20.4: Radioactive Decay
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Learning Objectives
By the end of this section, you will be able to:
- Recognize common modes of radioactive decay
- Identify common particles and energies involved in nuclear decay reactions
- Write and balance nuclear decay equations
- Calculate kinetic parameters for decay processes, including half-life
- Describe common radiometric dating techniques
Following the somewhat serendipitous discovery of radioactivity by Becquerel, many prominent scientists began to investigate this new, intriguing phenomenon. Among them were Marie Curie (the first woman to win a Nobel Prize, and the only person to win two Nobel Prizes in different sciences—chemistry and physics), who was the first to coin the term “radioactivity,” and Ernest Rutherford (of gold foil experiment fame), who investigated and named three of the most common types of radiation. During the beginning of the twentieth century, many radioactive substances were discovered, the properties of radiation were investigated and quantified, and a solid understanding of radiation and nuclear decay was developed.
The spontaneous change of an unstable nuclide into another is radioactive decay . The unstable nuclide is called the parent nuclide ; the nuclide that results from the decay is known as the daughter nuclide . The daughter nuclide may be stable, or it may decay itself. The radiation produced during radioactive decay is such that the daughter nuclide lies closer to the band of stability than the parent nuclide, so the location of a nuclide relative to the band of stability can serve as a guide to the kind of decay it will undergo (Figure \(\PageIndex{1}\)).
Link to Learning
Although the radioactive decay of a nucleus is too small to see with the naked eye, we can indirectly view radioactive decay in an environment called a cloud chamber. Click here to learn about cloud chambers and to view an interesting Cloud Chamber Demonstration from the Jefferson Lab.
Types of Radioactive Decay
Ernest Rutherford’s experiments involving the interaction of radiation with a magnetic or electric field (Figure \(\PageIndex{2}\)) helped him determine that one type of radiation consisted of positively charged and relatively massive \(α\) particles; a second type was made up of negatively charged and much less massive \(β\) particles; and a third was uncharged electromagnetic waves, γ rays. We now know that \(α\) particles are high-energy helium nuclei, \(β\) particles are high-energy electrons, and γ radiation compose high-energy electromagnetic radiation. We classify different types of radioactive decay by the radiation produced.
Alpha (\(α\)) decay is the emission of an \(α\) particle from the nucleus. For example, polonium-210 undergoes \(α\) decay:
\[\ce{_{84}^{210} Po ->_{2}^{4} He +_{82}^{206} Pb} \nonumber \]
or
\[\ce{_{84}^{210} Po ->_{2}^{4} \alpha +_{82}^{206} Pb} \nonumber \]
Alpha decay occurs primarily in heavy nuclei (\(A > 200\), \(Z > 83\)). Because the loss of an \(α\) particle gives a daughter nuclide with a mass number four units smaller and an atomic number two units smaller than those of the parent nuclide, the daughter nuclide has a larger n:p ratio than the parent nuclide. If the parent nuclide undergoing \(α\) decay lies below the band of stability (refer to Figure 21.2), the daughter nuclide will lie closer to the band.
Beta (\(β\)) decay is the emission of an electron (i.e., a \(\beta\) particle) from a nucleus. Iodine-131 is an example of a nuclide that undergoes \(β\) decay:
\[\ce{_{53}^{131} I ->_{-1}^0 e +_{54}^{131} Xe} \nonumber \]
or
\[ \ce{_{53}^{131} I ->_{-1}^0 \beta +_{54}^{131} Xe} \nonumber \]
Beta decay, which can be thought of as the conversion of a neutron into a proton and a \(β\) particle, is observed in nuclides with a large n:p ratio. The beta particle (electron) emitted is from the atomic nucleus and is not one of the electrons surrounding the nucleus. Such nuclei lie above the band of stability. Emission of an electron does not change the mass number of the nuclide but does increase the number of its protons and decrease the number of its neutrons. Consequently, the n:p ratio is decreased, and the daughter nuclide lies closer to the band of stability than did the parent nuclide.
Gamma emission (\(γ\) emission) is observed when a nuclide is formed in an excited state and then decays to its ground state with the emission of a \(γ\) ray, a quantum of high-energy electromagnetic radiation. The presence of a nucleus in an excited state is often indicated by an asterisk (*). Cobalt-60 emits \(γ\) radiation and is used in many applications including cancer treatment:
\[ \ce{_{27}^{60} Co^{*} ->_0^0 \gamma +_{27}^{60} Co} \nonumber \]
There is no change in mass number or atomic number during the emission of a \(γ\) ray unless the \(γ\) emission accompanies one of the other modes of decay.
Positron emission (\(β^{+}\) decay) is the emission of a positron from the nucleus. Oxygen-15 is an example of a nuclide that undergoes positron emission:
\[\ce{_{8}^{15} O ->_{+1}^0 e +_7^{15} N} \nonumber \]
or
\[\ce{_{8}^{15} O ->_{+1}^0 \beta +_7^{15} N} \nonumber \]
Positron emission is observed for nuclides in which the n:p ratio is low. These nuclides lie below the band of stability. Positron decay is the conversion of a proton into a neutron with the emission of a positron. The n:p ratio increases, and the daughter nuclide lies closer to the band of stability than did the parent nuclide.
Electron capture occurs when one of the inner electrons in an atom is captured by the atom’s nucleus. For example, potassium-40 undergoes electron capture:
\[\ce{_{19}^{40} K +_{-1}^0 e ->_{18}^{40} Ar} \nonumber \]
Electron capture occurs when an inner shell electron combines with a proton and is converted into a neutron. The loss of an inner shell electron leaves a vacancy that will be filled by one of the outer electrons. As the outer electron drops into the vacancy, it will emit energy. In most cases, the energy emitted will be in the form of an X-ray. Like positron emission, electron capture occurs for “proton-rich” nuclei that lie below the band of stability. Electron capture has the same effect on the nucleus as does positron emission: The atomic number is decreased by one and the mass number does not change. This increases the n:p ratio, and the daughter nuclide lies closer to the band of stability than did the parent nuclide. Whether electron capture or positron emission occurs is difficult to predict. The choice is primarily due to kinetic factors, with the one requiring the smaller activation energy being the one more likely to occur.
Figure \(\PageIndex{3}\) summarizes these types of decay, along with their equations and changes in atomic and mass numbers.
Chemistry in Everyday Life: PET Scan
Positron emission tomography (PET) scans use radiation to diagnose and track health conditions and monitor medical treatments by revealing how parts of a patient’s body function (Figure \(\PageIndex{4}\)). To perform a PET scan, a positron-emitting radioisotope is produced in a cyclotron and then attached to a substance that is used by the part of the body being investigated. This “tagged” compound, or radiotracer, is then put into the patient (injected via IV or breathed in as a gas), and how it is used by the tissue reveals how that organ or other area of the body functions.
For example, F-18 is produced by proton bombardment of \(\ce{^{ 18} O}\)
\[\ce{_{8}^{18} O +_{1}^{1} p ->_{9}^{18} F +_{0}^{1} n} \nonumber \]
and incorporated into a glucose analog called fludeoxyglucose (FDG). How FDG is used by the body provides critical diagnostic information; for example, since cancers use glucose differently than normal tissues, FDG can reveal cancers. The \(\ce{^{18}F}\) emits positrons that interact with nearby electrons, producing a burst of gamma radiation. This energy is detected by the scanner and converted into a detailed, three-dimensional, color image that shows how that part of the patient’s body functions. Different levels of gamma radiation produce different amounts of brightness and colors in the image, which can then be interpreted by a radiologist to reveal what is going on. PET scans can detect heart damage and heart disease, help diagnose Alzheimer’s disease, indicate the part of a brain that is affected by epilepsy, reveal cancer, show what stage it is, and how much it has spread, and whether treatments are effective. Unlike magnetic resonance imaging and X-rays, which only show how something looks, the big advantage of PET scans is that they show how something functions. PET scans are now usually performed in conjunction with a computed tomography scan.
Radioactive Decay Series
The naturally occurring radioactive isotopes of the heaviest elements fall into chains of successive disintegrations, or decays, and all the species in one chain constitute a radioactive family, or radioactive decay series . Three of these series include most of the naturally radioactive elements of the periodic table. They are the uranium series, the actinide series, and the thorium series. The neptunium series is a fourth series, which is no longer significant on the earth because of the short half-lives of the species involved. Each series is characterized by a parent (first member) that has a long half-life and a series of daughter nuclides that ultimately lead to a stable end-product—that is, a nuclide on the band of stability (Figure \(\PageIndex{5}\)). In all three series, the end-product is a stable isotope of lead. The neptunium series, previously thought to terminate with bismuth-209, terminates with thallium-205.
Radioactive Half-Lives
Radioactive decay follows first-order kinetics. Since first-order reactions have already been covered in detail in the kinetics chapter, we will now apply those concepts to nuclear decay reactions. Each radioactive nuclide has a characteristic, constant half-life (\(t_{1/2}\)), the time required for half of the atoms in a sample to decay. An isotope’s half-life allows us to determine how long a sample of a useful isotope will be available, and how long a sample of an undesirable or dangerous isotope must be stored before it decays to a low-enough radiation level that is no longer a problem.
For example, coba source, since half of the nuclei decay every 5.27 years, both the amount of material and the intensity of the radiation emitted is cut in half every 5.27 years. (Note that for a given substance, the intensity of radiation that it produces is directly proportional to the rate of decay of the substance and the amount of the substance.) This is as expected for a process following first-order kinetics. Thus, a cobalt-60 source that is used for cancer treatment must be replaced regularly to continue to be effective.
Since nuclear decay follows first-order kinetics, we can adapt the mathematical relationships used for first-order chemical reactions. We generally substitute the number of nuclei, \(N\), for the concentration. If the rate is stated in nuclear decays per second, we refer to it as the activity of the radioactive sample. The rate for radioactive decay is:
\[\text{decay rate} = λN \nonumber \]
with \(λ\) = the decay constant for the particular radioisotope.
