3.9: Exercises
Exercises
Exercise \(\PageIndex{1}\)
Let \(\mathscr{H}_A\) and \(\mathscr{H}_B\) denote single-particle Hilbert spaces with well-defined inner products. That is to say, for all vectors \(|\mu\rangle, |\mu'\rangle, |\mu''\rangle \in \mathscr{H}_A\) , that Hilbert space’s inner product satisfies the inner product axioms
-
\(\langle \mu|\mu' \rangle = \langle\mu'|\mu\rangle^*\)
-
\(\langle \mu|\mu \rangle \in \mathbb{R}^+_0\)
, and
\(\langle \mu|\mu \rangle = 0\)
if and only if
\(|\mu\rangle = 0\)
.
-
\(\langle\mu| \, \big(|\mu'\rangle + |\mu'' \rangle\big) = \langle \mu|\mu'\rangle + \langle \mu|\mu''\rangle\)
-
\(\langle \mu | \,\big(c|\mu'\rangle\big) = c\langle\mu|\mu'\rangle\)
for all
\(c\in\mathbb{C}\)
,
and likewise for vectors from \(\mathscr{H}_B\) with that Hilbert space’s inner product.
In Section 3.1, we defined a tensor product space \(\mathscr{H}_A\otimes\mathscr{H}_B\) as the space spanned by the basis vectors \(\{|\mu\rangle\otimes|\nu\rangle\}\) , where the \(|\mu\rangle\) ’s are basis vectors for \(\mathscr{H}_A\) and the \(|\nu\rangle\) ’s are basis vectors for \(\mathscr{H}_B\) . Prove that we can define an inner product using
\[\Big(\langle\mu| \otimes \langle\nu| \Big) \Big(|\mu'\rangle \otimes |\nu'\rangle\Big) \;\equiv\; \langle\mu|\mu'\rangle \, \langle\nu|\nu'\rangle = \delta_{\mu\mu'}\delta_{\nu\nu'}\]
which satisfies the inner product axioms.
Exercise \(\PageIndex{2}\)
Consider the density operator
\[\hat{\rho} = \frac{1}{2} |\!+\!z\rangle \langle+z| \,+\, \frac{1}{2} |\!+\!x\rangle \langle+x|\]
where \(|\!+\!x\rangle = \frac{1}{\sqrt{2}} \left(|\!+\!z\rangle + |\!-\!z\rangle\right)\) . This can be viewed as an equal-probability sum of two different pure states. However, the density matrix can also be written as
\[\hat{\rho} \,=\, p_1\, |\psi_1\rangle \langle \psi_1| \,+\, p_2\, |\psi_2\rangle \langle\psi_2|\]
where \(|\psi_{1}\rangle\) and \(|\psi_{2}\rangle\) are the eigenvectors of \(\hat{\rho}\) . Show that \(p_1\) and \(p_2\) are not 1/2.
Exercise \(\PageIndex{3}\)
Consider two distinguishable particles, \(A\) and \(B\) . The 2D Hilbert space of \(A\) is spanned by \(\{|m\rangle, |n\rangle\}\) , and the 3D Hilbert space of \(B\) is spanned by \(\{|p\rangle, |q\rangle, |r\rangle\}\) . The two-particle state is
\[|\psi\rangle = \frac{1}{3} \, |m\rangle|p\rangle + \frac{1}{\sqrt{6}} \, |m\rangle|q\rangle + \frac{1}{\sqrt{18}} \, |m\rangle|r\rangle + \frac{\sqrt{2}}{3} \, |n\rangle|p\rangle + \frac{1}{\sqrt{3}} \, |n\rangle|q\rangle + \frac{1}{3} \, |n\rangle|r\rangle.\]
Find the entanglement entropy.
Further Reading
[1] Bransden & Joachain, §14.1—14.4, §17.1–17.5
[2] Sakurai, §3.9
[3] A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , Physical Review 47 , 777 (1935).
[4] J. S. Bell, On the Einstein-Podolsky-Rosen paradox , Physics 1 , 195 (1964).
[5] N. D. Mermin, Bringing home the atomic world: Quantum mysteries for anybody , American Journal of Physics 49 , 940 (1981).
[6] A. Aspect, Bell’s inequality test: more ideal than ever , Nature (News and Views) 398 , 189 (1999).
[7] A. K. Ekert, Quantum Cryptography Based on Bell’s Theorem , Physical Review Letters 67 , 661 (1991).
[8] H. Everett, III, The Theory of the Universal Wave Function (PhD thesis), Princeton University (1956)
[9] A. Albrecht, Following a “collapsing” wave function , Physical Review D 48 , 3768 (1993).
[10] A. Edelman and N. R. Rao, Random matrix theory , Acta Numerica 14 , 233 (2005).


3.3: Formatting Document Content in Microsoft Word
By the end of this section, you will be able to:
- Format font types, sizes, and styles
- Modify paragraph styles in a document
- Use headings for reader and internal organization
- Adjust settings for how text and graphics flow together
You want your WorldCorp market trends report to look professional. To achieve this, you need to consider how the content should be formatted for its intended audience. Formatting applied to content includes line spacing, font type and size, alignment, and the use of organizational features like headers. Many employees in the organization, including those in upper management, will view the report, so you need the report to show your professionalism and skills in your role in the marketing department.
Formatting Font
There are many ways to change your text formatting in Microsoft Word. The most basic ways of adjusting your text are through the font, font size, and font style (bold, italic, or underlined).
The default Word font is currently Calibri. (Formerly, it was Times New Roman, and could change again.) Fonts are described as either serif or sans serif (Figure 3.14). A serif font is one that has short lines on the ends of the parts of each letter, whereas a sans serif (“without” serif) font doesn’t have those embellishments on the characters. Serif fonts are usually considered easier to read when there is a large amount of text being presented, and sans serif fonts are often considered to have a more contemporary look. For accessibility, simple fonts such as Arial are a better choice to accommodate all readers. Fonts that are curvy or more artistic in nature are difficult to read and decipher, particularly for people with vision-related impairment. However, curvy and artistic fonts may be used to attract attention and add flair to promotional materials, such as brochures.
You can select fonts using the drop-down menu within the Font options on the Home tab. There are many fonts in Word, most of which are not appropriate for business reports because they are too ornate or decorative. You should think carefully about the type of font you want to use and what it will convey to its readers. You want to stay professional and avoid “fun” fonts like Comic Sans and Papyrus. Font choice also affects the readability of your document. Script-like or blocky fonts can be difficult to read, especially with long documents. Additionally, some fonts are more appropriate for headings or logos instead of the body of a report or document.
Mac offers some fonts that are not included in the Microsoft OS version, and, by default, is missing some that can be added by downloading and loading the fonts into the application.
To adjust the font size, go to the Font Size drop-down menu, directly to the right of the Font menu on the Home tab. There are other ways to adjust the font in a selection in a document, but this is the most direct way to make the changes. The default font size is 12-point, but you may want to make your font larger or smaller. Most documents use fonts in sizes 10- to 12-point. For your market trends report, you will probably want an 11- or 12-point font for your main body text, and a larger size for your report title and section headings. You should ensure your font size is easily readable, especially if you plan to provide printed copies of your document.
You can apply additional styles to your font, such as bold, italic, or underline, using tools in the Font command group (Figure 3.15). There are also options for special text applications, such as adding superscripted text (text that is raised above the line) and subscripted text (text that appears below the line), and changing font color. Additionally, you can easily change the capitalization style through the Aa drop-down menu. This allows you to set a selection of text in all capitals, all lowercase, or to capitalize each word, such as is common in headers or titles.
Formatting Paragraphs
Paragraph formatting entails customizing the way the text appears on the page and how it flows from one paragraph to the next. Specifically, this includes line spacing, tab indentations, and alignment justification of text.
As you learned in Formatting Document Layout in Microsoft Word, line spacing determines how much space there is between the lines of text within a document. There are different advantages to single-spacing versus double-spacing . Most business documents, such as emails and printed letters, use single-spacing. This means that each line of text comes right after the other, with very little space between them. However, double-spacing may be used in working documents, and can be useful when there are multiple collaborators and you are using Track Changes. This allows for better visibility for the changes or edits, and makes it easier to see the revisions in progress. Double-spacing means that there is a complete line of space between lines. In addition to single-and double-spacing, users can use 1.5-spacing, or set custom spacing between lines within a paragraph (Figure 3.16).
You can also specify spacing between paragraphs, which is different from the line spacing within a paragraph. For example, you might want your paragraphs single-spaced, but want a visual break between paragraphs.
Paragraph separation is typically indicated in one of two ways: by indenting the first line of the paragraph with a tab indentation as Figure 3.17a shows, or by adding a space between paragraphs, as you can see in Figure 3.17b. In the latter case, the paragraph is usually not indented, as the space serves the same purpose as the indentation (i.e., to indicate a new paragraph). Most documents, including those used in business, have small 0.5” indentations at the start of each new paragraph as the default setting. If indentations are too small, they are difficult to distinguish, and large indentations can look awkward and confuse readers.
Paragraphs can also be formatted with different alignment , or justification , styles (Figure 3.18). In documents, the most common alignments for the body of the text are left-justified or fully justified . Left-justified means that the text all lines up in a straight line along the left margin, but where text ends on the right margin varies. Fully justified text lines up in a straight line along both the left and right margins. This produces a clean and professional look and is often used in publishing or print materials. However, full justification can also lead to awkward gaps within lines of text if the material contains a lot of long words or specialized content. Determining which alignment is appropriate for a document depends on the audience. For example, if you submit your WorldCorp market trends report for publication in an industry journal, it should be fully justified.
Other alignment options include centering text and right alignment. Centering is often used to give special treatment to a particular element of content. Right justification is often used in financial data, where, for example, numbers align best if they align on the right.
