal behavior of a system is described in terms of thermodynamic variables. For an ideal gas, these variables are pressure, volume, temperature, and number of molecules or moles of the gas.
- For systems in thermodynamic equilibrium, the thermodynamic variables are related by an equation of state.
- A heat reservoir is so large that when it exchanges heat with other systems, its temperature does not change.
- A quasi-static process takes place so slowly that the system involved is always in thermodynamic equilibrium.
- A reversible process is one that can be made to retrace its path and both the temperature and pressure are uniform throughout the system.
- There are several types of thermodynamic processes, including (a) isothermal, where the system’s temperature is constant; (b) adiabatic, where no heat is exchanged by the system; (c) isobaric, where the system’s pressure is constant; and (d) isochoric, where the system’s volume is constant.
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As a consequence of the first law of thermodymanics, here is a summary of the thermodymaic processes:
- (a) isothermal: \(ΔE_{int}=0,Q=W\);
- (b) adiabatic: \(Q=0,ΔE_{int}=−W\) ;
- (c) isobaric: \(ΔE_{int}=Q−W\); and
- (d) isochoric: \(W=0,ΔE_{int}=Q\).
3.6 Heat Capacities of an Ideal Gas
- For an ideal gas, the molar capacity at constant pressure \(C_p\) is given by \(C_p=C_V+R=dR/2+R\), where d is the number of degrees of freedom of each molecule/entity in the system.
- A real gas has a specific heat close to but a little bit higher than that of the corresponding ideal gas with \(C_p≃C_V+R\).
3.7 Adiabatic Processes for an Ideal Gas
- A quasi-static adiabatic expansion of an ideal gas produces a steeper pV curve than that of the corresponding isotherm.
- A realistic expansion can be adiabatic but rarely quasi-static.


2.2: Atoms and Basic Chemistry
A. Overview of Elements and Atoms
The difference between elements and atoms is often confused in casual conversation. Both terms describe matter , substances with mass . Different elements are different kinds of matter distinguished by different physical and chemical properties. In turn, the atom is the fundamental unit of matter…, that is, of an element.
The number of positively charged protons and neutral neutrons in an atomic nucleus account for most of the mass of an atom. Each negatively charged electron that orbits a nucleus is about 1/2000th of the mass of a proton or neutron. Thus, they do not add much to the mass of an atom. Electrons stay in atomic orbits because of electromagnetic forces, i.e., their attraction to the positively charged nuclei. Nuclear size (mass) and the cloud of electrons around its nucleus define structure of an atom. And that structure dictates the different properties of the elements.
Recall that atoms are chemically most stable when they are electrically uncharged, with an equal number of protons and electrons. Isotopes of the same element are atoms with the same number of protons and electrons, but a different number of neutrons. Therefore, isotopes are also chemically stable, but they may not be physically stable. For example, the most abundant isotope of hydrogen contains one proton, one electron and no neutrons . The nucleus of the deuterium isotope of hydrogen contains one neutron and that of tritium contains two neutrons. Both isotopes can be found in water molecules. Deuterium is stable. In contrast, the tritium atom is radioactive, subject to nuclear decay over time. Whether physically stable or not, all isotopes of an element share the same chemical and electromagnetic properties and behave the same way in chemical reactions.
The electromagnetic forces that keep electrons orbiting their nuclei allow the formation of chemical bonds in molecules. We model atoms to illustrate the average physical location of electrons ( the orbital model ) on one hand, and their potential energy levels (the Bohr , or shell model ) on the other. Look at the models for helium illustrated below.
Up to two electrons move in a space defined as an orbital . In addition to occupying different areas around the nucleus, electrons exist at different energy levels , moving with different kinetic energy . Electrons can also absorb or lose energy, jumping or falling from one energy level to another.