The decay constant, \(λ\), which is the same as a rate constant discussed in the kinetics chapter. It is possible to express the decay constant in terms of the half-life, \(t_{1/2}\):
\[\lambda=\dfrac{\ln 2}{t_{1 / 2}}=\dfrac{0.693}{t_{1 / 2}} \nonumber \]
or
\[t_{1 / 2}=\dfrac{\ln 2}{\lambda}=\dfrac{0.693}{\lambda} \nonumber \]
The first-order equations relating amount, \(N\), and time are:
\[N_t=N_0 e^{-\lambda t} \label{firstorder} \]
or
\[t=-\frac{1}{\lambda} \ln \left(\frac{N_t}{N_0}\right) \nonumber \]
Example \(\PageIndex{1}\): Rates of Radioactive Decay
\(\ce{^{60}_{27}Co}\) decays with a half-life of 5.27 years to produce \(\ce{^{60}_{28}Co}\)
- What is the decay constant for the radioactive disintegration of cobalt-60?
- Calculate the fraction of a sample of the \(\ce{^{60}_{27}Co}\) isotope that will remain after 15 years.
- How long does it take for a sample of \(\ce{^{60}_{27}Co}\) to disintegrate to the extent that only 2.0% of the original amount remains?
Solution
(a) The value of the rate constant is given by:
\[\lambda=\frac{\ln 2}{t_{1 / 2}}=\frac{0.693}{5.27 y }=0.132 y^{-1} \nonumber \](b) The fraction of \(\ce{^{60}_{27}Co}\) that is left after time \(t\) is given by \(\frac{N_t}{N_0}\). Rearranging the first-order relationship in Equation \ref{firstorder} (\(N_t = N_0e^{–λt}\) to solve for this ratio yields:
\[\frac{N_t}{N_0}=e^{-\lambda t}=e^{-(0.132 / \text{y} )(15 \, \text{y} )}=0.138 \nonumber \]
The fraction of \(\ce{^{60}_{27}Co}\) that will remain after 15.0 years is 0.138. Or put another way, 13.8% of the original \(\ce{^{60}_{27}Co}\) present will remain after 15 years.
(c) 2.00% of the original amount of \(\ce{^{60}_{27}Co}\) is equal to 0.0200 N 0 . Substituting this into the equation for time for first-order kinetics, we have:
\[t=-\frac{1}{\lambda} \ln \left(\frac{N_t}{N_0}\right)=-\frac{1}{0.132\, \text{y}^{-1}} \ln \left(\frac{0.0200 \times N_0}{N_0}\right)=29.6 y \nonumber \]
Exercise \(\PageIndex{1}\)
Radon-222, \(\ce{^{222}_{86}Rn}\) has a half-life of 3.823 days. How long will it take a sample of radon-222 with a mass of 0.750 g to decay into other elements, leaving only 0.100 g of radon-222?
- Answer
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11.1 days
Because each nuclide has a specific number of nucleons, a particular balance of repulsion and attraction, and its own degree of stability, the half-lives of radioactive nuclides vary widely. For example: the half-life of \(\ce{^{209}_{83}Bi}\) is \(1.9 \times 10^{19}\) years; \(\ce{^{239}_{94}Ra}\) is 24,000 years; \(\ce{^{222}_{86}Rn}\) is 3.82 days; and element-111 (Rg for roentgenium) is \(1.5 \times 10^{–3}\) seconds. The half-lives of a number of radioactive isotopes important to medicine are shown in Table \(\PageIndex{1}\), and others are listed in Appendix M .
| Type 1 | Decay Mode | Half-Life | Uses |
|---|---|---|---|
| F-18 | β + decay | 110. minutes | PET scans |
| Co-60 | β decay, γ decay | 5.27 years | cancer treatment |
| Tc-99m | γ decay | 8.01 hours | scans of brain, lung, heart, bone |
| I-131 | β decay | 8.02 days | thyroid scans and treatment |
| Tl-201 | electron capture | 73 hours | heart and arteries scans; cardiac stress tests |
Radiometric Dating
Several radioisotopes have half-lives and other properties that make them useful for purposes of “dating” the origin of objects such as archaeological artifacts, formerly living organisms, or geological formations. This process is radiometric dating and has been responsible for many breakthrough scientific discoveries about the geological history of the earth, the evolution of life, and the history of human civilization. We will explore some of the most common types of radioactive dating and how the particular isotopes work for each type.
Radioactive Dating Using Carbon-14
The radioactivity of carbon-14 provides a method for dating objects that were a part of a living organism. This method of radiometric dating, which is also called radiocarbon dating or carbon-14 dating, is accurate for dating carbon-containing substances that are up to about 30,000 years old, and can provide reasonably accurate dates up to a maximum of about 50,000 years old.
Naturally occurring carbon consists of three isotopes: \(\ce{^{12}_{6}C}\) which constitutes about 99% of the carbon on earth; \(\ce{^{13}_6C}\), about 1% of the total; and trace amounts of \(\ce{^{14}_6C}\). Carbon-14 forms in the upper atmosphere by the reaction of nitrogen atoms with neutrons from cosmic rays in space:
\[\ce{_{7}^{14} N +_{0}^{1}n ->_{6}^{14}C + _{1}^{1} H} \nonumber \]
All isotopes of carbon react with oxygen to produce \(\ce{CO2}\) molecules. The ratio of \(\ce{^{14}_{6}CO2}\) to \(\ce{^{12}_{6}CO2}\) depends on the ratio of \(\ce{^{14}_{6}CO}\) to \(\ce{^{12}_{6}CO}\) in the atmosphere. The natural abundance of \(\ce{^{14}_{6}CO}\) in the atmosphere is approximately 1 part per trillion; until recently, this has generally been constant over time, as seen is gas samples found trapped in ice. The incorporation of \(\ce{^{14}_{6}CO2}\) and \(\ce{^{14}_{6}CO2}\) into plants is a regular part of the photosynthesis process, which means that the \(\ce{^{14}_{6}C} : \ce{^{12}_{6}C}\) ratio found in a living plant is the same as the \(\ce{^{14}_{6}C} : \ce{^{12}_{6}C}\) ratio in the atmosphere. But when the plant dies, it no longer traps carbon through photosynthesis. Because \(\ce{^{12}_{6}C}\) is a stable isotope and does not undergo radioactive decay, its concentration in the plant does not change. However, carbon-14 decays by \(β\) emission with a half-life of 5730 years:
\[\ce{_{6}^{14} C ->_{7}^{14} N +_{-1}^0 e} \nonumber \]
Thus, the ratio gradually decreases after the plant dies. The decrease in the ratio with time provides a measure of the time that has elapsed since the death of the plant (or other organism that ate the plant). Figure \(\PageIndex{7}\): visually depicts this process.
For example, with the half-life of being 5730 years, if the ratio in a wooden object found in an archaeological dig is half what it is in a living tree, this indicates that the wooden object is 5730 years old. Highly accurate determinations of ratios can be obtained from very small samples (as little as a milligram) by the use of a mass spectrometer.
Example \(\PageIndex{2}\): Radiocarbon Dating
A tiny piece of paper (produced from formerly living plant matter) taken from the Dead Sea Scrolls has an activity of 10.8 disintegrations per minute per gram of carbon. If the initial C-14 activity was 13.6 disintegrations/min/g of C, estimate the age of the Dead Sea Scrolls.
Solution
The rate of decay (number of disintegrations/minute/gram of carbon) is proportional to the amount of radioactive C-14 left in the paper, so we can substitute the rates for the amounts, \(N\), in the relationship:
\[t=-\frac{1}{\lambda} \ln \left(\frac{N_t}{N_0}\right) \longrightarrow t=-\frac{1}{\lambda} \ln \left(\frac{\text { Rate }_t}{\text { Rate }_0}\right) \nonumber \]
where the subscript 0 represents the time when the plants were cut to make the paper, and the subscript t represents the current time.
The decay constant can be determined from the half-life of C-14, 5730 years:
\[\lambda=\frac{\ln 2}{t_{1 / 2}}=\frac{0.693}{5730 \,\text{y}}=1.21 \times 10^{-4}\, \text{y}^{-1} \nonumber \]
Substituting and solving, we have:
\[t=-\frac{1}{\lambda} \ln \left(\frac{\text { Rate }_t}{\text { Rate }_0}\right) = -\frac{1}{1.21 \times 10^{-4}\, \text{y}^{-1}} \ln \left(\frac{10.8 \, \cancel{ \text{dis} / \text{min} / \text{g}\, \ce{C}} }{13.6 \, \cancel{ \text{dis} / \text{min} / \text{g}\, \ce{C}} }\right)=1910\, \text{y} \nonumber \]
Therefore, the Dead Sea Scrolls are approximately 1900 years old (Figure \(\PageIndex{8}\)).
Exercise \(\PageIndex{1}\)
More accurate dates of the reigns of ancient Egyptian pharaohs have been determined recently using plants that were preserved in their tombs. Samples of seeds and plant matter from King Tutankhamun’s tomb have a C-14 decay rate of 9.07 disintegrations/min/g of C. How long ago did King Tut’s reign come to an end?
- Answer
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about 3350 years ago, or approximately 1340 BC
There have been some significant, well-documented changes to the \(\ce{^{14}_{6}C} : \ce{^{12}_{6}C}\) ratio. The accuracy of a straightforward application of this technique depends on the \(\ce{^{14}_{6}C} : \ce{^{12}_{6}C}\) ratio in a living plant being the same now as it was in an earlier era, but this is not always valid. Due to the increasing accumulation of \(\ce{CO2}\) molecules (largely \(\ce{^{12}_{6}C}\)) in the atmosphere caused by combustion of fossil fuels (in which essentially all of the \(\ce{^{14}_{6}C}\) has decayed), the ratio of \(\ce{^{14}_{6}C} : \ce{^{12}_{6}C}\) in the atmosphere may be changing. This manmade increase in \(\ce{^{12}_{6}C}\) in the atmosphere causes the \(\ce{^{14}_{6}C} : \ce{^{12}_{6}C}\) ratio to decrease, and this in turn affects the ratio in currently living organisms on the earth. Fortunately, however, we can use other data, such as tree dating via examination of annual growth rings, to calculate correction factors. With these correction factors, accurate dates can be determined. In general, radioactive dating only works for about 10 half-lives; therefore, the limit for carbon-14 dating is about 57,000 years.