Headings
A heading helps readers understand the organization of a document by breaking it into meaningful chunks. Different heading levels can be used to create a hierarchy of content that also helps users best understand the material. In Word, headings can be set using styles that give them additional functionality, such as quickly displaying an outline of your document and providing the ability to link to or between sections. You can also generate a table of contents using headings.
As an example, let’s select three section titles from your market trends report. Let’s say that the major sections of your report are as follows:
- Introduction/Executive Summary
- Industry and Market Analysis
- Competition
- SWOT (strength, weaknesses, opportunities, threats)
- Recommendations/Key Findings
- Summary
Open a blank Word document and type in the first three headings from the list above. For each header, select the text, go to the Styles command group, and select Heading 1 (H1). H1 represents the top-level heading, which you might want to use for a title or a high-level section title. As you can see, the font size and the color changes automatically because you are selecting from the preset heading styles in Word. Repeat this formatting for your next two headings. If you open the Navigation pane, you will now see that your three H1 headings appear in outline format (Figure 3.19).
Heading hierarchies use the design of the heading to indicate levels of sections. The heading levels are usually referred to by numbers (such as Heading 1) and sometimes the shorthand H1, H2, H3 is used. Word’s default heading styles are designed to have a logical and intuitive hierarchy, which typically includes font size, and sometimes font style. In general, color should not be used to indicate levels in a hierarchy since this is neither logical (i.e., it is not clear why one color would be higher or lower than another) nor accessible (some colors are not readily conveyed to users who may be visually impaired or have other accessibility needs).
Adjusting Graphic and Text Layouts
If you are using graphics in your document, you will need to determine how the graphics and text should interact in the layout. When you insert a figure into a text document, the figure can be positioned in several ways in relation to the text using the text wrapping menu, as Figure 3.20 shows. Text wrapping refers to how the text is placed around an image or figure you place in the document. Text wrapping is accessed through the Layout tab in the Arrange command group. Your wrapping style may depend on the size of the graphic, as well as its purpose. If it is an important figure being discussed in the text and/or if it has a caption, you may want to clearly separate it from the text with the “Top and bottom” option, allowing the text to flow above and below the image, but not to either side of it. If the image functions more as a design element, such as a logo or photo to add interest, you might have the text wrap around it.
For example, let’s assume you want to add an image of one of WorldCorp’s products to the market trends report. As you may recall, WorldCorp sells products such as computer accessories, laptops, and TVs. When discussing trends in the laptop industry, you may want to include a picture of a laptop from a top-selling brand in the industry, such as HP. To insert the image into the report, place your cursor in the area of the report where you want the image. Then, copy and paste the image into the market trends report. Then, from the Layout tab, select the Wrap Text tool and select the appropriate text wrapping style to present a professional look for the inserted picture. The Wrap Text tool can also be accessed by right-clicking on the inserted image or figure, as shown in Figure 3.21.
Notice that you can change the wrapping style using the tool that appears in the upper-right corner of the image when you paste it in the document (Figure 3.22).


6.6: Metric tensor
A metric tensor is used to measure distances in a space. In crystallography the spaces considered are vector spaces with Euclidean metrics, i.e. ones for which the rules of Euclidean geometry apply. In that case, given a basis e i of a Euclidean space , E n , the metric tensor is a rank 2 tensor the components of which are:
g ij = e i . e j = e j . e i = g ji .
It is a symmetrical tensor. Using the metric tensor, the scalar product of two vectors, x = x i e i and y = y j e j is written:
x . y = x i e i . y j e j = g ij x i y j .
In a three-dimensional space with basis vectors a , b , c , the coefficients g ij of the metric tensor are:
g
11
=
a
2
;
g
12
=
a . b
;
g
13
=
a . c
;
g
21
=
b . a
;
g
22
=
b
2
;
g
23
=
b . c
;
g
31
=
c . a
;
g
32
=
c . b
;
g
33
=
c
2
;
Because the metric tensor is symmetric, g 12 = g 21 , g 13 = g 31 , and g 13 = g 31 . Thus there are only six unique elements, often presented as
g
11
g
22
g
33
g
23
g
13
g
12
or, multiplying the second row by 2, as a so-called G 6 ("G" for Gruber) vector
( a 2 , b 2 , c 2 , 2 b . c , 2 a . c , 2 a . b )
The inverse matrix of g ij , g ij , ( g ik g kj = δ k j , Kronecker symbol, = 0 if i ≠ j , = 1 if i = j ) relates the dual basis, or reciprocal space vectors e i to the direct basis vectors e i through the relations:
e j = g ij e j
In three-dimensional space, the dual basis vectors are identical to the reciprocal space vectors and the components of g ij are:
g
11
=
a*
2
;
g
12
=
a* . b*
;
g
13
=
a* . c*
;
g
21
=
b* . a*
;
g
22
=
b*
2
;
g
23
=
b* . c*
;
g
31
=
c* . a*
;
g
32
=
c* . b*
;
g
33
=
c*
2
;
with:
g 11 = b 2 c 2 sin 2 α/ V 2 ; g 22 = c 2 a 2 sin 2 β/ V 2 ; g 33 = a 2 b 2 sin 2 γ/ V 2 ;
g 12 = g 21 = ( abc 2 / V 2 )(cos α cos β - cos γ); g 23 = g 32 = ( a 2 bc / V 2 )(cos β cos γ - cos α); g 31 = g 13 = ( ab 2 c / V 2 )(cos γ cos α - cos β)
where V is the volume of the unit cell ( a , b , c ).
Change of basis
In a change of basis the direct basis vectors and coordinates transform like:
e' j = A j i e i ; x' j = B i j x i ,
where A j i and B i j are transformation matrices, transpose of one another. According to their definition, the components g ij , of the metric tensor transform like products of basis vectors:
g' kl = A k i A l j g ij .
They are the doubly covariant components of the metric tensor.
The dual basis vectors and coordinates transform in the change of basis according to:
e' j = B i j e i ; x' j = A j i x i ,
and the components g ij transform like products of dual basis vectors:
g' kl = A i k A j l g ij .
They are the doubly contravariant components of the metric tensor.
The mixed components, g i j = δ i j , are once covariant and once contravariant and are invariant.
Properties of the metric tensor
- The tensor nature of the metric tensor is demonstrated by the behaviour of its components in a change of basis. The components g ij and g ij are the components of a unique tensor.
- The squares of the volumes V and V* of the direct space and reciprocal space unit cells are respectively equal to the determinants of the g ij 's and the g ij 's:
V 2 = Δ ( g ij ) = abc (1 - cos 2 α - cos 2 β - cos 2 γ + 2 cos α cos α cos α)
V* 2 = Δ ( g ij ) = 1/ V 2 .
- One changes the variance of a tensor by taking the contracted tensor product of the tensor by the suitable form of the metric tensor. For instance:
g im t ij.. kl.. = t j.. klm..
Multiplying by the doubly covariant form of the metric tensor increases the covariance by one, multiplying by the doubly contravariant form increases the contravariance by one.
See also
- Section 1.1.3 of International Tables of Crystallography, Volume B
- Section 1.1.2 of International Tables of Crystallography, Volume D


10.2A: Neuroglia of the Central Nervous System
Glia, named from the Greek word for “glue,” support and scaffold neurons while performing other unique functions.
- Identify the types of neuroglia in central nervous system
Key Points
- Neuroglia in the CNS include astrocytes, microglial cells, ependymal cells and oligodendrocytes.
- Neuroglia in the PNS include Schwann cells and satellite cells.Astrocytes support and brace the neurons and anchor them to their nutrient supply lines. They also play an important role in making exchanges between capillaries and neurons.
- Microglial cells can transform into a special type of macrophage that can clear up the neuronal debris, while monitoring the health of the neuron.
- Ependymal cells are another glial subtype that line the ventricles of the CNS to help circulate the CSF.
- Oligodendrocytes are cells that wrap their process tightly around the fibers producing an insulating covering called myelin sheath.
- Schwann cells are similar in function to oligodendrocytes and microglial cells.
- Satellite cells perform a similar function to astrocytes,
Key Terms
- myelin : A white, fatty material, composed of lipids and lipoproteins, that surrounds the axons of nerves.
- glia : Non-neuronal cells that maintain homeostasis, form myelin, and provide support and protection for neurons in the brain, and for neurons in other parts of the nervous system such as in the autonomic nervous system.
- astrocyte : a neuroglial cell, in the shape of a star, in the brain
Neurogila or glial cells, are non-neuronal cells that maintain homeostasis, form myelin, and provide support and protection for neurons in the central (CNS) and peripheral nervous systems (PNS). It was long believed that neuroglia did not play any role in neuro-transmission, however recent advances have demonstrated that neuroglia play a key role in synapse formation and maintenance.
Neuroglia of the CNS
Neuroglia in the CNS include astrocytes, microglial cells, ependymal cells, and oligodendrocytes. In the human brain, it is estimated that the total number of glia roughly equals the number of neurons, although the proportions vary in different brain areas.
- Astrocytes are delicate, star-shaped branching glial cells. Their numerous radiating processes cling to neurons and their synaptic endings. These astrocytes cover nearly all the capillaries in the CNS. They support and brace the neurons and anchor them to their nutrient supply lines. They also play an important role in making exchanges between capillaries and neurons. Astrocytes also regulate the external chemical environment of neurons by removing excess ions and recycling neurotransmitters released during synaptic transmission.
- Microglial cells are small and have thorny processes that can touch the neighboring neurons. Microglial cells can transform into a special type of macrophage that can clear up the neuronal debris. They are also able to monitor the health of neurons by detecting injuries to the neuron.
- Ependymal cells are another glial subtype that line the ventricles of the CNS, forming a permeable barrier between the cerebrospinal fluid (CSF) and underlying cells, and also aid in the circulation of CSF through cilial beat.
- Oligodendrocytes are cells that have fewer processes compared to astrocytes. They line up along the nerve fibers in the CNS and wrap their process tightly around the fibers producing the insulating myelin sheath.