A unique atomic number (number of protons) and atomic mass (usually measured in Daltons , or Da ) characterize different elements. A unique symbol with a superscripted atomic number and a subscripted atomic mass number defines each element. Take the most common isotope of carbon (C) for example. Its atomic number is 6 (the number of protons in its nucleus) and its mass is 12 Da (6 protons and 6 neutrons at 1 Da each!). Remember that the mass of the electrons in a carbon (C) atom is negligible!
Find the C atom and look at some of the other atoms of elements in the partial periodic table below.
This partial periodic table shows the elements essential for all life in greater or lesser amounts, as well as some that may also be essential in humans.
B. Electron Configuration – Shells and Subshells
The Bohr model of the atom reveals how electrons can absorb and release energy. The shells indicate the energy levels of electrons. Electrons can absorb different kinds of energy (radiation, light, electrical). For example, beaming UV light at atoms can excite electrons. If an electron absorbs a full quantum of energy (or a photon of radiant energy), it will be boosted from the ground state (the shell it normally occupies) into a higher shell, an excited state . Excited electrons move at greater speed around the nucleus, with more kinetic energy than it did at ground . Excited electrons also have more potential energy than ground state electrons. This is because they are unstable, releasing some of the energy gained during excitation as they return to ground , i.e., their starting energy level (shell), as shown below.
Electrons falling back to ground typically release excitation energy as heat. Atoms whose excited electrons release their energy as light fluoresce ; they are fluorescent . A fluorescent light is an example of this phenomenon; electrical energy excites electrons out of atomic orbitals in molecules coating the interior surface of the bulb. As all those excited electrons return to ground state, they fluoresce , releasing light. These atoms can be repeatedly excited by electricity. As we shall see, biologists and chemists have turned fluorescence into tools of biochemistry, molecular biology and microscopy. The ground state is also called the resting state , but electrons at ground are by no means resting! They just move with less kinetic energy excited electrons.


9.3: Characteristic Features
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What is a language? What kinds of languages do exist? Are there characteristic features that are unique in human language?
There are plenty of approaches how to describe languages. Especially in computational linguistics, researchers try to find formal definitions for different kinds of languages. But for psychology other aspects of language than its function as pure system of communication are of central interest. Language is also a tool we use for social interactions starting with the exchange of news up to the identification of social groups by their dialect. We use it for expressing our feelings, thoughts, ideas etc.
Although there are plenty ways to communicate (consider Non-Human-Language) humans expect their system of communication - the human language to be unique. But what is it that makes the human language so special and unique?
Four major criteria have been proposed by Professor Franz Schmalhofer from the University of Osnabrück as explained below:
- semanticity
- displacement
- creativity
- structure dependency
Semanticity means the usage of symbols. Symbols can either refer to objects or to relations between objects. In the human language words are the basic form of symbols. For example the word "book" refers to an object made of paper on which something might be written. A relation symbol is the verb "to like" which refers to the sympathy of somebody to something or someone.
The criterion of displacement means that not only objects or relations at presence can be described but there are also symbols which refer to objects in another time or place. The word "yesterday" refers to day before and objects mentioned in a sentence with "yesterday" refer to objects from another time than the present one. Displacement is about the communication of events which had happened or will happen and the objects belonging to that event.
Having a range of symbols to communicate these symbols can be newly combined. Creativity is the probable most important feature. Our communication is not restricted to a fixed set of topics or predetermined messages. The combination of a finite set of symbols to an infinite number of sentences and meaning. With the infinite number of sentences the creation of novel messages is possible. How creative the human language is can be illustrated by some simple examples like the process that creates verbs from nouns. New words can be created, which do not exist so far, but we are able to understand them.
Examples :
leave the boat on the beach -> beach the boat
keep the aeroplane on the ground -> ground the aeroplane
write somebody an e-mail -> e-mail somebody
Creative systems are also found in other aspects of language, like the way sounds are combined to form new words. i.e. prab, orgu, zabi could be imagined as names for new products.