Radioactive Dating Using Nuclides Other than Carbon-14
Radioactive dating can also use other radioactive nuclides with longer half-lives to date older events. For example, uranium-238 (which decays in a series of steps into lead-206) can be used for establishing the age of rocks (and the approximate age of the oldest rocks on earth). Since U-238 has a half-life of 4.5 billion years, it takes that amount of time for half of the original U-238 to decay into Pb-206. In a sample of rock that does not contain appreciable amounts of Pb-208, the most abundant isotope of lead, we can assume that lead was not present when the rock was formed. Therefore, by measuring and analyzing the ratio of U-238:Pb-206, we can determine the age of the rock. This assumes that all of the lead-206 present came from the decay of uranium-238. If there is additional lead-206 present, which is indicated by the presence of other lead isotopes in the sample, it is necessary to make an adjustment. Potassium-argon dating uses a similar method. K-40 decays by positron emission and electron capture to form Ar-40 with a half-life of 1.25 billion years. If a rock sample is crushed and the amount of Ar-40 gas that escapes is measured, determination of the Ar-40:K-40 ratio yields the age of the rock. Other methods, such as rubidium-strontium dating (Rb-87 decays into Sr-87 with a half-life of 48.8 billion years), operate on the same principle. To estimate the lower limit for the earth’s age, scientists determine the age of various rocks and minerals, making the assumption that the earth is older than the oldest rocks and minerals in its crust. As of 2014, the oldest known rocks on earth are the Jack Hills zircons from Australia, found by uranium-lead dating to be almost 4.4 billion years old.
Example \(\PageIndex{3}\): Radioactive Dating of Rocks
An igneous rock contains \(9.58 \times 10^{–5} \, \text{g}\) of U-238 and \(2.51 \times 10^{–5} \, \text{g}\) of Pb-206, and much, much smaller amounts of Pb-208. Determine the approximate time at which the rock formed.
Solution
The sample of rock contains very little Pb-208, the most common isotope of lead, so we can safely assume that all the Pb-206 in the rock was produced by the radioactive decay of U-238. When the rock formed, it contained all of the U-238 currently in it, plus some U-238 that has since undergone radioactive decay.
The amount of U-238 currently in the rock is:
\[9.58 \times 10^{-5}\, \cancel{\text{g}\, \ce{U}} \times\left(\frac{1\, \text{mol}\, \ce{U} }{238\, \cancel{\text{g}\, \ce{U}}}\right)=4.03 \times 10^{-7} \, \text{mol}\, \ce{U} \nonumber \]
Because when one mole of U-238 decays, it produces one mole of Pb-206, the amount of U-238 that has undergone radioactive decay since the rock was formed is:
\[2.51 \times 10^{-5}\, \cancel{ \text{g}\, \ce{Pb}} \times\left(\frac{1\, \bcancel{\text{mol}\, \ce{Pb}} }{206\, \cancel{ \text{g}\, \ce{Pb}} }\right) \times\left(\frac{1\, \text{mol}\, \ce{U}}{1\, \bcancel{\text{mol}\, \ce{Pb}} }\right)=1.22 \times 10^{-7}\, \text{mol}\, \ce{U} \nonumber \]
The total amount of U-238 originally present in the rock is therefore:
\[4.03 \times 10^{-7}\, \text{mol}\, \ce{U} + 1.22 \times 10^{-7}\, \text{mol}\, \ce{U} = 5.25 \times 10^{-7}\, \text{mol}\, \ce{U} \nonumber \]
The amount of time that has passed since the formation of the rock is given by:
\[t=-\frac{1}{\lambda} \ln \left(\frac{N_t}{N_0}\right) \nonumber \]
with \(N_0\) representing the original amount of U-238 and \(N_t\) representing the present amount of U-238.
U-238 decays into Pb-206 with a half-life of \(4.5 \times 10^9\, \text{y}\), so the decay constant \(λ\) is:
\[\lambda=\frac{\ln 2}{t_{1 / 2}}=\frac{0.693}{4.5 \times 10^9\, \text{y} }=1.54 \times 10^{-10} \, \text{y}^{-1} \nonumber \]
Substituting and solving, we have:
\[t=-\frac{1}{1.54 \times 10^{-10}\, \text{y}^{-1}} \ln \left(\frac{4.03 \times 10^{-7} \, \cancel{\text{mol}\, \ce{U}}}{5.25 \times 10^{-7} \, \cancel{\text{mol}\, \ce{U}}}\right)=1.7 \times 10^9 \, \text{y} \nonumber \]
Therefore, the rock is approximately 1.7 billion years old.
Exercise \(\PageIndex{1}\)
A sample of rock contains \(6.14 \times 10^{–4}\) g of Rb-87 and \(3.51 \times 10^{–5} g\) of Sr-87. Calculate the age of the rock. (The half-life of the \(β\) decay of Rb-87 is \(4.7 \times 10^{10}\, \text{y}\).)
- Answer
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3.7 10 9 y
Footnotes
- 1 The “m” in Tc-99m stands for “metastable,” indicating that this is an unstable, high-energy state of Tc-99. Metastable isotopes emit γ radiation to rid themselves of excess energy and become (more) stable.


6.8: Outcome- Understanding the Earth’s Interior
Understand how we know about the Earth’s interior and its magnetism.
This section extends the previous section by using models to understand the Earth’s interior and its features.
What You’ll Learn to Do
- Compare the different seismic waves and understand how seismic waves help interpret the Earth’s interior.
- Understand what the Earth’s magnetic field is and where it originates.
Learning Activities
The learning activities for this section include the following:
- Reading: Studying the Earth’s Interior
- Self Check: Understanding the Earth’s Interior
Contributors and Attributions
CC licensed content, Original
- Authored by : Kimberly Schulte and Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution


1.9: Maintaining a Healthy Weight
By the end of this chapter you will be able to:
- Recognize the role fat plays in health and disease
- Compare and contrast the use of BMI and body composition measurements
- Describe negative health consequences of obesity and overweight
- Explain the difference between type 1 and type 2 diabetes
- Identify actions that could be implemented to reduce obesity
- Recognize the signs of body dysmorphic disorders and eating disorders
How much of your body weight comes from your bones, muscles, organs, or body fat?
Have you ever tried a diet to lose weight?
Are there differences in health outcomes based on where you store body fat?
The information in this chapter comes primarily from the following websites:
- The Center for Disease Control- Overweight and Obesity
- The World Health Organization- Obesity and Overweight


5.1: Prelude to Discrete Random Variables
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CHAPTER OBJECTIVES
By the end of this chapter, the student should be able to:
- Recognize and understand discrete probability distribution functions, in general.
- Calculate and interpret expected values.
- Recognize the binomial probability distribution and apply it appropriately.
- Recognize the Poisson probability distribution and apply it appropriately.
- Recognize the geometric probability distribution and apply it appropriately.
- Recognize the hypergeometric probability distribution and apply it appropriately.
- Classify discrete word problems by their distributions.
- A student takes a ten-question, true-false quiz. Because the student had such a busy schedule, he or she could not study and guesses randomly at each answer. What is the probability of the student passing the test with at least a 70%?
- Small companies might be interested in the number of long-distance phone calls their employees make during the peak time of the day. Suppose the average is 20 calls. What is the probability that the employees make more than 20 long-distance phone calls during the peak time?
These two examples illustrate two different types of probability problems involving discrete random variables. Recall that discrete data are data that you can count. A random variable describes the outcomes of a statistical experiment in words. The values of a random variable can vary with each repetition of an experiment.
Figure 4.1.1 You can use probability and discrete random variables to calculate the likelihood of lightning striking the ground five times during a half-hour thunderstorm. (Credit: Leszek Leszczynski)Random Variable Notation
Upper case letters such as \(X\) or \(Y\) denote a random variable. Lower case letters like \(x\) or \(y\) denote the value of a random variable. If \(X\) is a random variable, then \(X\) is written in words, and x is given as a number.
For example, let \(X =\) the number of heads you get when you toss three fair coins. The sample space for the toss of three fair coins is TTT ; THH ; HTH ; HHT ; HTT ; THT ; TTH ; HHH . Then, \(x =\) 0, 1, 2, 3. \(X\) is in words and x is a number. Notice that for this example, the \(x\) values are countable outcomes. Because you can count the possible values that \(X\) can take on and the outcomes are random (the x values 0, 1, 2, 3), \(X\) is a discrete random variable.
COLLABORATIVE EXERCISE
Toss a coin ten times and record the number of heads. After all members of the class have completed the experiment (tossed a coin ten times and counted the number of heads), fill in Table . Let \(X =\) the number of heads in ten tosses of the coin.
| \(x\) | Frequency of \(x\) | Relative Frequency of \(x\) |
|---|---|---|
- Which value(s) of \(x\) occurred most frequently?
- If you tossed the coin 1,000 times, what values could \(x\) take on? Which value(s) of \(x\) do you think would occur most frequently?
- What does the relative frequency column sum to?
Glossary
- Random Variable (RV)
- a characteristic of interest in a population being studied; common notation for variables are upper case Latin letters \(X, Y, Z\),...; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters \(x\), \(y\), and \(z\). For example, if \(X\) is the number of children in a family, then \(x\) represents a specific integer 0, 1, 2, 3,.... Variables in statistics differ from variables in intermediate algebra in the two following ways.
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- The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if \(X =\) hair color then the domain is {black, blond, gray, green, orange}.
- We can tell what specific value \(x\) the random variable \(X\) takes only after performing the experiment.
Contributors and Attributions
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Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


8: Cognitive Development in Early Childhood
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Learning Objectives
After reading this chapter, you should be able to:
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Compare and contrast Piaget and Vygotsky’s beliefs about cognitive development.
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Explain the role of information processing in cognitive development.
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Discuss how preschool-aged children understand their worlds.
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Put cognitive and language milestones into the order in which they appear in typically developing children.
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Discuss how early child education supports development and how our understanding of development influence education.
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Describe autism spectrum disorder, including characteristics and possible interventions.