Oligodendrocyte : Oligodendrocytes form the electrical insulation around the axons of CNS nerve cells.
Neuroglia of the PNS
Neuroglia in the PNS include Schwann cells and satellite cells.
- Schwann cells are similar in function to oligodendrocytes and microglial cells, providing myelination to axons in the PNS. They also have phagocytotic activity and clear cellular debris that allows for regrowth of PNS neurons.
- Satellite cells are similar in function to astrocytes small cells that surround neurons in sensory, sympathetic, and parasympathetic ganglia, helping to regulate the external chemical environment. They are highly sensitive to injury and inflammation, and appear to contribute to pathological states, such as chronic pain.
Neuroglia : Types of neuroglia found in the CNS and PNS.


8.8: Exercises
Explain how σ and π bonds are similar and how they are different.
Draw a curve that describes the energy of a system with H and Cl atoms at varying distances. Then, find the minimum energy of this curve two ways.
- Use the bond energy found in Table 8.1 to calculate the energy for one single HCl bond (Hint: How many bonds are in a mole?)
- Use the enthalpy of reaction and the bond energies for H 2 and Cl 2 to solve for the energy of one mole of HCl bonds.
Explain why bonds occur at specific average bond distances instead of the atoms approaching each other infinitely close.
Use valence bond theory to explain the bonding in F 2 , HF, and ClBr. Sketch the overlap of the atomic orbitals involved in the bonds.
Use valence bond theory to explain the bonding in O 2 . Sketch the overlap of the atomic orbitals involved in the bonds in O 2 .
How many σ and π bonds are present in the molecule HCN?
A friend tells you N 2 has three π bonds due to overlap of the three p -orbitals on each N atom. Do you agree?
Draw the Lewis structures for CO 2 and CO, and predict the number of σ and π bonds for each molecule.
- CO 2
- CO
Why is the concept of hybridization required in valence bond theory?
Give the shape that describes each hybrid orbital set:
- sp 2
- sp 3 d
- sp
- sp 3 d 2
Explain why a carbon atom cannot form five bonds using sp 3 d hybrid orbitals.
What is the hybridization of the central atom in each of the following?
- BeH 2
- SF 6
- PCl 5
A molecule with the formula AB 3 could have one of four different shapes. Give the shape and the hybridization of the central A atom for each.
Methionine, CH 3 SCH 2 CH 2 CH(NH 2 )CO 2 H, is an amino acid found in proteins. The Lewis structure of this compound is shown below. What is the hybridization type of each carbon, oxygen, the nitrogen, and the sulfur?
Sulfuric acid is manufactured by a series of reactions represented by the following equations:
Draw a Lewis structure, predict the molecular geometry by VSEPR, and determine the hybridization of sulfur for the following:
- circular S 8 molecule
- SO 2 molecule
- SO 3 molecule
- H 2 SO 4 molecule (the hydrogen atoms are bonded to oxygen atoms)
Two important industrial chemicals, ethene, C 2 H 4 , and propene, C 3 H 6 , are produced by the steam (or thermal) cracking process:
For each of the four carbon compounds, do the following:
- Draw a Lewis structure.
- Predict the geometry about the carbon atom.
- Determine the hybridization of each type of carbon atom.
Analysis of a compound indicates that it contains 77.55% Xe and 22.45% F by mass.
- What is the empirical formula for this compound? (Assume this is also the molecular formula in responding to the remaining parts of this exercise) .
- Write a Lewis structure for the compound.
- Predict the shape of the molecules of the compound.
- What hybridization is consistent with the shape you predicted?
Consider nitrous acid, HNO 2 (HONO).
- Write a Lewis structure.
- What are the electron pair and molecular geometries of the internal oxygen and nitrogen atoms in the HNO 2 molecule?
- What is the hybridization on the internal oxygen and nitrogen atoms in HNO 2 ?
Strike-anywhere matches contain a layer of KClO 3 and a layer of P 4 S 3 . The heat produced by the friction of striking the match causes these two compounds to react vigorously, which sets fire to the wooden stem of the match. KClO 3 contains the ion. P 4 S 3 is an unusual molecule with the skeletal structure.
- Write Lewis structures for P 4 S 3 and the ion.
- Describe the geometry about the P atoms, the S atom, and the Cl atom in these species.
- Assign a hybridization to the P atoms, the S atom, and the Cl atom in these species.
- Determine the oxidation states and formal charge of the atoms in P 4 S 3 and the ion.
Identify the hybridization of each carbon atom in the following molecule. (The arrangement of atoms is given; you need to determine how many bonds connect each pair of atoms.)
Write Lewis structures for NF 3 and PF 5 . On the basis of hybrid orbitals, explain the fact that NF 3 , PF 3 , and PF 5 are stable molecules, but NF 5 does not exist.
In addition to NF 3 , two other fluoro derivatives of nitrogen are known: N 2 F 4 and N 2 F 2 . What shapes do you predict for these two molecules? What is the hybridization for the nitrogen in each molecule?
The bond energy of a C–C single bond averages 347 kJ mol −1 ; that of a triple bond averages 839 kJ mol −1 . Explain why the triple bond is not three times as strong as a single bond.
For the carbonate ion, draw all of the resonance structures. Identify which orbitals overlap to create each bond.
A useful solvent that will dissolve salts as well as organic compounds is the compound acetonitrile, H 3 CCN. It is present in paint strippers.
- Write the Lewis structure for acetonitrile, and indicate the direction of the dipole moment in the molecule.
- Identify the hybrid orbitals used by the carbon atoms in the molecule to form σ bonds.
- Describe the atomic orbitals that form the π bonds in the molecule. Note that it is not necessary to hybridize the nitrogen atom.
For the molecule allene, give the hybridization of each carbon atom. Will the hydrogen atoms be in the same plane or perpendicular planes?
Identify the hybridization of the central atom in each of the following molecules and ions that contain multiple bonds:
-
(f) XeO
2
F
2
(Xe is the central atom)
(g) (Cl is the central atom)
Describe the molecular geometry and hybridization of the N, P, or S atoms in each of the following compounds.
- H 3 PO 4 , phosphoric acid, used in cola soft drinks
- NH 4 NO 3 , ammonium nitrate, a fertilizer and explosive
- S 2 Cl 2 , disulfur dichloride, used in vulcanizing rubber
- K 4 [O 3 POPO 3 ], potassium pyrophosphate, an ingredient in some toothpastes
For each of the following molecules, indicate the hybridization requested and whether or not the electrons will be delocalized:
- ozone (O 3 ) central O hybridization
- carbon dioxide (CO 2 ) central C hybridization
- nitrogen dioxide (NO 2 ) central N hybridization
- phosphate ion central P hybridization
For each of the following structures, determine the hybridization requested and whether the electrons will be delocalized:
(a) Hybridization of each carbon
(b) Hybridization of sulfur
(c) All atoms
Draw the orbital diagram for carbon in CO 2 showing how many carbon atom electrons are in each orbital.
Sketch the distribution of electron density in the bonding and antibonding molecular orbitals formed from two s orbitals and from two p orbitals.
How are the following similar, and how do they differ?
- σ molecular orbitals and π molecular orbitals
- ψ for an atomic orbital and ψ for a molecular orbital
- bonding orbitals and antibonding orbitals
If molecular orbitals are created by combining five atomic orbitals from atom A and five atomic orbitals from atom B combine, how many molecular orbitals will result?
Can a molecule with an odd number of electrons ever be diamagnetic? Explain why or why not.
Can a molecule with an even number of electrons ever be paramagnetic? Explain why or why not.
Why are bonding molecular orbitals lower in energy than the parent atomic orbitals?
Calculate the bond order for an ion with this configuration:
Explain why an electron in the bonding molecular orbital in the H 2 molecule has a lower energy than an electron in the 1 s atomic orbital of either of the separated hydrogen atoms.
Predict the valence electron molecular orbital configurations for the following, and state whether they will be stable or unstable ions.
Determine the bond order of each member of the following groups, and determine which member of each group is predicted by the molecular orbital model to have the strongest bond.
- H 2 ,
- O 2 ,
- Li 2 , Be 2
- F 2 ,
- N 2 ,
For the first ionization energy for an N 2 molecule, what molecular orbital is the electron removed from?
Compare the atomic and molecular orbital diagrams to identify the member of each of the following pairs that has the highest first ionization energy (the most tightly bound electron) in the gas phase:
- H and H 2
- N and N 2
- O and O 2
- C and C 2
- B and B 2
Which of the period 2 homonuclear diatomic molecules are predicted to be paramagnetic?
A friend tells you that the 2 s orbital for fluorine starts off at a much lower energy than the 2 s orbital for lithium, so the resulting σ 2 s molecular orbital in F 2 is more stable than in Li 2 . Do you agree?
True or false: Boron contains 2 s 2 2 p 1 valence electrons, so only one p orbital is needed to form molecular orbitals.
What charge would be needed on F 2 to generate an ion with a bond order of 2?
Predict whether the MO diagram for S 2 would show s-p mixing or not.
Explain why is diamagnetic, while which has the same number of valence electrons, is paramagnetic.
Using the MO diagrams, predict the bond order for the stronger bond in each pair:
- B 2 or
- F 2 or
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1.3: Observations can be Spontaneous or Planned
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- Gina Peterson and Emily Elam
- College of the Canyons
Spontaneous observations occur all the time. Whether teachers are actively engaged with their children during an activity or in the background cleaning up after an activity, teachers have numerous opportunities to see and hear some wonderful developments as they randomly occur. According to Piaget, children require long uninterrupted periods of play and exploration so that they can discover things for themselves. If we truly believe that children are capable of socializing, problem solving, and creating complex systems with rules, then we can successfully use spontaneous observations to capture a child’s development as it unfolds naturally.