To avoid an arbitrary combination of symbols without any regular arrangement "true" languages need structure dependency. Combining symbols the syntax is relevant. A change in the symbol order might have an impact on the meaning of the sentence. For example “The dog bites the cat” has obviously a different meaning than “The cat bites the dog” based on the different word arrangement of the two sentences. [edit] Non-Human Language - Animal Communication [edit] Forms of Communication
As mentioned before human language is just one of quite a number of communication forms. Different forms of communication can be found in the world of animals. From a little moth to a giant whale, all animals appear to have the use of communication.
Not only humans use facial expression for stressing utterances or feeling, facial expressions can be found among apes. The expression, for example "smiling" indicates cooperativeness and friendliness in both the human and the ape world. On the other hand an ape showing teeth indicates the willingness to fight.
Posture is a very common communicative tool among animals. Lowering the front part of the body and extending the front legs is a sign of dogs that they are playful whereas lowering the full body is a dog’s postural way to show its submissiveness. Postural communication is known in both human and non-human primates.
Besides facial expression, gesture and posture that are found in human communication, there are other communicative devices which are either just noticeable by the sub-consciousness of humans like scent or cannot be found amongst humans like light, colour and electricity. The chemicals which are used for a communicative function are called pheremones. Those pheremones are used to mark territorial or to signal its reproductive readiness. For animals scent is a very important tool which predominates their mating behaviour. Humans are influenced in their mating behaviour by scent as well but there are more factors to that behaviour so that scent is not predominating.
The insects use species-dependent light patterns to signal identity, sex and location. For example the octopus changes colour for signalling territorial defence and mating readiness. In the world of birds colour is wide spread, too. The male peacock has colourful feathering to impress female peahens as a part of mating behaviour. These ways of communication help to live in a community and survive in certain environment. [edit] Characteristic Language Features in Animal Communication
As mentioned above it is possible to describe the uniqueness of human language by four criteria (semanticity, displacement, creativity and structural dependency) which are important devices in the human language to form a clear communication between humans. To see if these criteria exist in animal communication - i.e. if animals possess a "true" language - several experiments with non-human primates were performed. Non-human primates were taught American Sign Language (ASL) and a specially developed token language to detect in how far they are capable of linguistic behaviour. Can semanticity, displacement, creativity and structure dependency be found in non-human language?
Experiments
- In 1931, comparative psychologist Winthrop Niles Kellogg and his wife started an experiment with a chimpanzee, which he raised alongside his own child. The purpose was of course to see how environment influenced development, could chimpanzee be more like human? Eventually the experiment failed, the factors are: the behavior of their son started to become more and more chimpanzee-like and also the tiredness of having to do both experiment and raising two babies at the same time.
- Human language In 1948, in Orange Park, Florida, Keith and Cathy Hayes tried to teach English words to a chimpanzee named Viki. She was raised as if she were a human child. The chimpanzee was taught to "speak" easy English words like "cup". The experiment failed since with the supralanyngal anatomy and the vocal fold structure that chimpanzees have it is impossible for them to produce human speech sounds. The failure of the Viki experiment made scientists wonder how far are non-human primates able to communicate linguistically.
- Sign language From 1965 to 1972 the first important evidence showing rudiments of linguistic behaviour was "Washoe", a young female chimpanzee. The experimenters Allen and Beatrice Gardner conducted an experiment where Washoe learned 130 signs of the American Sign Language within three years. Showing pictures of a duck to Washoe and asking WHAT THAT? she combined the symbols of WATER and BIRD to create WATER BIRD as she had not learned the word DUCK (the words in capital letters refer to the signs the apes use to communicate with the experimenter).
It was claimed that Washoe was able to arbitrarily combine signs spontaneously and creatively. Some scientists criticised the ASL experiment of Washoe because they claimed that ASL is a loose communicative system and strict syntactic rules are not required. Because of this criticism different experiments were developed and performed which focus on syntactic rules and structure dependency as well as on creative symbol combination.