Early childhood is a time of pretending, blending fact and fiction, and learning to think of the world using language. As young children move away from needing to touch, feel, and hear about the world toward learning some basic principles about how the world works, they hold some pretty interesting initial ideas. For example, while adults have no concerns with taking a bath, a child of three might genuinely worry about being sucked down the drain. 1
A child might protest if told that something will happen “tomorrow” but be willing to accept an explanation that an event will occur “today after we sleep.” Or the young child may ask, “How long are we staying? From here to here?” while pointing to two points on a table. Concepts such as tomorrow, time, size and distance are not easy to grasp at this young age. Understanding size, time, distance, fact and fiction are all tasks that are part of cognitive development in the preschool years. 3
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8.1: Piaget’s Preoperational Intelligence
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Piaget’s stage that coincides with early childhood is the preoperational stage. The word operational means logical, so these children were thought to be illogical. However, they were learning to use language or to think of the world symbolically. Let’s examine some of Piaget’s assertions about children’s cognitive abilities at this age.
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8.2: Vygotsky’s Sociocultural Theory of Cognitive Development
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Lev Vygotsky was a Russian psychologist who argued that culture has a major impact on a child’s cognitive development. He believed that the social interactions with adults and more knowledgeable peers can facilitate a child’s potential for learning. Without this interpersonal instruction, he believed children’s minds would not advance very far as their knowledge would be based only on their own discoveries. Let’s review some of Vygotsky’s key concepts.
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8.3: Information Processing
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Information processing researchers have focused on several issues in cognitive development for this age group, including improvements in attention skills, changes in the capacity, and the emergence of executive functions in working memory. Additionally, in early childhood memory strategies, memory accuracy, and autobiographical memory emerge. Early childhood is seen by many researchers as a crucial time period in memory development.
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8.4: Children’s Understanding of the World
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Both Piaget and Vygotsky believed that children actively try to understand the world around them. More recently developmentalists have added to this understanding by examining how children organize information and develop their own theories about the world.
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8.5: Milestones of Cognitive Development
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The many theories of cognitive development and the different research that has been done about how children understand the world, has allowed researchers to study the milestones that children who are typically developing experience in early childhood. Here is a table that summarizes those.
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8.6: Language Development
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A child’s vocabulary expands between the ages of 2 to 6 from about 200 words to over 10,000 words through a process called fast-mapping. Words are easily learned by making connections between new words and concepts already known. The parts of speech that are learned depend on the language and what is emphasized. Children speaking verb-friendly languages such as Chinese and Japanese, tend to learn nouns more readily.
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8.7: Early Childhood Education
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Universal preschool covering all four-year-olds in the country would require significant funding. Further, how effective preschools are in preparing children for elementary school, and what constitutes high quality early childhood education have been debated. To set criteria for designation as a high quality preschool, the National Association for the Education of Young Children (NAEYC) identifies 10 standards (NAEYC, 2016).
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8.8: Applications to Early Education
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Understanding how children think and learn has proven useful for improving education. Activities like playing games that involve working with numbers and spatial relationships can give young children a developmental advantage over peers who have less exposure to the same concepts.
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8.9: Cognitive Differences
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Sometimes children’s brains work differently. One form of this neurodiversity is Autism spectrum disorder.
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8.S: Summary
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Thumbnail: pixabay.com/photos/kids-girl...ebook-1093758/


4.4: Finding Angles
- How can we use inverse trigonometric functions to determine missing angles in right triangles?
- What situations require us to use technology to evaluate inverse trignometric functions?
In our earlier work in Section 4.1 and Section 4.2 , we observed that in any right triangle, if we know the measure of one additional angle and the length of one additional side, we can determine all of the other parts of the triangle. With the inverse trigonometric functions that we developed in Section 4.3 , we are now also able to determine the missing angles in any right triangle where we know the lengths of two sides.
While the original trigonometric functions take a particular angle as input and provide an output that can be viewed as the ratio of two sides of a right triangle, the inverse trigonometric functions take an input that can be viewed as a ratio of two sides of a right triangle and produce the corresponding angle as output. Indeed, it's imperative to remember that statements such as
say the exact same thing from two different perspectives, and that we read “\(\arccos(x)\)” as “the angle whose cosine is \(x\)”.
Consider a right triangle that has one leg of length \(3\) and another leg of length \(\sqrt{3}\text{.}\)
- Sketch a labeled picture of the triangle.
- What is the exact length of the triangle's hypotenuse?
- What is the exact value of \(\sin(\theta)\text{?}\)
- Rewrite your equation from (b) using the arcsine function in the form \(\arcsin(\Box) = \Delta\text{,}\) where \(\Box\) and \(\Delta\) are numerical values.
- What special angle from the unit circle is \(\theta\text{?}\)
Evaluating inverse trigonometric functions
Like the trigonometric functions themselves, there are a handful of important values of the inverse trigonometric functions that we can determine exactly without the aid of a computer. For instance, we know from the unit circle ( Figure 2.3.1 ) that \(\arcsin(-\frac{\sqrt{3}}{2}) = -\frac{\pi}{3}\text{,}\) \(\arccos(-\frac{\sqrt{3}}{2}) = \frac{5\pi}{6}\text{,}\) and \(\arctan(-\frac{1}{\sqrt{3}}) = -\frac{\pi}{6}\text{.}\) In these evaluations, we have to be careful to remember that the range of the arccosine function is \([0,\pi]\text{,}\) while the range of the arcsine function is \([-\frac{\pi}{2},\frac{\pi}{2}]\) and the range of the arctangent function is \((-\frac{\pi}{2},\frac{\pi}{2})\text{,}\) in order to ensure that we choose the appropriate angle that results from the inverse trigonometric function.
In addition, there are many other values at which we may wish to know the angle that results from an inverse trigonometric function. To determine such values, we use a computational device (such as Desmos ) in order to evaluate the function.
Consider the right triangle pictured in Figure \(\PageIndex{2}\) and assume we know that the vertical leg has length \(1\) and the hypotenuse has length \(3\text{.}\) Let \(\alpha\) be the angle opposite the known leg. Determine exact and approximate values for all of the remaining parts of the triangle.
- Solution
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Because we know the hypotenuse and the side opposite \(\alpha\text{,}\) we observe that \(\sin(\alpha) = \frac{1}{3}\text{.}\) Rewriting this statement using inverse function notation, we have equivalently that \(\alpha = \arcsin(\frac{1}{3})\text{,}\) which is the exact value of \(\alpha\text{.}\) Since this is not one of the known special angles on the unit circle, we can find a numerical estimate of \(\alpha\) using a computational device. Entering
arcsin(1/3)
in Desmos , we find that \(\alpha \approx 0.3398\) radians. Note well: whatever device we use, we need to be careful to use degree or radian mode as dictated by the problem we are solving. We will always work in radians unless stated otherwise.We can now find the remaining leg's length and the remaining angle's measure. If we let \(x\) represent the length of the horizontal leg, by the Pythagorean Theorem we know that
\[ x^2 + 1^2 = 3^2\text{,} \nonumber \]and thus \(x^2 = 8\) so \(x = \sqrt{8} \approx 2.8284\text{.}\) Calling the remaining angle \(\beta\text{,}\) since \(\alpha + \beta = \frac{\pi}{2}\text{,}\) it follows that
\[ \beta = \frac{\pi}{2} - \arcsin \left(\frac{1}{3}\right) \approx 1.2310\text{.} \nonumber \]
For each of the following different scenarios, draw a picture of the situation and use inverse trigonometric functions appropriately to determine the missing information both exactly and approximately.
- Consider a right triangle with legs of length \(11\) and \(13\text{.}\) What are the measures (in radians) of the non-right angles and what is the length of the hypotenuse?
- Consider an angle \(\alpha\) in standard position (vertex at the origin, one side on the positive \(x\)-axis) for which we know \(\cos(\alpha) = -\frac{1}{2}\) and \(\alpha\) lies in quadrant III. What is the measure of \(\alpha\) in radians? In addition, what is the value of \(\sin(\alpha)\text{?}\)
- Consider an angle \(\beta\) in standard position for which we know \(\sin(\beta) = 0.1\) and \(\beta\) lies in quadrant II. What is the measure of \(\beta\) in radians? In addition, what is the value of \(\cos(\beta)\text{?}\)
Finding angles in applied contexts
Now that we have developed the (restricted) sine, cosine, and tangent functions and their respective inverses, in any setting in which we have a right triangle together with one side length and any one additional piece of information (another side length or a non-right angle measurement), we can determine all of the remaining pieces of the triangle. In the activities that follow, we explore these possibilities in a variety of different applied contexts.
A roof is being built with a “7-12 pitch.” This means that the roof rises \(7\) inches vertically for every \(12\) inches of horizontal span; in other words, the slope of the roof is \(\frac{7}{12}\text{.}\) What is the exact measure (in degrees) of the angle the roof makes with the horizontal? What is the approximate measure? What are the exact and approximate measures of the angle at the peak of the roof (made by the front and back portions of the roof that meet to form the ridge)?
On a baseball diamond (which is a square with \(90\)-foot sides), the third baseman fields the ball right on the line from third base to home plate and \(10\) feet away from third base (towards home plate). When he throws the ball to first base, what angle (in degrees) does the line the ball travels make with the first base line? What angle does it make with the third base line? Draw a well-labeled diagram to support your thinking.
What angles arise if he throws the ball to second base instead?
A camera is tracking the launch of a SpaceX rocket. The camera is located \(4000\)' from the rocket's launching pad, and the camera angle changes in order to keep the rocket in focus. At what angle \(\theta\) (in radians) is the camera tilted when the rocket is \(3000\)' off the ground? Answer both exactly and approximately.
Now, rather than considering the rocket at a fixed height of \(3000\)', let its height vary and call the rocket's height \(h\text{.}\) Determine the camera's angle, \(\theta\) as a function of \(h\text{,}\) and compute the average rate of change of \(\theta\) on the intervals \([3000,3500]\text{,}\) \([5000,5500]\text{,}\) and \([7000,7500]\text{.}\) What do you observe about how the camera angle is changing?
Summary
- Anytime we know two side lengths in a right triangle, we can use one of the inverse trigonometric functions to determine the measure of one of the non-right angles. For instance, if we know the values of \(\text{opp}\) and \(\text{adj}\) in Figure \(\PageIndex{3}\) , then since
\[ \tan(\theta) = \frac{\text{opp}}{\text{adj}}\text{,} \nonumber \]
it follows that \(\theta = \arctan(\frac{\text{opp}}{\text{adj}})\text{.}\)
If we instead know the hypotenuse and one of the two legs, we can use either the arcsine or arccosine function accordingly.