As intentional teachers, we can also appreciate when teachable moments arise unexpectedly. These golden moments are noteworthy as well. For example, as we witness a child attempting to master a milestone, we may provide some verbal support or guidance to scaffold the child’s learning. For example, when Abraham is becoming frustrated with not being able to get a piece of his puzzle to fit, a teacher might ask, “What happens when you turn the piece around?” During spontaneous situations, we must remember to simultaneously make mental notes so that we can later write down and reflect on a more formal plan of action that can be later used to help the child achieve their developmental goals.
Let’s review the advantages and disadvantages associated with spontaneous observations .
- Advantages: Being in the moment allows you to enjoy your children, and children appreciate your presence. When you are present, you can celebrate a child’s success or provide positive reinforcements to help them master major milestones. While being spontaneous, you can focus on the child’s interests and pose thoughtful questions to extend and enrich their learning experience. When a teacher keeps a low profile, a child is less likely to be self-conscious or nervous.
- Disadvantages : The longer you wait to document your spontaneous observation evidence, the harder it will be to remain objective and recall the vital details which is important when tracking behaviors or assessing development. Also, the more time that passes, the more difficult it will be to access accurate data. For example, by not documenting the children’s dialogue or capturing their key quotes in a timely manner, you may find it difficult to remember their actual word choices and use of vocabulary which is essential for assessing a child’s expressive language development.
Let’s now discuss focused or planned observations . Becoming a skilled observer takes practice. At first you may be slightly overwhelmed with trying to incorporate an official observation time into your already busy schedule. You may struggle with finding that delicate balance between knowing when to interact with your children and realizing when to step back and observe. Once you do observe, you might be surprised by the amount of evidence you have collected on each child. What’s more, you will have to sift through all the evidence, and that can be both time consuming and exhausting. Since your time is limited and you cannot possibly observe everything, incorporating a planned observation will help you navigate through your busy day and you will be able to gather more specific evidence (Grouland & James, 2013).


2.6.4: The Geology of Mars
Learning Objectives
- Discuss the main missions that have explored Mars
- Explain what we have learned from examination of meteorites from Mars
- Describe the various features found on the surface of Mars
- Compare the volcanoes and canyons on Mars with those of Earth
- Describe the general conditions on the surface of Mars
Mars is more interesting to most people than Venus because it is more hospitable. Even from the distance of Earth, we can see surface features on Mars and follow the seasonal changes in its polar caps (Figure \(\PageIndex{1}\)). Although the surface today is dry and cold, evidence collected by spacecraft suggests that Mars once had blue skies and lakes of liquid water. Even today, it is the sort of place we can imagine astronauts visiting and perhaps even setting up permanent bases.
Figure \(\PageIndex{1}\) Mars Photographed by the Hubble Space Telescope. This is one of the best photos of Mars taken from our planet, obtained in June 2001 when Mars was only 68 million kilometers away. The resolution is about 20 kilometers—much better than can be obtained with ground-based telescopes but still insufficient to reveal the underlying geology of Mars. (credit: modification of work by NASA and the Hubble Heritage Team (STScI/AURA))Spacecraft Exploration of Mars
Mars has been intensively investigated by spacecraft. More than 50 spacecraft have been launched toward Mars, but only about half were fully successful. The first visitor was the US Mariner 4, which flew past Mars in 1965 and transmitted 22 photos to Earth. These pictures showed an apparently bleak planet with abundant impact craters. In those days, craters were unexpected; some people who were romantically inclined still hoped to see canals or something like them. In any case, newspaper headlines sadly announced that Mars was a “dead planet.”
In 1971, NASA’s Mariner 9 became the first spacecraft to orbit another planet, mapping the entire surface of Mars at a resolution of about 1 kilometer and discovering a great variety of geological features, including volcanoes, huge canyons, intricate layers on the polar caps, and channels that appeared to have been cut by running water. Geologically, Mars didn’t look so dead after all.
The twin Viking spacecraft of the 1970s were among the most ambitious and successful of all planetary missions. Two orbiters surveyed the planet and served to relay communications for two landers on the surface. After an exciting and sometimes frustrating search for a safe landing spot, the Viking 1 lander touched down on the surface of Chryse Planitia (the Plains of Gold) on July 20, 1976, exactly 7 years after Neil Armstrong’s historic first step on the Moon. Two months later, Viking 2 landed with equal success in another plain farther north, called Utopia. The landers photographed the surface with high resolution and carried out complex experiments searching for evidence of life, while the orbiters provided a global perspective on Mars geology.
Mars languished unvisited for two decades after Viking. Two more spacecraft were launched toward Mars, by NASA and the Russian Space Agency, but both failed before reaching the planet.
The situation changed in the 1990s as NASA began a new exploration program using spacecraft that were smaller and less expensive than Viking. The first of the new missions, appropriately called Pathfinder, landed the first wheeled, solar-powered rover on the martian surface on July 4, 1997 (Figure \(\PageIndex{2}\)). An orbiter called Mars Global Surveyor (MGS) arrived a few months later and began high-resolution photography of the entire surface over more than one martian year. The most dramatic discovery by this spacecraft, which is still operating, was evidence of gullies apparently cut by surface water, as we will discuss later. These missions were followed in 2003 by the NASA Mars Odyssey orbiter, and the ESA Mars Express orbiter, both carrying high-resolution cameras. A gamma-ray spectrometer on Odyssey discovered a large amount of subsurface hydrogen (probably in the form of frozen water). Subsequent orbiters included the NASA Mars Reconnaissance Orbiter to evaluate future landing sites, MAVEN to study the upper atmosphere, and India’s Mangalayaan , also focused on study of Mars’ thin layers of air. Several of these orbiters are also equipped to communicate with landers and rovers on the surface and serve as data relays to Earth.
Figure \(\PageIndex{2}\) Surface View from Mars Pathfinder. The scene from the Pathfinder lander shows a windswept plain, sculpted long ago when water flowed out of the martian highlands and into the depression where the spacecraft landed. The Sojourner rover, the first wheeled vehicle on Mars, is about the size of a microwave oven. Its flat top contains solar cells that provided electricity to run the vehicle. You can see the ramp from the lander and the path the rover took to the larger rock that the mission team nicknamed “Yogi.” (credit: NASA/JPL)In 2003, NASA began a series of highly successful Mars landers. Twin Mars Exploration Rovers (MER), named Spirit and Opportunity , have been successful far beyond their planned lifetimes. The design goal for the rovers was 600 meters of travel; in fact, they have traveled jointly more than 50 kilometers. After scouting around its rim, Opportunity drove down the steep walls into an impact crater called Victoria, then succeeded with some difficulty in climbing back out to resume its route (Figure \(\PageIndex{3}\)). Dust covering the rovers’ solar cells caused a drop in power, but when a seasonal dust storm blew away the dust, the rovers resumed full operation. In order to survive winter, the rovers were positioned on slopes to maximize solar heating and power generation. In 2006, Spirit lost power on one of its wheels, and subsequently became stuck in the sand, where it continued operation as a fixed ground station. Meanwhile, in 2008, Phoenix (a spacecraft “reborn” of spare parts from a previous Mars mission that had failed) landed near the edge of the north polar cap, at latitude 68°, and directly measured water ice in the soil.
Figure \(\PageIndex{3}\) Victoria Crater. (a) This crater in Meridiani Planum is 800 meters wide, making it slightly smaller than Meteor crater on Earth. Note the dune field in the interior. (b) This image shows the view from the Opportunity rover as it scouted the rim of Victoria crater looking for a safe route down into the interior.In 2011, NASA launched its largest (and most expensive) Mars mission since Viking. The 1-ton rover Curiosity , the size of a subcompact car, has plutonium-powered electrical generators, so that it is not dependent on sunlight for power. Curiosity made a pinpoint landing on the floor of Gale crater, a site selected for its complex geology and evidence that it had been submerged by water in the past. Previously, Mars landers had been sent to flat terrains with few hazards, as required by their lower targeting accuracy. The scientific goals of Curiosity include investigations of climate and geology, and assessment of the habitability of past and present Mars environments. In 2018, NASA’s InSight Lander touched down on Mars, carrying a suite of scientific instruments. These include a package (nicknamed “the mole”) that will dig into the surface of Mars 1 mm at a time, hoping to reach a depth of 5 meters with heat sensors. Neither of these missions carries a specific life detection instrument, however. So far, scientists have not been able to devise a simple instrument that could distinguish living from nonliving materials on Mars.
The Curiosity rover required a remarkably complex landing sequence and NASA made a video about it called “7 Minutes of Terror” that went viral on the Internet.
A dramatic video summary of the first two years of Curiosity ’s exploration of the martian surface can be viewed as well.
Martian Samples
Much of what we know of the Moon, including the circumstances of its origin, comes from studies of lunar samples, but spacecraft have not yet returned martian samples to Earth for laboratory analysis. It is with great interest, therefore, that scientists have discovered that samples of martian material are nevertheless already here on Earth, available for study. These are all members of a rare class of meteorites (Figure \(\PageIndex{4}\))—rocks that have fallen from space.
Figure \(\PageIndex{4}\) Martian Meteorite. This fragment of basalt, ejected from Mars in a crater-forming impact, eventually arrived on Earth’s surface.How would rocks have escaped from Mars? Many impacts have occurred on the red planet, as shown by its heavily cratered surface. Fragments blasted from large impacts can escape from Mars, whose surface gravity is only 38% of Earth’s. A long time later (typically a few million years), a very small fraction of these fragments collide with Earth and survive their passage through our atmosphere, just like other meteorites. (We’ll discuss meteorites in more detail in the chapter on Cosmic Samples and the Origin of the Solar System.) By the way, rocks from the Moon have also reached our planet as meteorites, although we were able to demonstrate their lunar origin only by comparison with samples returned by the Apollo missions
Most of the martian meteorites are volcanic basalts; most of them are also relatively young—about 1.3 billion years old. We know from details of their composition that they are not from Earth or the Moon. Besides, there was no volcanic activity on the Moon to form them as recently as 1.3 billon years ago. It would be very difficult for ejecta from impacts on Venus to escape through its thick atmosphere. By the process of elimination, the only reasonable origin seems to be Mars, where the Tharsis volcanoes were active at that time.