A non-human primate named "Kanzi" was trained by Savage-Rumbaugh in 1990. Kanzi was able to deal with 256 geometric symbols and understood complex instructions like GET THE ORANGE THAT IS IN THE COLONY ROOM. The experimenter worked with rewards.
A question which arose was whether these non-human primates were able to deal with human-like linguistic capacities or if they were just trained to perform a certain action to get the reward.
For more detailed explanations of the experiments see The Mind of an Ape.
Can the characteristic language features be found in non-human communication?
Creativity seems to be present in animal communication as amongst others Washoe showed with the creation of WATER BIRD for DUCK. Although some critics claimed that creativity is often accidental or like in the case of Washoe’s WATER BIRD the creation relays on the fact that water and bird were present. Just because of this presence Washoe invented the word WATER BIRD.
In the case of Kanzi a certain form of syntactic rules was observed. In 90% of Kanzi’s sentences there was first the invitation to play and then the type of game which Kanzi wanted to play like CHASE HIDE, TICKLE SLAP and GRAB SLAP. The problem which was observed was that it is not always easy to recognise the order of signs. Often facial expression and hand signs are performed at the same time. One ape signed the sentence I LIKE COKE by hugging itself for “like” and forming the sign for “coke” with its hands at the same time. Noticing an order in this sign sentence was not possible.
A certain structural dependency could be observed at Kanzi’s active and passive sentences. When Matata, a fellow chimpanzee was grabbed Kanzi signed GRAB MATATA and when Matata was performing an action such as biting Kanzi produced MATATA BITE. It has not yet been proved that symbolic behaviour is occurring. Although there are plenty evidences that creativity and displacement occur in animal communication some critics claim that these evidences can be led back to dressage and training. It was claimed that linguistic behaviour cannot be proved as it is more likely to be a training to correctly use linguistic devices. Apes show just to a little degree syntactic behaviour and they are not able to produce sentences containing embedded structures. Some linguists claim that because of such a lack of linguistic features non-human communication cannot be a “true” language. Although we do not know the capacity of an ape's mind it does not seem that the range of meanings observed in ape's wild life approach the capaciousness of semanticity of human communication. Furthermore apes seem not to care to much about displacement as it appears that they do not communicate about imaginary pasts or futures.
All in all non-human primate communication consisting of graded series of communication shows little arbitrariness. The results with non-human primates led to a controversial discussion about linguistic behaviour. Many researchers claimed that the results were influenced by dressage.
For humans language is a communication form suited to the patterns of human life. Other communication systems are better suited for fellow creatures and their mode of existence.
Now that we know that there is a difference between animal communication and human language we will see detailed features of the human language. [edit] Language Comprehension & Production [edit] Language features – Syntax and Semantics
In this chapter the main question will be “how do we understand sentences?”. To find an answer to that problem it is necessary to have a closer look at the structure of languages. The most important properties every human language provides are rules which determine the permissible sentences and a hierarchical structure (phonemes as basic sounds, which constitute words, which in turn constitute phrases, which constitute sentences, which constitute texts). These feature of a language enable humans to create new unique sentences. The fact that all human languages have a common ground even if they developed completely independent from one another may lead to the conclusion that the ability to process language must be innate. Another evidence of a inborn universal grammar is that there were observations of deaf children who were not taught a language and developed their own form of communication which provided the same basic constituents. Two basic abilities human beings have to communicate is to interpret the syntax of a sentence and the knowledge of the meaning of single words, which in combination enables them to understand the semantic of whole sentences. Many experiments have been done to find out how the syntactical and semantical interpretation is done by human beings and how syntax and semantics works together to construct the right meaning of a sentence. Physiological experiments had been done in which for example the event-related potential (ERP) in the brain was measured as well as behavioristic experiments in which mental chronometry, the measurement of the time-course of cognitive processes, was used. Physiological experiments showed that the syntactical and the semantical interpretation of a sentence takes place separately from each other. These results will be presented below in more detail.