- For situations other than angles or ratios that involve the \(16\) special points on the unit circle, technology is required in order to evaluate inverse trignometric functions. For instance, from the unit circle we know that \(\arccos(\frac{1}{2}) = \frac{\pi}{3}\) (exactly), but if we want to know \(\arccos(\frac{1}{3})\text{,}\) we have to estimate this value using a computational device such as Desmos . We note that “\(\arccos(\frac{1}{3})\)” is the exact value of the angle whose cosine is \(\frac{1}{3}\text{.}\)
Exercises
At an airshow, a pilot is flying low over a runway while maintaining a constant altitude of \(2000\) feet and a constant speed. On a straight path over the runway, the pilot observes on her laser range-finder that the distance from the plane to a fixed building adjacent to the runway is \(7500\) feet. Five seconds later, she observes that distance to the same building is now \(6000\) feet.
- What is the angle of depression from the plane to the building when the plane is \(7500\) feet away from the building? (The angle of depression is the angle that the pilot's line of sight makes with the horizontal.)
- What is the angle of depression when the plane is \(6000\) feet from the building?
- How far did the plane travel during the time between the two different observations?
- What is the plane's velocity (in miles per hour)?
On a calm day, a photographer is filming a hot air balloon. When the balloon launches, the photographer is stationed \(850\) feet away from the balloon.
- When the balloon is \(200\) feet off the ground, what is the angle of elevation of the camera?
- When the balloon is \(275\) feet off the ground, what is the angle of elevation of the camera?
- Let \(\theta\) represent the camera's angle of elevation when the balloon is at an arbitrary height \(h\) above the ground. Express \(\theta\) as a function of \(h\text{.}\)
- Determine \(AV_{[200,275]}\) for \(\theta\) (as a function of \(h\)) and write at least one sentence to carefully explain the meaning of the value you find, including units.
Consider a right triangle where the two legs measure \(5\) and \(12\) respectively and \(\alpha\) is the angle opposite the shorter leg and \(\beta\) is the angle opposite the longer leg.
- What is the exact value of \(\cos(\alpha)\text{?}\)
- What is the exact value of \(\sin(\beta)\text{?}\)
- What is the exact value of \(\tan(\beta)\text{?}\) of \(\tan(\alpha)\text{?}\)
- What is the exact radian measure of \(\alpha\text{?}\) approximate measure?
- What is the exact radian measure of \(\beta\text{?}\) approximate measure?
- True or false: for any two angles \(\theta\) and \(\gamma\) such that \(\theta + \gamma = \frac{\pi}{2}\) (radians), it follows that \(\cos(\theta) = \sin(\gamma)\text{.}\)


25.3: Heat and the First Law
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"Direct Exchange of Thermal Energy" and Early Theories of Heat
In the previous section I have considered the possibility of “direct exchange of thermal energy” between two objects. This is a phenomenon with which we are all familiar: when a colder object is placed in contact with a warmer one, the warmer one cools off and the colder one warms up. This “warmth” that seems to flow out of one object and into the other is conventionally called “heat.”
Naturally, this observation was made long before the concept of “energy” was even developed, and so heat was thought of, for a time, as an “invisible fluid” (called, at one point, “caloric fluid”), a sort of indestructible “substance” that literally passed from one body to another. By “indestructible” I mean that they had a notion of this caloric fluid being conserved: it was not created or destroyed, only exchanged from one body to another. This makes sense, in a way: if it was really something material, how could it be created or destroyed? Conservation of matter was pretty much accepted scientific “dogma” already by the end of the 18th century.
This idea of conservation of the caloric fluid led to the whole field of “calorimetry,” as essentially a way to try to quantify (that is, measure) the amount of “caloric” that materials would take in or give off. The connection with temperature led directly to the definition of heat capacities and specific heats, just as I have introduced them above (in section 2.1 ); only instead of “change in energy” you would use “change in caloric content.” This would be measured in units, called calories, defined by the amount of caloric that led to a given temperature change in a reference substance, such as water.
To be precise, let 1 calorie be the amount of “caloric” needed to raise the temperature of one gram of water by one degree Celsius at a pressure of one atmosphere. This makes the specific heat of water, by definition, 1 calorie/\(^{\circ}\)C·gram. Now imagine you place a hot object in a container of water, insulated from the rest of the world, and wait until thermal equilibrium is reached. Then you can calculate the “amount of caloric that flowed into the water,” from the change in its temperature, and if you assume that all this came from the hot object then you can calculate its heat capacity (in calories/\(^{\circ}\)C) from the change in its temperature. By proceeding in this fashion, scientists developed tables of specific heats that do not need any change today—only the recognition that “caloric” is not really a fluid at all, but a form of energy, and can, therefore, be measured in energy units.
Clearly, conservation of caloric was a very good idea in its own way, since much of what was established back then still works if you simply replace the word “caloric” or “heat” by “thermal energy.” It was, however, ultimately unsatisfactory precisely because it restricted itself to what we would today recognize as just one kind of energy, and so it failed to recognize thermal energy as something that could be converted into, or from, other kinds of energy
In hindsight, it is a bit surprising that the belief in the conservation of caloric could have held for so long. What today appear to us like obvious instances of the transformation of (macroscopic) mechanical energy into thermal energy, such as the warmth generated when you rub two objects together, were explained away as instances of mechanically “squeezing” caloric fluid out of the objects. Around the turn of the 19th century, an American expatriate, Count Rumford, observed one of the most egregious instances of this in the enormous amount of “heat” that was generated in the boring of cannons (which involved, basically, a huge metal tool drilling a hole in a large metal cylinder). He noticed that the total mass of the metal, including all the shavings, did not appear to change in the process, and concluded that caloric had to be virtually massless, since enormous quantities of it could be “squeezed” out without an appreciable mass loss. He speculated that caloric was not a fluid at all, but rather “a form of motion,” since only something like that could be made to increase without any apparent limit.
Rumford’s theory was not generally accepted at the time, but later in the 19th century the direct conversion of mechanical energy into thermal energy was established beyond a doubt by James Prescott Joule in a series of painstaking experiments in which he used a system of weights to turn some vanes, or paddles, that stirred water in a container and eventually caused its temperature to rise. By measuring the mechanical energy deficit (gravitational plus kinetic) of his system of weights and paddles, he could tell how much energy the water must have gained, and by measuring the water’s change in temperature he could then establish the equivalent “amount of caloric” that had gone into it. He thus established what was called “the mechanical equivalent of heat,” which we would express today by saying that a calorie does not measure the amount of some (nonexistent) caloric fluid, but simply an amount of energy equal to 4.18 joules (and yes, the Joule is named after him!).
The First Law of Thermodynamics
The upshot of all this experimentation was the full development of the concept of energy as a conserved quantity that manifested itself in different ways and could be “converted” among different kinds. To the observation, already familiar from macroscopic mechanics, that the energy of a system could be changed by doing work on it (or letting it do work on its environment) was added the observation, coming from thermal physics, that thermal energy could also be directly exchanged between two objects merely by placing them in contact, without any macroscopic work being involved. The two things taken together led to the principle of conservation of energy in its most general (pre-relativistic) form:
\[ \Delta E=W+Q \label{eq:13.8} \]
which says simply that a change in the total energy of a system may result from work (\(W\)) or from “heat exchange” (\(Q\)). “Heat,” in physics usage today, is simply what we call the thermal energy that is directly transferred from one object to another, typically by contact; the convention used for this term is the same as for the work term, that is, \(Q\) is positive if thermal energy flows into the system and negative if thermal energy leaves the system.
Equation (\ref{eq:13.8}) is the first law of thermodynamics . Note that, in terms of \(Q\), the precise definition of a system’s heat capacity is \(C = Q/\Delta T\), and so this will only be equal to \(\Delta E/\Delta t\) when the system does no work, which is why I was careful to include that condition in the derivation of Equation ( 13.2.2 ).


15.2C: Chemistry of Hormones
There are three classes of hormones: peptide hormones, lipid hormones, and monoamine hormones.
- Distinguish between the hydrophilic and lipophilic types of endocrine hormones based on their chemical structures
Key Points
- Peptide hormones are comprised of short (peptides) and long ( proteins ) chains of amino acids. They are water-soluble but cannot pass through the plasma membrane alone.
- Glyco-protein hormones have a carbohydrate moiety attached to the protein.
- Lipid hormones include steroid and eicosanoid hormones. They are lipid-soluble and can pass through the plasma membrane.
- Steroid hormones are derived from the cholesterol and eicosanoid hormones from fatty acids that compose the plasma membrane.
- The third class of hormones is the monoamines that are derived from aromatic amino acids like phenylalanine, tyrosine, and tryptophan.
A hormone is a chemical released by a cell or a gland in one part of the body that sends out messages that affect cells in other parts of the organism.
There are three classes of hormones:
- Peptide hormones
- Lipid-derived hormones
- Monoamine hormones
Peptide Hormones
Peptide hormones consist of short chains of amino acids, such as vasopressin, that are secreted by the pituitary gland and regulate osmotic balance; or long chains, such as insulin, that are secreted by the pancreas, which regulates glucose metabolism.
Some peptide hormones contain carbohydrate side chains and are termed glyco-proteins, such as the follicle-stimulating hormone. All peptide hormones are hydrophilic and are therefore unable to cross the plasma membrane alone.
Peptide hormone : Representation of the molecular structure of a peptide hormone.
Lipid-Derived Hormones
Lipid and phospholipid-derived hormones are produced from lipids such as linoleic acid and arachidonic acid. Steroid hormones, which form the majority of lipid hormones, are derived from carbohydrates; for example, testosterone is produced primarily in the testes and plays a key role in development of the male reproductive system.
Eicosanoids are also lipid hormones that are derived from fatty acids in the plasma membrane. Unlike other hormones, eicosanoids are not stored in the cell—they are synthesized as required. Both are lipophillic and can cross the plasma membrane.
Monoamine Hormones
Monoamine hormones are derived from single aromatic amino acids like phenylalanine, tyrosine, and tryptophan. For example, the tryptophan-derived melatonin that is secreted by the pineal gland regulates sleep patterns.