The martian origin of these meteorites was confirmed by the analysis of tiny gas bubbles trapped inside several of them. These bubbles match the atmospheric properties of Mars as first measured directly by Viking. It appears that some atmospheric gas was trapped in the rock by the shock of the impact that ejected it from Mars and started it on its way toward Earth.
One of the most exciting results from analysis of these martian samples has been the discovery of both water and organic (carbon-based) compounds in them, which suggests that Mars may once have had oceans and perhaps even life on its surface. As we have already hinted, there is other evidence for the presence of flowing water on Mars in the remote past, and even extending to the present.
In this and the following sections, we will summarize the picture of Mars as revealed by all these exploratory missions and by about 40 samples from Mars.
Global Properties of Mars
Mars has a diameter of 6790 kilometers, just over half the diameter of Earth, giving it a total surface area very nearly equal to the continental (land) area of our planet. Its overall density of 3.9 g/cm 3 suggests a composition consisting primarily of silicates but with a small metal core. The planet has no global magnetic field, although there are areas of strong surface magnetization that indicate that there was a global field billions of years ago. Apparently, the red planet has no liquid material in its core today that would conduct electricity.
Thanks to the Mars Global Surveyor , we have mapped the entire planet, as shown in Figure \(\PageIndex{5}\). A laser altimeter on board made millions of separate measurements of the surface topography to a precision of a few meters—good enough to show even the annual deposition and evaporation of the polar caps. Like Earth, the Moon, and Venus, the surface of Mars has continental or highland areas as well as widespread volcanic plains. The total range in elevation from the top of the highest mountain (Olympus Mons) to the bottom of the deepest basin (Hellas) is 31 kilometers.
Figure \(\PageIndex{5}\) Mars Map from Laser Ranging. These globes are highly precise topographic maps, reconstructed from millions of individual elevation measurements made with the Mars Global Surveyor. Color is used to indicate elevation. The hemisphere on the left includes the Tharsis bulge and Olympus Mons, the highest mountain on Mars; the hemisphere on the right includes the Hellas basin, which has the lowest elevation on Mars.Approximately half the planet consists of heavily cratered highland terrain, found primarily in the southern hemisphere. The other half, which is mostly in the north, contains younger, lightly cratered volcanic plains at an average elevation about 5 kilometers lower than the highlands. Remember that we saw a similar pattern on Earth, the Moon, and Venus. A geological division into older highlands and younger lowland plains seems to be characteristic of all the terrestrial planets except Mercury.
Lying across the north-south division of Mars is an uplifted continent the size of North America. This is the 10-kilometer-high Tharsis bulge, a volcanic region crowned by four great volcanoes that rise still higher into the martian sky.
Volcanoes on Mars
The lowland plains of Mars look very much like the lunar maria, and they have about the same density of impact craters. Like the lunar maria, they probably formed between 3 and 4 billion years ago. Apparently, Mars experienced extensive volcanic activity at about the same time the Moon did, producing similar basaltic lavas.
The largest volcanic mountains of Mars are found in the Tharsis area (you can see them in Figure \(\PageIndex{5}\)), although smaller volcanoes dot much of the surface. The most dramatic volcano on Mars is Olympus Mons (Mount Olympus), with a diameter larger than 500 kilometers and a summit that towers more than 20 kilometers above the surrounding plains—three times higher than the tallest mountain on Earth (Figure \(\PageIndex{6}\)). The volume of this immense volcano is nearly 100 times greater than that of Mauna Loa in Hawaii. Placed on Earth’s surface, Olympus would more than cover the entire state of Missouri.
Figure \(\PageIndex{6}\) Olympus Mons. The largest volcano on Mars, and probably the largest in the solar system, is Olympus Mons, illustrated in this computer-generated rendering based on data from the Mars Global Surveyor’s laser altimeter. Placed on Earth, the base of Olympus Mons would completely cover the state of Missouri; the caldera, the circular opening at the top, is 65 kilometers across, about the size of Los Angeles.Images taken from orbit allow scientists to search for impact craters on the slopes of these volcanoes in order to estimate their age. Many of the volcanoes show a fair number of such craters, suggesting that they ceased activity a billion years or more ago. However, Olympus Mons has very, very few impact craters. Its present surface cannot be more than about 100 million years old; it may even be much younger. Some of the fresh-looking lava flows might have been formed a hundred years ago, or a thousand, or a million, but geologically speaking, they are quite young. This leads geologists to the conclusion that Olympus Mons possibly remains intermittently active today—something future Mars land developers may want to keep in mind.
Martian Cracks and Canyons
The Tharsis bulge has many interesting geological features in addition to its huge volcanoes. In this part of the planet, the surface itself has bulged upward, forced by great pressures from below, resulting in extensive tectonic cracking of the crust. Among the most spectacular tectonic features on Mars are the canyons called the Valles Marineris (or Mariner Valleys, named after Mariner 9, which first revealed them to us), which are shown in Figure \(\PageIndex{7}\). They extend for about 5000 kilometers (nearly a quarter of the way around Mars) along the slopes of the Tharsis bulge. If it were on Earth, this canyon system would stretch all the way from Los Angeles to Washington, DC. The main canyon is about 7 kilometers deep and up to 100 kilometers wide, large enough for the Grand Canyon of the Colorado River to fit comfortably into one of its side canyons.
Figure \(\PageIndex{7}\) Heavily Eroded Canyonlands on Mars. This image shows the Valles Marineris canyon complex, which is 3000 kilometers wide and 8 kilometers deep.An excellent 4-minute video tour of Valles Marineris, narrated by planetary scientist Phil Christensen, is available for viewing.
The term “canyon” is somewhat misleading here because the Valles Marineris canyons have no outlets and were not cut by running water. They are basically tectonic cracks, produced by the same crustal tensions that caused the Tharsis uplift. However, water has played a later role in shaping the canyons, primarily by seeping from deep springs and undercutting the cliffs. This undercutting led to landslides that gradually widened the original cracks into the great valleys we see today (Figure \(\PageIndex{8}\)). Today, the primary form of erosion in the canyons is probably wind.
Figure \(\PageIndex{8}\) Martian Landslides. This Viking orbiter image shows Ophir Chasma, one of the connected valleys of the Valles Marineris canyon system. Look carefully and you can see enormous landslides whose debris is piled up underneath the cliff wall, which tower up to 10 kilometers above the canyon floor.While the Tharsis bulge and Valles Marineris are impressive, in general, we see fewer tectonic structures on Mars than on Venus. In part, this may reflect a lower general level of geological activity, as would be expected for a smaller planet. But it is also possible that evidence of widespread faulting has been buried by wind-deposited sediment over much of Mars. Like Earth, Mars may have hidden part of its geological history under a cloak of soil.
The View on the Martian Surface
The first spacecraft to land successfully on Mars were Vikings 1 and 2 and Mars Pathfinder. All sent back photos that showed a desolate but strangely beautiful landscape, including numerous angular rocks interspersed with dune like deposits of fine-grained, reddish soil (Figure \(\PageIndex{9}\)).
Figure \(\PageIndex{9}\) Three Martian Landing Sites. The Mars landers Viking 1 in Chryse, Pathfinder in Ares Valley, and Viking 2 in Utopia, all photographed their immediate surroundings. It is apparent from the similarity of these three photos that each spacecraft touched down on a flat, windswept plain littered with rocks ranging from tiny pebbles up to meter-size boulders. It is probable that most of Mars looks like this on the surface.All three of these landers were targeted to relatively flat, lowland terrain. Instruments on the landers found that the soil consisted of clays and iron oxides, as had long been expected from the red color of the planet. All the rocks measured appeared to be of volcanic origin and roughly the same composition. Later landers were targeted to touch down in areas that apparently were flooded sometime in the past, where sedimentary rock layers, formed in the presence of water, are common. (Although we should note that nearly all the planet is blanketed in at least a thin layer of wind-blown dust).
The Viking landers included weather stations that operated for several years, providing a perspective on martian weather. The temperatures they measured varied greatly with the seasons, due to the absence of moderating oceans and clouds. Typically, the summer maximum at Viking 1 was 240 K (–33 °C), dropping to 190 K (–83 °C) at the same location just before dawn. The lowest air temperatures, measured farther north by Viking 2, were about 173 K (–100 °C). During the winter, Viking 2 also photographed water frost deposits on the ground (Figure \(\PageIndex{10}\)). We make a point of saying “water frost” here because at some locations on Mars, it gets cold enough for carbon dioxide (dry ice) to freeze out of the atmosphere as well.
Figure \(\PageIndex{10}\) Water Frost in Utopia. This image of surface frost was photographed at the Viking 2 landing site during late winter.Most of the winds measured on Mars are only a few kilometers per hour. However, Mars is capable of great windstorms that can shroud the entire planet with windblown dust. Such high winds can strip the surface of some of its loose, fine dust, leaving the rock exposed. The later rovers found that each sunny afternoon the atmosphere became turbulent as heat rose off the surface. This turbulence generated dust devils, which play an important role in lifting the fine dust into the atmosphere. As the dust devils strip off the top layer of light dust and expose darker material underneath, they can produce fantastic patterns on the ground (Figure \(\PageIndex{11}\)).
Wind on Mars plays an important role in redistributing surface material. Figure \(\PageIndex{11}\) shows a beautiful area of dark sand dunes on top of lighter material. Much of the material stripped out of the martian canyons has been dumped in extensive dune fields like this, mostly at high latitudes.