1.9: Hints to get started on some exercises
Exercise 1.2. You could do this with a Venn diagram. However, once there are more than three sets (see Exercise 1.13), this approach will be difficult. An algebraic proof will generalize more easily, so try to find one here. Argue for the two inclusions \[\begin{aligned} (X \cup Y)^{c} & \subseteq X^{c} \cap Y^{c} \\ X^{c} \cap Y^{c} & \subseteq(X \cup Y)^{c} \end{aligned}\] separately. In the first one, for example, assume that \(x \in(X \cup Y)^{c}\) and show that it must be in both \(X^{c}\) and \(Y^{c}\) .
Exercise 1.13. Part of the problem here is notation - what if you have more sets than letters? Start with a finite number of sets contained in \(U\) , and call them \(X_{1}, \ldots, X_{n}\) . What do you think the complement of their union is? Prove it as you did when \(n=2\) in Exercise 1.2. (See the advantage of having a proof in Exercise \(1.2\) that did not use Venn diagrams? One of the reasons mathematicians like to have multiple proofs of the same theorem is that each proof is likely to generalize in a different way). Can you make the same argument work if your sets are indexed by some infinite index set?
Now do the same thing with the complement of the intersection.
Exercise 1.14. Again there is a notational problem, but while \(Y\) and \(Z\) play the same rôle in Exercise 1.3, \(X\) plays a different rôle. So rewrite the equations as \[\begin{aligned} &X \cap\left(Y_{1} \cup Y_{2}\right)=\left(X \cap Y_{1}\right) \cup\left(X \cap Y_{2}\right) \\ &X \cup\left(Y_{1} \cap Y_{2}\right)=\left(X \cup Y_{1}\right) \cap\left(X \cup Y_{2}\right), \end{aligned}\] and see if you can generalize these.
Exercise 1.35. (i) Again, this reduces to proving two containments. If \(y\) is in the left-hand side, then there must be some \(x_{0}\) in some \(U_{\alpha_{0}}\) such that \(f(x)=y\) . But then \(y\) is in \(f\left(U_{\alpha_{0}}\right)\) , so \(y\) is in the right-hand side.
Conversely, if \(y\) is in the right-hand side, then it must be in \(f\left(U_{\alpha_{0}}\right)\) for some \(\alpha_{0} \in A\) . But then \(y\) is in \(f\left(\cup_{\alpha \in A} U_{\alpha}\right)\) , and so is in the left-hand side.


15: Equilibria of Other Reaction Classes
We previously learned about aqueous solutions and their importance, as well as about solubility rules. While this gives us a picture of solubility, that picture is not complete if we look at the rules alone. Solubility equilibrium, which we will explore in this chapter, is a more complex topic that allows us to determine the extent to which a slightly soluble ionic solid will dissolve, and the conditions under which precipitation.
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- 15.1: Precipitation and Dissolution
- The equilibrium constant for an equilibrium involving the precipitation or dissolution of a slightly soluble ionic solid is called the solubility product, Ksp, of the solid. The solubility product of a slightly soluble electrolyte can be calculated from its solubility; conversely, its solubility can be calculated from its Ksp, provided the only significant reaction that occurs when the solid dissolves is the formation of its ions.
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- 15.2: Lewis Acids and Bases
- A Lewis acid is a species that can accept an electron pair, whereas a Lewis base has an electron pair available for donation to a Lewis acid. Complex ions are examples of Lewis acid-base adducts. In a complex ion, we have a central atom, often consisting of a transition metal cation, which acts as a Lewis acid, and several neutral molecules or ions surrounding them called ligands that act as Lewis bases. Complex ions form by sharing electron pairs to form coordinate covalent bonds.
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- 15.3: Coupled Equilibria
- Several systems we encounter consist of multiple equilibria, systems where two or more equilibria processes are occurring simultaneously. Some common examples include acid rain, fluoridation, and dissolution of carbon dioxide in sea water. When looking at these systems, we need to consider each equilibrium separately and then combine the individual equilibrium constants into one solubility product or reaction quotient expression using the tools from the first equilibrium chapter.
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- 15.E: Equilibria of Other Reaction Classes (Exercises)
- These are homework exercises to accompany the Textmap created for "Chemistry" by OpenStax. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.
Contributors
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Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


7.15A: Gene Families
Gene families are groups of functionally related genes arising from a duplicated gene.
LEARNING OBJECTIVES
Distinguish gene families from gene complexes
Key Takeaways
A gene family is a set of several similar genes, formed by duplication of a single original gene, that generally have similar biochemical functions. One such family are the genes for human haemoglobin subunits. The 10 genes are in two clusters on different chromosomes, called the α-globin and β-globin loci. Genes are categorized into families based on shared nucleotide or protein sequences. Phylogenetic techniques can be used as a more rigorous test. The positions of exons within the coding sequence can be used to infer common ancestry. Knowing the sequence of the protein encoded by a gene can allow researchers to apply methods that find similarities among protein sequences that provide more information than similarities or differences among DNA sequences. Furthermore, knowledge of the protein’s secondary structure gives further information about ancestry, since the organization of secondary structural elements presumably would be conserved even if the amino acid sequence changes considerably.
These methods often rely upon predictions based upon the DNA sequence. If the genes of a gene family encode proteins, the term protein family is often used in an analogous manner to gene family. The expansion or contraction of gene families along a specific lineage can be due to chance or can be the result of natural selection. To distinguish between these two cases is often difficult in practice. Recent work uses a combination of statistical models and algorithmic techniques to detect gene families that are under the effect of natural selection.
In contrast, gene complexes are simply tightly linked groups of genes, often created via gene duplication (sometimes called segmental duplication if the duplicates remain side-by-side). Here, each gene has a similar though slightly diverged function.
Key Points
- Genes duplicate over evolutionary times. As they duplicate this can lead to families of related genes. Since they come from the same progenitor gene, they often have related biochemical functions.
- Gene families can expand and contract over evolutionary time scales.
- Gene complexes are groups of genes that work in a fashion similar to gene families; however, they need not arise from gene duplication.
Key Terms
- phylogenetic : Of or relating to the evolutionary development of organisms.
- secondary structure : The general three-dimensional structure of a biopolymer such as DNA or a protein.


3.5: Day 0- Emergency Room
Day: 0
Time: 18h00
Place: Emergency Room Triage
Sitting back in her chair, Jackie sighs. “Wow, this has been a long shift. I’m exhausted.”
Looking up from the desk, she sees an old green Ford truck stop in front of the Emergency Room. From the passenger door, an elderly lady slowly emerges.
The older lady makes her way slowly to the doors, with the dog trailing her on a leash. Once she is inside the doors, Jackie notes that the woman displays pursed lip breathing, has a slight blue tinge to her lips and a very slow gait.
Finally making it to the triage desk, the lady leans against the desk and sighs loudly.
Jackie comes out from behind the desk and moves a wheelchair close to Erin for her to sit in.
“Hi, my name is Jackie and I’m the triage nurse today. How can I help you?”
“Thank you. My name. Erin. I feel awful. Can’t catch. My breath.”
Jackie pulls the blood pressure and pulse oximetry machine close to Erin and wraps the cuff around her right arm. She presses a button and the cuff inflates. On Erin’s left index finger she places a pulse oximeter.
After about 30 seconds, the machine beeps and displays the following vital signs:
| Day: 0 | Pulse Rate | Blood Pressure | Respiratory Rate | Temperature | O 2 Saturation |
| Time: 18h00 | 96 | 180/90 | 28 | 36.5° C | 85% |
Grabbing a clipboard with an emergency assessment record on it, Jackie fills out the initial vital signs.
Referring to the Triage and Acuity Scale along with the vital signs, Jackie grades Erin’s condition as “Triage Level III – Urgent”.
A tall middle-aged man in workman’s clothes approaches the triage desk. “How is my Mom doing?” asks Thomas.
“I think it would be best if Mrs. Johns stays with us awhile and has a doctor take a look at her. I will make arrangements for a spot for her to stay once we get her admission paperwork done. Can you and your Mom answer a few questions from Denise, the clerk who is just to the left of my desk?”
Denise, the admission clerk, comes over and introduces herself to Erin.
“Good evening. My name is Denise.”
“My name is. Erin. This is my son. Thomas,” Erin states breathlessly.
“Ok. Thomas, can you wheel your Mom close to my desk so I can input her information into the computer, please? That way we can get her a space in the ER quickly and have a doctor see her as well.”
Thomas pushes the wheelchair over to the admissions desk.
“Do you have your Care Card with you?” asks Denise.
Erin hands over her Care Card to Denise, who rapidly inputs the information into the system.
“I see, Mrs. Johns, that you were at a clinic last week. Is this correct?”
Erin nods ‘yes’. Thomas explains: “They changed her puffers and said to come back if there was any problem.”
Denise nods her head. “Make sure you tell the nurses that.”
Denise then asks, “Do you see anyone regularly at the clinic?”
“No. I see whoever is available. They change so often.”
Looking up at Thomas, Denise asks, “Can I have your contact information, Thomas, in case we need to contact you?”
Thomas recites his cell phone number and tells Denise that he currently lives with his Mom, due to a complicated divorce that has left him a bit depressed and short of cash.
Denise nods and inputs the contact information into the computer.
“Well, that is all I need right now. I have called for a porter and they will move you to a spot where the doctor can see you.”
Denise watches as the porter comes up to both Thomas and Erin and begins pushing the wheelchair through the doors into the back area of the Emergency Ward.
Denise shakes her head slightly and wiggles her nose. She thinks to herself, “That dog needs a bath. Poor thing.”
“Is this where. You are. Going to leave. Me. It’s a hallway!” Erin looks up at the porter pleadingly.
The porter looks at her. “You will need to wait here till there is a better spot for you,” and he walks away.
Erin pulls Trixie closer to her as she sits in the wheelchair. Thomas looks around at the chaos and sees people moving from curtained area to curtained area, all dressed alike in light blue scrubs. No one makes eye contact or even acknowledges them as the new arrivals.
Just as he is thinking this to himself, he feels a presence behind him. Turning around, he sees another nurse dressed in light blue holding a clipboard.
“Are you Mrs. Johns and her son, Thomas?”
Both nod affirmatively.
“My name is Jason. I’ve just come on shift. I see the triage nurse started your chart and that you have been admitted. What I need to do now is listen to your chest and ask you some questions. Is that ok?”
Jason watches both of them nod ‘yes’.