Figure \(\PageIndex{11}\) Dust Devil Tracks and Sand Dunes. (a) This high-resolution photo from the Mars Global Surveyor shows the dark tracks of several dust devils that have stripped away a thin coating of light-colored dust. This view is of an area about 3 kilometers across. Dust devils are one of the most important ways that dust gets redistributed by the martian winds. They may also help keep the solar panels of our rovers free of dust. (b) These windblown sand dunes on Mars overlay a lighter sandy surface. Each dune in this high-resolution view is about 1 kilometer across.Key Concepts and Summary
Most of what we know about Mars is derived from spacecraft: highly successful orbiters, landers, and rovers. We have also been able to study a few martian rocks that reached Earth as meteorites. Mars has heavily cratered highlands in its southern hemisphere, but younger, lower volcanic plains over much of its northern half. The Tharsis bulge, as big as North America, includes several huge volcanoes; Olympus Mons is more than 20 kilometers high and 500 kilometers in diameter. The Valles Marineris canyons are tectonic features widened by erosion. Early landers revealed only barren, windswept plains, but later missions have visited places with more geological (and scenic) variety. Landing sites have been selected in part to search for evidence of past water.


3.1: Structure of low-level programs
Introduction
This section introduces the learner to the low-level programming languages. The learners should distinguish the low-level languages and their different uses in computer programming
Activity Details
In computer science, a low-level programming language is a programming language that provides little or no abstraction from a computer’s instruction set architecture—commands or functions in the language map closely to processor instructions. This refers to either machine code or assembly language. The word “low” refers to the small or nonexistent amount of abstraction between the language and machine language; because of this, low-level languages are sometimes described as being “close to the hardware.” Because of the close relationship between the language and the hardware architecture programs written in low-level languages tend to be relatively non-portable.
Low-level languages can convert to machine code without a compiler or interpreter— second- generation programming languages use a simpler processor called an assembler— and the resulting code runs directly on the processor. A program written in a low-level language can be made to run very quickly, with a small memory footprint. An equivalent program in a high- level language can be less efficient and use more memory. Low-level languages are simple, but considered difficult to use, due to numerous technical details that the programmer must remember. By comparison, a high-level programming language isolates execution semantics of computer architecture from the specification of the program, which simplifies development.
Machine codes
Machine code is the only language a computer can process directly without a previous transformation. Currently, programmers almost never write programs directly in machine code, because it requires attention to numerous details that a high-level language handles automatically, requires memorizing or looking up numerical codes for every instruction, and is extremely difficult to modify.
True machine code is a stream of raw, usually binary, data. A programmer coding in “machine code” normally codes instructions and data in a more readable form such as decimal, octal, or hexadecimal which is translated to internal format by a program called a loader or toggled into the computer’s memory from a front panel.
Assembly language
Second-generation languages provide one abstraction level on top of the machine code. In the early days of coding on computers like the TX-0 and PDP-1, the first thing MIT hackers did was write assemblers. Assembly language has little semantics or formal specification, being only a mapping of human-readable symbols, including symbolic addresses, to opcodes, addresses, numeric constants, strings and so on.
Typically, one machine instruction is represented as one line of assembly code. Assemblers produce object files that can link with other object files or be loaded on their own. Most assemblers provide macros to generate common sequences of instructions.
Limitations of low-level architectures
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Very hard to read or learn for the uninitiated.
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Not very self-documenting like higher level languages.
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Harder to modify and maintain.
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Less support, than high level languages, in development and debug environments.
Conclusion
The learner should distinguish the various levels of low-level programming used in programming. They can also state the limitations arising from comparing the two low-level of programming languages
Assessment
Distinguish between machine and assembly languages
Machine language is the actual bits used to control the processor in the computer, usually viewed as a sequence of hexadecimal numbers (typically bytes). The processor reads these bits in from program memory, and the bits represent “instructions” as to what to do next.
Thus machine language provides a way of entering instructions into a computer (whether through switches, punched tape, or a binary file).
While assembly language is a more human readable view of machine language. Instead of representing the machine language as numbers, the instructions and registers are given names (typically abbreviated words, or mnemonics, like ld means “load”). Unlike a high level language, assembler is very close to the machine language. The main abstractions (apart from the mnemonics) are the use of labels instead of fixed memory addresses, and comments.
An assembly language program (ie a text file) is translated to machine language by an assembler. A disassembler performs the reverse function (although the comments and the names of labels will have been discarded in the assembler process).
Machine language faster than assembly language even than assembly language depend upon machine language


11.6: The Simple Random Walk
The simple random walk process is a minor modification of the Bernoulli trials process. Nonetheless, the process has a number of very interesting properties, and so deserves a section of its own. In some respects, it's a discrete time analogue of the Brownian motion process.
The Basic Process
Suppose that \(\bs{U} = (U_1, U_2, \ldots)\) is a sequence of independent random variables, each taking values 1 and \(-1\) with probabilities \(p \in [0, 1]\) and \(1 - p\) respectively. Let \(\bs{X} = (X_0, X_1, X_2, \ldots)\) be the partial sum process associated with \(\bs{U}\), so that \[ X_n = \sum_{i=1}^n U_i, \quad n \in \N \] The sequence \(\bs{X}\) is the simple random walk with parameter \(p\).
We imagine a person or a particle on an axis, so that at each discrete time step, the walker moves either one unit to the right (with probability \(p\)) or one unit to the left (with probability \(1 - p\)), independently from step to step. The walker could accomplish this by tossing a coin with probability of heads \(p\) at each step, to determine whether to move right or move left. Other types of random walks, and additional properties of this random walk, are studied in the chapter on Markov Chains.
The mean and standard deviation, respectively of a step \(U\) are
- \(\E(U) = 2 p - 1\)
- \(\var(U) = 4 p (1 - p)\)
Let \(I_j = \frac{1}{2}\left(U_j + 1\right)\) for \(j \in \N_+\). Then \(\bs{I} = (I_1, I_2, \ldots)\) is a Bernoulli trials sequence with success parameter \(p\).
Proof
Note that \(I_j = 1\) if \(U_j = 1\) and \(I_j = 0\) if \(I_j = -1\).
In terms of the random walker, \(I_j\) is the indicator variable for the event that the \(j\)th step is to the right.
Let \(R_n = \sum_{i=1}^n I_j\) for \(n \in \N\), so that \( \bs{R} = (R_0, R_1, \ldots) \) is the partial sum process associated with \( \bs{I} \). Then
- \(X_n = 2 R_n - n\) for \(n \in \N\).
- \(R_n\) has the binomial distribution with trial parameter \(n\) and success parameter \(p\).
In terms of the walker, \(R_n\) is the number of steps to the right in the first \(n\) steps.
\(X_n\) has probability density function \[ \P(X_n = k) = \binom{n}{(n + k) / 2} p^{(n + k)/2} (1 - p)^{(n-k) / 2}, \quad k \in \{-n, -n + 2, \ldots, n - 2, n\}\]
Proof
Since \(R_n\) takes values in \(\{0, 1, \ldots, n\}\), \(X_n\) takes values in \(\{-n, -n + 2, \ldots, n-2, n\}\). For \(k\) in this set, \(\P(X_n = k)\ = \P\left[R_n = (n + k) / 2\right]\), so the result follows from the binomial distribution of \(R_n\).
The mean and variance of \(X_n\) are
- \(\E(X_n) = n (2 p - 1)\)
- \(\var(X_n) = 4 n p (1 - p)\)
The Simple Symmetric Random Walk
Suppose now that \(p =\frac{1}{2}\). In this case, \(\bs{X} = (X_0, X_1, \ldots)\) is called the simple symmetric random walk . The symmetric random walk can be analyzed using some special and clever combinatorial arguments. But first we give the basic results above for this special case.
For each \(n \in \N_+\), the random vector \(\bs{U}_n = (U_1, U_2, \ldots, U_n)\) is uniformly distributed on \(\{-1, 1\}^n\), and therefore \[ \P(\bs{U}_n \in A) = \frac{\#(A)}{2^n}, \quad A \subseteq S \]
\(X_n\) has probability density function \[ \P(X_n = k) = \binom{n}{(n + k) / 2} \frac{1}{2^n}, \quad k \in \{-n, -n + 2, \ldots, n - 2, n\} \]
The mean and variance of \(X_n\) are
- \(\E(X_n) = 0\)
- \(\var(X_n) = n\)
In the random walk simulation, select the final position. Vary the number of steps and note the shape and location of the probability density function and the mean\(\pm\)standard deviation bar. For selected values of the parameter, run the simulation 1000 times and compare the empirical density function and moments to the true probability density function and moments.
In the random walk simulation, select the final position and set the number of steps to 50. Run the simulation 1000 times and compute and compare the following:
- \(\P(-6 \le X_{50} \le 10)\)
- The relative frequency of the event \(\{-6 \le X_{50} \le 10\}\)
- The normal approximation to \(\P(-6 \le X_{50} \le 10)\)
Answer
- 0.7794
- 0.7752
The Maximum Position
Consider again the simple, symmetric random walk. Let \(Y_n = \max\{X_0, X_1, \ldots, X_n\}\), the maximum position during the first \(n\) steps. Note that \(Y_n\) takes values in the set \(\{0, 1, \ldots, n\}\). The distribution of \(Y_n\) can be derived from a simple and wonderful idea known as the reflection principle .
For \(n \in \N\) and \(y \in \{0, 1, \ldots, n\}\), \[ \P(Y_n = y) = \begin{cases} \P(X_n = y) = \binom{n}{(y + n) / 2} \frac{1}{2^n}; & y, \, n \text{ have the same parity (both even or both odd)} \\ \P(X_n = y + 1) = \binom{n}{(y + n + 1) / 2} \frac{1}{2^n}; & y, \, n \text{ have opposite parity (one even and one odd)} \end{cases} \]
Proof
Note first that \(Y_n \ge y\) if and only if \(X_i = y\) for some \(i \in \{0, 1, \ldots, n\}\). Suppose that \(k \le y \le n\). For each path that satisfies \(Y_n \ge y\) and \(X_n = k\) there is another path that satisfies \(X_n = 2 y - k\). The second path is obtained from the first path by reflecting in the line \(x = y\), after the first path hits \(y\). Since the paths are equally likely, \[ \P(Y_n \ge y, X_n = k) = \P(X_n = 2 y - k), \quad k \le y \le n \] Hence it follows that \[ \P(Y_n = y, X_n = k) = \P(X_n = 2 y - k) - \P[X_n = 2 (y + 1) - k], \quad k \le y \le n \]
In the random walk simulation, select the maximum value variable. Vary the number of steps and note the shape and location of the probability density function and the mean/standard deviation bar. Now set the number of steps to 30 and run the simulation 1000 times. Compare the relative frequency function and empirical moments to the true probability density function and moments.
For every \(n\), the probability density function of \(Y_n\) is decreasing.
The last result is a bit surprising; in particular, the single most likely value for the maximum (and hence the mode of the distribution) is 0.
Explicitly compute the probability density function, mean, and standard deviation of \(Y_5\).
Answer
- Probability density function of \(Y_5\): \(f(0) = f(1) = \frac{10}{32}\), \(f(2) = f(3) = \frac{5}{32}\), \(f(4) = f(5) = \frac{1}{32}\)
- \(\E(Y_5) = \frac{11}{8}\)
- \(\var(Y_5) = \frac{111}{64}\)
A fair coin is tossed 10 times. Find the probability that the difference between the number of heads and the number of tails is never greater than 4.
Answer
\(\P(Y_{10} \le 4) = \frac{57}{64}\)
The Last Visit to 0
Consider again the simple, symmetric random walk. Our next topic is the last visit to 0 during the first \(2 n\) steps: \[ Z_{2 n} = \max \left\{ j \in \{0, 2, \ldots, 2 n\}: X_j = 0 \right\}, \quad n \in \N \] Note that since visits to 0 can only occur at even times, \(Z_{2 n}\) takes the values in the set \(\{0, 2, \ldots, 2 n\}\). This random variable has a strange and interesting distribution known as the discrete arcsine distribution . Along the way to our derivation, we will discover some other interesting results as well.
The probability density function of \(Z_{2 n}\) is \[ \P(Z_{2 n} = 2 k) = \binom{2 k}{k} \binom{2 n - 2 k}{n - k} \frac{1}{2^{2 n}}, \quad k \in \{0, 1, \ldots, n\} \]
Proof
Note that \[ \P(Z_{2 n} = 2 k) = \P(X_{2 k} = 0, X_{2 k+1} \ne 0, \ldots, X_{2 n} \ne 0), \quad k \in \{0, 1, \ldots, n\} \] From independence and symmetry it follows that \[ \P(Z_{2 n} = 2 k) = \P(X_{2 k} = 0) \P(X_1 \ne 0, X_2 \ne 0, \ldots, X_{2 n - 2 k} \ne 0), \quad k \in \{0, 1, \ldots, n\} \] We know the first factor on the right from the distribution of \(X_{2 k}\). Thus, we need to compute the second factor, the probability that our random walk never returns to 0 during a time interval. Using results for the maximum position we have \[ \P(X_1 \le 0, X_2 \le 0, \ldots, X_{2 j} \le 0) = \P(Y_{2 j} = 0) \ \binom{2 j}{j} \frac{1}{2^{2 j}} \] From symmetry (which is just the reflection principle at \(y = 0\)), it follows that \[ \P(X_1 \ge 0, X_2 \ge 0, \ldots, X_{2 n} \ge 0) = \binom{2 n}{n} \frac{1}{2^{2 n}} \] Next, \(\{X_1 \gt 0, X_2 \gt 0, \ldots, X_{2 j} \gt 0\} = \{X_1 = 1, X_2 \ge 1, \ldots, X_{2 j} \ge 1\}\). From independence and symmetry, \[ \P(X_1 \gt 0, X_2 \gt 0, \ldots, X_{2 j} \gt 0\} = \P(X_1 = 0) \P(X_1 \ge 0, X_2 \ge 0, \ldots, X_{2 j - 1} \ge 0) \] But \(X_{2 j - 1} \ge 0\) implies \(X_{2 j} \ge 0\). Hence \[ \P(X_1 \gt 0, X_2 \gt 0, \ldots, X_{2 j} \gt 0) = \binom{2 j}{j} \frac{1}{2^{2 j + 1}} \] From symmetry, \[ \P(X_1 \ne 0, X_2 \ne 0, \ldots, X_{2 j} \ne 0) = \binom{2 j}{j} \frac{1}{2^{2 j}} \]
In the random walk simulation, choose the last visit to 0 and then vary the number of steps with the scroll bar. Note the shape and location of the probability density function and the mean/standard deviation bar. For various values of the parameter, run the simulation 1000 times and compare the empirical density function and moments to the true probability density function and moments.
The probability density function of \(Z_{2 n}\) is symmetric about \(n\) and is \(u\)-shaped:
- \(\P(Z_{2 n} = 2 k) = \P(Z_{2 n} = 2 n - 2 k)\)
- \(\P(Z_{2 n} = 2 j) \gt \P(Z_{2 n} = 2 k)\) if and only if \(j \lt k\) and \(2 k \le n\)
In particular, 0 and \(2 n\) are the most likely values and hence are the modes of the distribution. The discrete arcsine distribution is quite surprising. Since we are tossing a fair coin to determine the steps of the walker, you might easily think that the random walk should be positive half of the time and negative half of the time, and that it should return to 0 frequently. But in fact, the arcsine law implies that with probability \(\frac{1}{2}\), there will be no return to 0 during the second half of the walk, from time \(n + 1\) to \(2 n\), regardless of \(n\), and it is not uncommon for the walk to stay positive (or negative) during the entire time from 1 to \(2 n\).
Explicitly compute the probability density function, mean, and variance of \(Z_{10}\).
Answer
- Probability density function of \(Z_{10}\): \(f(0) = f(10) = \frac{63}{256}\), \(f(2) = f(8) = \frac{35}{256}\), \(f(4) = f(6) = \frac{30}{256}\)
- \(\E(Z_{10}) = 5\)
- \(\var(Z_{10}) = 15\)
The Ballot Problem and the First Return to Zero
The Ballot Problem
Suppose that in an election, candidate \(A\) receives \(a\) votes and candidate \(B\) receives \(b\) votes where \(a \gt b\). Assuming a random ordering of the votes, what is the probability that \(A\) is always ahead of \(B\) in the vote count? This is an historically famous problem known as the Ballot Problem , that was solved by Joseph Louis Bertrand in 1887. The ballot problem is intimately related to simple random walks.
Comment on the validity of the assumption that the voters are randomly ordered for a real election.
The ballot problem can be solved by using a simple conditional probability argument to obtain a recurrence relation. Let \(f(a, b)\) denote the probability that \(A\) is always ahead of \(B\) in the vote count.
\(f\) satisfies the initial condition \(f(1, 0) = 1\) and the following recurrence relation: \[ f(a, b) = \frac{a}{a + b} f(a - 1,b) + \frac{b}{a + b} f(a, b - 1) \]
Proof
This follows by conditioning on the candidate that receives the last vote.
The probability that \(A\) is always ahead in the vote count is \[ f(a, b) = \frac{a - b}{a + b} \]
Proof
This follows from the recurrence relation and induction on the total number of votes \(n = a + b\)
In the ballot experiment, vary the parameters \(a\) and \(b\) and note the change the ballot probability. For selected values of the parameters, run the experiment 1000 times and compare the relative frequency to the true probability.
In an election for mayor of a small town, Mr. Smith received 4352 votes while Ms. Jones received 7543 votes. Compute the probability that Jones was always ahead of Smith in the vote count.
Answer
\(\frac{3191}{11895} \approx 0.2683\)
Relation to Random Walks
Consider again the simple random walk \(\bs{X}\) with parameter \(p\).
Given \(X_n = k\),
- There are \(\frac{n + k}{2}\) steps to the right and \(\frac{n - k}{2}\) steps to the left.
- All possible orderings of the steps to the right and the steps to the left are equally likely.
For \(k \gt 0\), \[ \P(X_1 \gt 0, X_2 \gt 0, \ldots, X_{n - 1} \gt 0 \mid X_n = k) = \frac{k}{n} \]
Proof
This follows from the previous result and the ballot probability .
In the ballot experiment, vary the parameters \(a\) and \(b\) and note the change the ballot probability. For selected values of the parameters, run the experiment 1000 times and compare the relative frequency to the true probability.
An American roulette wheel has 38 slots; 18 are red, 18 are black, and 2 are green. Fred bet $1 on red, at even stakes, 50 times, winning 22 times and losing 28 times. Find the probability that Fred's net fortune was always negative.
Answer
\(\frac{3}{25}\)
Roulette is studied in more detail in the chapter on Games of Chance.
The Distribution of the First Zero
Consider again the simple random walk with parameter \(p\), as in the last subsection. Let \(T\) denote the time of the first return to 0: \[ T = \min\{n \in \N_+: X_n = 0\} \] Note that returns to 0 can only occur at even times; it may also be possible that the random walk never returns to 0. Thus, \(T\) takes values in the set \(\{2, 4, \ldots\} \cup \{\infty\}\).
The probability density funtion of \(T_{2 n}\) is given by \[ \P(T = 2 n) = \binom{2 n}{n} \frac{1}{2 n - 1} p^n (1 - p)^n, \quad n \in \N_+ \]
Proof
For \(n \in \N_+\) \[ \P(T = 2 n) = \P(T = 2 n, X_{2 n} = 0) = \P(T = 2 n \mid X_{2 n} = 0 ) \P(X_{2 n} = 0) \] From the ballot problem, \[ \P(T = 2 n \mid X_{2 n} = 0) = \frac{1}{2 n - 1} \]
Fred and Wilma are tossing a fair coin; Fred gets a point for each head and Wilma gets a point for each tail. Find the probability that their scores are equal for the first time after \(n\) tosses, for each \(n \in \{2, 4, 6, 8, 10\}\).