“Ok, then. Thomas, would you mind taking the dog outside so I can assess your mother?”
Thomas reaches down and gently extracts Trixie from Erin.
“Can you come get me after you’re done?” asks Erin.
Thomas: “Mom, I’ll walk Trixie and then put her in the truck. I have some biscuits that I can give her and she should be perfectly fine there.”
Thomas cradles the small dog, who begins to whimper quietly, and strides out through the doors to the emergency exit.
Jason pulls a chair closer to Erin. “I am going to ask you a few questions. This helps us to help you. Do you feel up to answering a few questions?”
“Yes.”
“When did you begin to feel short of breath?”
“About a week. Ago. I went. Clinic. Gave me new puffers. Seemed to help. Today. Walking Trixie. Cold out. Really short of breath. Called Thomas. Brought me here.”
Jason writes the information directly into the second page of the nursing record.
“The clinic notes indicate you have COPD. Is this correct?”
“Yes.”
“Do you have any other conditions?”
“No.” Erin smiles weakly. “Otherwise. Healthy.”
“Ok. That is enough right now. Let’s take your vital signs, and then I’m going to listen to your lungs and heart.”
Jason pulls the vital sign machine close to the wheelchair, attaches the BP cuff and the pulse oximeter, and presses the button.
As the cuff inflates, Jason looks carefully at Erin. He notes that her airway is patent and her breathing is rapid at 28/minute and appears shallow, with some nasal flaring.
The blood pressure cuff dings and the result appears on the screen.
“Ok Mrs. Johns, your blood pressure is higher than I would expect. Is this normal for you?”
Erin leans forward and peers closely at the numbers, “I think so. Top number. 150 to. 170. Normally.”
| Day: 0 | Pulse Rate | Blood Pressure | Respiratory Rate | Temperature | O 2 Saturation |
| Time: 20h00 | 92 | 170/90 | 26 | 36.4° C | 84% |
Jason nods. “Your oxygen saturation is a bit low, so I am going to put you on a little oxygen. Is that ok with you?”
“Yes.”
Jason reaches over to draw in a cart from the hallway. He pulls out a set of nasal prongs and attaches them to an oxygen tank fitted at the back of the wheelchair. He thinks to himself and then sets the flow at 2 LPM.
“Let’s see if that helps with your shortness of breath. I’m now going to listen to your heart and lungs. I know we are in the hallway and I’ll do my best to not expose you. Are you ok with me examining you?”
“Yes. Not happy. In hallway.”
“I can understand that, but we’re very busy and I have no other place to give you. I hope this will only be for a couple of hours.”
Jason then carefully slips his stethoscope between Erin’s clothes and skin. Closing his eyes, he moves the stethoscope systematically first to the anterior chest then posterior chest. After listening, he quickly examines her abdomen and extremities.
“Ok, Mrs. Johns. I’m done right now. I see your oxygen levels appear to be a bit higher. Are you feeling a little less short of breath?”
“Yes, I feel a bit better.”
“Great! I am going to find the doctor and see what the plan will be for you. If you need any help, just wave your arms.”
Erin nods that she understands. Looking around, she shivers slightly at being sick and so exposed in the hallway. She watches Jason move towards the nursing station where there are two people who look like doctors. She thinks to herself, “They look so young. How can they be doctors? I’m stuck in a hallway, can’t believe all the money we pay for taxes and this is the best they can do for me. When Thomas comes back, I’ll ask him to take me and Trixie home. This is ridiculous.”
Jason looks at the various people huddled around the nursing station.
He shakes his head slightly and mumbles, “Yeah, shift change for everyone.”
He walks up to Dr. Singh, whom he is most familiar with. As he approaches he hears Dr. Singh announce, “I’ll take the back rooms and the hallway patients. Stan, can you take the triage and trauma? I did that yesterday, and with that patient dying in the trauma room, I still have to sign off the chart and have a discussion with the coroner.”
Stan looks up at his peer. “Ok, but if it gets really busy, we’ll need to call someone in or you will need to help.”
Dr. Singh sighs. “If you need help, I will stay.”
Dr. Singh moves off to check the computer for emergency admissions and to start planning his shift.
Jason moves up beside him. “Can I interrupt?”
“Sure thing, Jason. What’s up?
Trying to keep to SBAR, Jason says, “I just came on shift as well. New patient, Mrs. Johns, 72 years old, in Hallway B. Exacerbation of COPD, maybe pneumonia, no other medical history, quite short of breath with low sats. I placed her on 2 LPM prongs with some relief and better sats. Breath sounds are quite quiet to the lower fields and she has a slight wheeze in the upper fields. She’s stable right now but I need some orders, please.”
“Ok, Jason. I agree that she’s stable right now, but with a big potential to deteriorate. I will follow the COPD protocol and write orders for a chest X-ray, some labs, puffers, spirometry, and an ABG. Let’s hold off on antibiotics till we have a firmer picture of pneumonia. I don’t want to overreact and prescribe something she doesn’t need right now. With her diagnosis and potentially frequent antibiotic use, we could set her up for a superbug. How does that sound?”
“I agree, and thank you. I’ll get the RT for the ABG and see if Medrad can do the X-ray portably.”
Dr. Singh pulls out a doctor’s order sheet. Jason places a sticker with Erin Johns’s identification on the top right corner.
Jason takes the orders from Dr. Singh and goes over to the unit clerk, Sheila.
Sheila looks at him with raised eyebrows. “I just got here, so please don’t tell me this is a long order set! My commute was terrible and daycare was late opening up. I already feel behind before I’ve even started.”
Jason smiles. “Aww, Sheila. I hate when my day starts like that. I once had to bring little Jim in to work when my daycare was late as well. Cathy picked him up a half hour into the shift. The orders are really short, as you would expect from Dr. Singh. Just what you need, no extras. Since you are settling in, do you want me to enter them into the computer?”
“That would be awesome!! I see Dr. Greg’s admitted a patient to 7B and the order set for that patient is seven pages. I would rather get started on that set, if you don’t mind.”
“No problem.” Jason moves away from the nursing station and signs on to a computer located just a few feet from Erin.
He types in all the information and generates the requisitions for the orders Dr. Singh wrote: CBC,lytes,BUN,creatinine,spirometry, and a portable chest X-ray, and medications as per COPD protocol.
Jason quietly moves towards Erin and notes that she is sleeping in the chair.
“Wow, I wonder when she last had a good sleep.”Jason gently touches her arm to wake her and updates her on her tests. He tells her that Dr. Singh will come by in a little bit, after the tests are done, to check on her.
Erin nods and then closes her eyes.
Place: Medical Laboratory
Alexa has just started her shift. Smiling inwardly, she thinks, “This is my third shift by myself after orientation. Can’t believe it. School does a good job of preparing you for the job, but nothing can prepare you for the work. It’s so busy. My feet already hurt.”
Straightening her scrub top, she leans over and double-checks her cart to make sure she has enough supplies to last the majority of the shift.
The lab supervisor approaches her. “Emergency is really busy right now. Would you mind going down there first before heading to the rest of the hospital? Sheila, the clerk down there, says there are about 20 lab reqs waiting.”
“Ok, I haven’t been there since I was a student.”
“No worries. James is already down there and he can help you out. He thoroughly enjoys the atmosphere of the Emergency.”
Alexa pushes her cart out of the lab area and heads to the elevator that goes to Emergency. She pushes the button for the Emergency floor and watches the buttons slowly creep towards that floor. Exiting, she pushes her cart up to the emergency staff doors, and taking a deep breath she pushes the button. As soon as the doors open, she sways back from the noise and the smells and the overwhelming sense of chaos.
“Oh my. Yep, school did not prepare me for this. Wow.”
Navigating her cart through the Emergency Department, she thinks to herself, “It’s just like driving in rush hour in a foreign country. There are rules but no one sticks to the lines.”
She quickly finds herself at the nursing station and moves towards the desk area where all the reqs are waiting. She notes that James has taken all the stat ones, as there is not one in the pile. Looking through reqs, she notes that they are all pretty similar and all the reqs have close to the same time on them.
“Ok, let’s start with this one,” she says as she places Erin Johns’s req on the top of her board. Looking at the req, she pulls out the appropriate lab tubes and labels them with Erin Johns’ stickers.
That done, she looks up. A frown creases her forehead, and she mumbles, “Hallway B. Where the heck is that?”
Jason, walking by, hears Alexa mumble and stops. “Hi, I’m Jason and Hallway B is my assignment. Who are you looking for?”
Alexa, looking somewhat sheepish, says, “I didn’t think anyone would hear me mumble in this noise.”
“It’s not so noisy and you do get used to it.”
“I’m looking for Erin Johns.”
“Erin is my patient. Let’s walk over here and down this corridor. I’ll introduce you. I haven’t seen you before. Are you new?”
“Yes, this is my third shift by myself after orientation. I’ve mainly been in the lab department or on the medical floors. I was in Emergency for some of my final preceptorship.”
“Excellent. This is a great place to work. Busy, but the people are knowledgeable and quite caring.”
As they move down the hallway, Alexa sees an elderly lady, still in her normal clothes and with a light blanket wrapped around her shoulders, sleeping in a wheelchair.
“Is that…?”
“Yes. That is Erin Johns.”
Jason moves confidently up to Erin and lightly touches her on the arm. Alexa notes that Erin’s eyes open quickly and they appear sharp and not withdrawn, like some of the patients she has seen.
“Mrs. Johns, this is Alexa, one of our lab technicians. She’s here to take some blood from you. Is that ok?
Erin nods ‘yes’.
Alexa moves her cart closer. Looking at the req and then at Mrs. Johns, she says, “Can you tell me your name?”
“Erin Johns.”
“Your birthday?”
“06/06/19xx. ”
“Excellent, thank you.” Alexa checks the identification band on Erin’s right wrist against the information on the requisition. Satisfied, she gathers the tubes, double-checks them, and picks up the venipuncture equipment and tourniquet. Following the World Health Organization guidelines, Alexa prepares to take the required blood specimens.
Alexa first asks Erin to roll her sleeve up a bit more. Carefully putting the tourniquet around Erin’s right upper arm, Alexa then swabs her inner antecubital space.
“Ok, this will pinch a bit.”
Carefully sliding the needle under the skin, Alexa quickly finds the vein and pushes the first of three tubes into the vacutainer.
Once all the tubes are full, Alexa shakes them slowly and carefully to mix the blood and the anticoagulant. After that, she carefully places the tubes in the holder in the front of her cart.
“I’m all done, Mrs. Johns. I hope you feel better soon.”
Alexa moves away and heads towards the nursing station. She looks down at the next req on her list and notes that it’s not a hallway but a number. Looking around, she quickly finds number 12 and heads towards the next patient.
Place: Medical Radiography
Gurpreet checks the list of patients requisitions that need to be done. Looking at the list, she sees there are a number of emergency patients and floor patients. No reqs are marked as stat.
“Ok, looks like we need a porter.”
Glen looks across the lobby from where he is sitting. “What’s that, Gurpreet? Do you need me?”
“Sorry, Glen, didn’t see you there. Yes, can you go pick up Mrs. Erin Johns from Hallway B in Emergency, please?”
“Yes, no problem.”
Glen pulls himself out of the chair and strides through the double doors of the Radiology Department. Looking quickly up and down the hallway, Glen makes his way down the back stairs to the Emergency Department.
Glen has been working in the hospital for about 15 years and knows every short cut there is. Taking the stairs two at a time, he arrives at a little used doorway into Hallway B of the Emergency Department.
Walking up to the nursing station at the far end of the hallway, he looks at Sheila, the unit clerk. “Hi ya, Sheila.”
“Oh, hi Glen. What can I do for you?”
“Oi, how about dinner?”
“That’s not what I meant!” Sheila smiles at her boyfriend and winks at him.
“I’m here to escort Mrs. Erin Johns to the Radiology Department for a picture.”
Sheila looks at her assignment list and finds that Jason is the nurse. “Ok, Jason is caring for her. And there he is talking with Mrs. Johns.”
“Thanks. See you after work?”
“I’m done at seven. Come down here when you’re finished. We can share a bus seat home.”
Glen smiles and walks towards Erin and Jason.
“Hi, my name is Glen and I’ve been asked to escort Mrs. Johns here to the X-ray Department.”
Jason frowns. “Can’t that be done portably?”
Glen shakes his head. “Not my call. Gurpreet asked me to escort her to the department.”
Jason leans down and explains to Erin that she needs a chest X-ray to help them figure out why she is short of breath.
Erin, looking a bit more tired, says, “I’ve had quite a few of those. I’d be glad to get out of this hallway. It’s so noisy.”
Glen grabs the back of the wheelchair, quickly turns her around and points the chair out the door. Striding to the elevator, Glen recaps for Erin the weather outside, the hockey game, and recent city events. Erin sits in her chair and pretends to listen.
Glen and Erin roll through the doors of the Radiology Department to see Gurpreet standing at the desk.
“Here is Mrs. Erin Johns, from Hallway B in the Emergency Department.”
“Thank you, Glen. Can you place her in Room 2, please? I’ll be right behind you.”
Time: 11h30
Place: Emergency, Hallway B
“When will I get my results?”
Glen looks at Erin. “I’m not the one to ask, I’ll let Sheila know you are back, so the doctor and Jason can look at your picture.”
“Thank you.”
Glen walks quickly away to the nursing station to inform Sheila that the chest X-ray is completed.
Erin looks up and down the hallway and sees less activity and some empty stretcher bays.
“I do hope I can get a bed to lie down in,” she thinks to herself. “My backside is getting sore.”
Without realizing it, Erin closes her eyes. Suddenly she feels a touch on her hand. Startled, she gives a little shout.
“Oh oh oh, it’s ok. My name is Matt. I had no intention of scaring you. Wow. Really sorry, Mrs. Johns.”
“It’s ok. I didn’t realize I had fallen asleep.”
“I’m a respiratory therapist and a couple of tests have been ordered for you. One is spirometry, which I think you have had before, from the results in your chart, and the second one is a blood gas.”
“Spirometry is the blowing test, right?”
“Yes, that’s the one. Shall we do that one first?”
“Ok.”
Matt opens a small plastic bag to retrieve a freshly sterilized kit tube with a gauge on it. He quickly describes what he wants Erin to do.
“Mrs. Johns, I’m going to ask you to take a deep breath and then blow it out as hard as you can through this tube. We’re going to do this three times to make sure we get an accurate measurement.”
Erin sits a bit straighter in her wheelchair and nods. “I’ll try my best.”
Matt hands Erin the device. “Good. Ok, take a deep breath, then blow through the tube.”
Erin does as instructed, three times. After each time, Jason records the results on the requisition for spirometry.
“Ok, that is now done. You did a great job, Mrs. Johns.”

“Next, I need to do an Arterial Blood Gas or ABG, so I must draw a small sample of blood from your wrist. This is a bit more uncomfortable than having your lab work done.”
Erin looks up questioningly. “Is it necessary? I had a blood gas done before and it really hurt!”
“I’ll try my best to not hurt you, but it is uncomfortable. Which hand do you use the most?”
“I am right-handed.”
Matt gently grabs Erin’s left hand and bends her elbow 90 degrees. He then performs the Allen test.
“Ok, ok, everything looks good, Mrs. Johns.”
Matt then rubs an alcohol swab vigorously across Mrs. Johns’ wrist. Then he waves his hand back and forth to disperse the smell.
“I need you to relax and stay still while I do this, ok?”
Erin nods nervously.
Matt, holding the syringe at a 45 degree angle, slips the needle under Erin’s skin. Quickly the syringe fills with red fluid. Matt then withdraws the syringe and holds a gauze over the site.
“That wasn’t too bad. You are very good at this.”
“I’ve had a bit of practice, Mrs. Johns.” While holding pressure on her left wrist, Matt deftly removes the needle from the sample and caps the syringe. After a couple of minutes, he asks Erin to hold pressure but not to peek and not to let go until he comes back.
Taking the sample, Matt goes to the back area of the Emergency Department and runs the sample through the blood gas machine. The machine quickly prints out the result.
Matt goes back to Erin.
“Ok, let’s look under the gauze.”
Matt see no bleeding but notes a small bruise at the puncture site. He places a small gauze over the site and wraps a small dressing right around Erin’s wrist.
“Please leave this dressing on. We can take it off later tonight, but I want to make sure you don’t get left with a big bruise.”
Erin nods.
Matt steps away to find Jason and show him the results from spirometry and the arterial blood gas.
| Day: 0 | pH | O 2 | CO 2 | HCO 3 |
| Time: 23h00 | 7.45 | 80 | 50 | 35 |
Matt finds Jason at the computer in the nursing station.
“Hi Jason, I have the results from spirometry and blood gases for Mrs. Johns.”
Jason, looks up, smiles and says, “Ok, anything special?”
“Spirometry shows a decrease in vital capacity from what was taken at the clinic a couple of months ago, with her FEV1 / FVC ratio < 0.7. That’s not surprising, given that she is back here. The ABG shows a rise in CO 2 and just normal PaO 2 on 2 LPM oxygen. She is a bit compromised right now. I took a listen to her chest a little while ago. She sounds typically COPD-like with nothing I didn’t expect.”
“Ok. Are the results on the clipboard?”
“Yes, and I hope you don’t mind that I entered the ABG in her chart as well.”
“You are awesome, I will go find Dr. Singh when I am done here and see what he would like to do, but my guess is she is staying the night.”


3.2: Homework 3
-
Create a truth table for each of the following circuits and identify the logical function of each (what’s it take for the pilot light to energize?).
- You’ve been given a partial ladder diagram. Finish the diagram so that an OR function is formed (the indicator lamp energizes if either button A OR B is actuated).
- Analyze this AC motor control circuit diagram, explaining the meaning of each symbol. Also, explain the operation of this motor control circuit. What happens when someone pushes the “Run” button? What happens when they let go of the “Run” button? When does the motor stop?
- The L-side of the contactor is often known as the _______ side, while the T-side of the contactor is often known as the _______ side.
- What do the auxiliary contacts of a contactor do?
- Describe, in your own words, the difference between pick-up, hold-in, and dropout voltage.
- According to the video, how much greater is inrush current than full load current?
- Use IEC numbering to label the following two schematics (you can re-draw these on separate paper, if necessary):
- List 5 possible causes of overload in an industrial setting.
- What are the two components of a motor starter?
- What’s the difference between a manual and automatic reset on an overload relay?
- Name three types of overloads discussed in the video.
- Draw the NEMA schematic symbol for an overload and show how overloads are represented in a ladder diagram.
- Draw a diagram (not one used in the video) of a 2-wire circuit.
- Draw a diagram (not one used in the video) of a 3-wire circuit.
This chapter is an adaptation of
Lessons in Electric Circuits
by Tony R. Kuphaldt (on
allaboutcircuits.com
), and is used under a
Design Science License
.
Media Attributions
- Relay Schematics


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acne vulgaris
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a skin condition in which skin pores and hair follicles become blocked, resulting in inflamed skin lesions
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atopic dermatitis (eczema)
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a long-term, systemic inflammatory response mediated by both genetic and environmental factors expressed as patchy, red, inflamed lesions
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contact dermatitis
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an acute inflammatory skin reaction to an aggravating factor resulting in local redness, itching, and fluid-filled vesicles
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cutaneous warts
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bumps on the skin surface that result from a viral infection
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dermis
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the innermost layer of the skin, composed of two sublayers, found between the epidermis and hypodermis
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epidermis
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the outermost layer of the skin, composed of five sublayers; rests above the dermis
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hypodermis
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the foundation of the skin that anchors the dermis to muscles
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impetigo
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a cutaneous bacterial infection that develops as a honey-colored crust on the skin surface
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Langerhans cells
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cells located within the epidermis that act against invading organisms
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papillae
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fingerlike projections that extend from the dermis into the epidermis and hold the two layers together
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plaque
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a raised, well-demarcated skin lesion arising from damage or deposits on the skin
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psoriasis
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a systemic condition of the skin resulting from increased skin cell mitosis
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rosacea
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a reddened facial rash characterized by broken blood vessels and small red bumps
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sebum
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an oily, lipid-based substance that lubricates the skin and hair
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superficial fascia
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the foundation of the skin that anchors the dermis to the muscles
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vesicant
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any IV drug capable of causing blistering and tissue damage if leakage around the IV site occurs