Answer
\(f(2) = \frac{1}{2}\), \(f(4) = \frac{1}{8}\), \(f(6) = \frac{1}{16}\), \(f(8) = \frac{5}{128}\), \(f(10) = \frac{7}{512}\)


6.7: Preparing for an Interview
Resumés and cover letters interest the employer in hiring you. However, most employers compile a short list of candidates using the applications they receive, and then interview the people on this short list. This is especially true in the food service and hospitality industry where personal suitability and presentation is a key ingredient in customer service.
Remember that when you drop off a resumé or application, or call regarding a job opening, employees of the company are forming an impression of you. Always be polite and friendly. If you visit the company, dress appropriately and pay attention to your grooming. The person with whom you speak may pass along her or his impressions of you to the person doing the hiring.
It takes a lot of work to get the stage where you are offered an interview, so it is important to make the interview count. When employers are asked why applicants interviewed for jobs are rejected, interpersonal skills and personal characteristics are often key factors.
Applicants may be rejected because of:
- Poor personal appearance and hygiene
- An overbearing, conceited attitude
- Poor communication skills
- Lack of clear career goals
- Lack of interest, commitment, and enthusiasm for the job
- Lack of confidence and poise
- Overemphasis on what the employer offers them (salary, benefits, vacation)
- Lack of tact, maturity, and courtesy
- Poor attitude about the job, previous employers, or school
- Failure to look interviewer in the eye and limp handshake
- Inability to relate skills and experience to the job
- Lack of knowledge about the company
- Obvious personal problems
- Lack of tolerance, strong prejudices, and narrow interests
Types of Interviews
Often you will be interviewed in person. However, in larger companies or when applying for a job in another province, you may also be interviewed by telephone. Today, it is quite common to have an interview via Skype. This allows the interviewer to see you and make an opinion on your appearance. It is important to look professional in this situation as well. Some companies conduct screening interviews as a way of reducing the number of applicants who are considered for a job. Screening interviews may be conducted by someone other than the person who is responsible for the actual hiring. These initial interviews may be a preliminary step to an in-depth personal interview.
Being Prepared
Before going to an interview, you should make sure that you have prepared carefully. You should research the company so that you know what the company sells and how your skills might fit their needs. When applying for a position as a cook, you might visit the restaurant, study the menu, and perhaps even order and eat a meal. Take a good look around. What does the restaurant look like? What is the general ambiance and tone? Do the staff appear to get along well? Do staff members work as a team? Is this a place where you would like to work? Do you feel that you would fit in? Doing your homework about the potential employer makes you look interested in the job and committed to the new employer.
Before going to an interview, you should:
- Be able to describe how your experience and skills would benefit the company.
- Anticipate possible questions you might be asked and have answers prepared.
- Plan transportation to arrive a few minutes early.
- Choose appropriate, business-like clothing and accessories to wear. Take a look at how the staff are dressed when you visit, and dress accordingly. A suit or sports jacket, tie, and dress slacks are appropriate for men. A suit or skirt and blouse are acceptable for women. Women may also wear dress slacks.
- Make sure that clothing is clean, well-pressed, and in good condition. Shoes should be freshly shined and in good condition.
- Be immaculately groomed (for men, freshly shaved or carefully trimmed beard or moustache; for women, simply styled hair and subdued makeup).
- Wear only simple, subdued jewellery and perfume.
- Make sure that you have a clean copy of your application letter, job ad, resumé and references and/or reference letters, and copies of transcripts or certificates relevant to the position to take to the interview.
- Take a pen and paper.
- Prepare questions to ask the interviewer and write them neatly or print them on a piece of paper.
Anticipating Questions the Interviewer May Ask
Employers use interviews to gauge whether you have the qualities to perform the job well. They are looking for ability and aptitude, a willingness to work and learn, a desire to help accomplish the organization’s goals, and maturity and compatibility. For the most part, the interviewer will already have established that you have the minimum training and experience for the job by reading your resumé.
Interviews use a question-and-answer format. You should be prepared to answer questions such as those listed below. Even if these are not the exact questions which will be asked, you should rehearse the subject matter so you have a well-rounded complete answer to give when the question is asked.
Can you tell me something about yourself?
This is usually an invitation to talk about yourself on a personal but not intimate level. Stress such points as your family background, length of time in the community, work with community groups, hobbies, and interests. End by focusing on your work experience, work values, aptitudes, and qualities and how these are relevant to the job in question.
What are your future plans?
Describe your specific career plans and how this job fits into these plans.
Why do you want to work here?
You want to emphasize how this position will use your existing skills and develop additional skills. You might also mention the company’s reputation as a leader in the industry, a fair employer, or a good corporate citizen, its reputation for providing high-quality training to staff, and other relevant considerations.
Can you work under pressure and deadlines?
This question usually indicates that pressure is a feature of the job. Use examples from your work, school, and personal life to illustrate your ability to handle pressure and deadlines.
Why did you leave your last employer ? or Why do you want to leave your present employer?
Mention acceptable reasons for leaving a job such as lay-off, illness, relocation, or retraining, or wanting a new challenge. If you were fired, be honest about the reason and explain why you think you would be a good employee now (e.g., learned from mistakes, dealt with personal problems).
What are your strengths?
Your strengths should present you as an efficient and committed worker who can perform the job competently. Other strengths required in every job are honesty, dependability, enthusiasm, and cooperation. Mention them if appropriate.
What are your weaknesses or limitations?
This question may sometimes be phrased in more subtle ways, such as “What are some areas in which you can improve?” “How have you grown over the past few years?” or “Where do you see yourself needing to grow in the next few years?” It is not a good strategy to avoid mentioning shortcomings because you may come across as dishonest, defensive, or weak.
Mention one or two shortcomings in a way that is not damaging. You can do this by mentioning a weakness that is a mirror of one of your assets or by mentioning those that are easily remedied. For example, you might say, “I drive myself very hard and have to be careful not to assume that other staff have the energy that I have.” Or you might say, “I would like to take a course in menu planning. So far, I have some on-the-job experience and have done some reading on my own.” These type of responses indicate a willingness to be open, a knowledge of your shortcomings, and a willingness to address them. This will create a favourable impression on interviewers.
Why should I hire you?
Your answer should stress how your skills and experience benefit the company and help meet the company’s goals. If you are being hired to address a specific problem, explain how you have handled similar situations in the past.
Other things you might be asked about include:
- An explanation of any gaps in your resumé, poor grades, or a change in career direction
- How you might handle a specific problem on the job
- How you would describe your personality
- How you feel about overtime, working on holidays, or other job conditions
- How much you expect to be paid (be flexible; either indicate a range you would find acceptable, or invite the employer to make the decision based on your previous jobs, experience, and salary)
- What you value at work and in life, what you look for in a job, or what is your ideal job
- What you find difficult to do or who you find difficult to work with
When planning responses, be positive. Indicate how you have learned from experience, what benefits you have gained, and how this learning benefits the employer. Be honest and sincere. Some employers may ask about your leisure activities. Often these employers are looking for someone who is well rounded and contributes to the community.
Handling Discriminatory Questions in Interviews
The Human Rights Code prohibits discrimination in the recruitment of employees except in the case of bona fide (genuine) occupational requirements. Most employers avoid questions regarding these prohibited grounds in interviews because they know that otherwise they may be open to complaints of discrimination by unsuccessful candidates. Review the section earlier in the book on the B.C. Human Rights Code for more information.
Behaviour in the Interview
Interviews are short and interviewers have only a brief time to make a personal assessment. Small details can make a big impact. If you display confidence in yourself and in your ability to do the job, much of this confidence will be transmitted to the interviewer.
If you have not participated in an interview before, you can practise your responses with a friend or fellow student to build confidence and reduce nervousness. It can be very useful to videotape your mock interview. You will get useful feedback from watching yourself which can be used to improve your performance in interviews.
Be courteous and friendly in the interview, without being overly familiar. Interviewers respond to pleasantness and respect.
Some tips on coming across well in an interview include the following:
- Arrive alone and a little early for the interview.
- Remove sunglasses and coat before the interview.
- Get the interviewer’s correct name and use it during the interview.
- Smile and be ready to shake hands firmly.
- Look the interviewer in the eye. If there is more than one person conducting the interview, make sure you look at each of them when they are speaking with you, rather than only maintaining eye contact with the “lead” or more senior person.
- Remain standing until you are invited to sit.
- Do not bring your personal problems to the interview.
- Answer all questions clearly, specifically and honestly.
- Do not make jokes or wisecracks or get into arguments.
- Be poised and calm. Do not fidget, crack your knuckles, or engage in other nervous mannerisms.
- Ask a few pertinent questions about the job.
- Thank the interviewer for his or her time and shake hands.
Questions You Can Ask
Asking some questions yourself in the interview demonstrates that you have confidence in your abilities and that you are genuinely interested in the job and in the company. You can ask the following:
- Do you have any questions about my resumé?
- Can you tell me more about the responsibilities of this job?
- What possibilities are there for promotion and advancement if I do a good job?
- What are the future plans of the company (e.g., expansion, franchising)?
- When will you make your decision about this job?
- What training programs do you have for employees?
- What opportunities are there to transfer to other properties owned by the company (if your research indicates that the company is part of a chain)?
Following an interview, you should assess your performance so that you can improve your interviewing skills.
Activities
- Prepare a career plan for the next 10 years
- Prepare or update your resumé
- Create or update your profile on LinkedIn


7.5: Cardioversion and Defibrillation
As a nurse becomes familiar with the various types of heart rhythms, it is important to recognize that some rhythms will require immediate intervention and an attempt to restore normal electrical activity within the heart. Without prompt intervention for certain arrhythmias, the client is at risk for cardiac arrest. With any rhythm interpretation, the nurse is responsible for assessing rhythm, identifying the rhythm, and treating the rhythm in collaboration with the medical team.
The purpose of prompt rhythm identification and intervention is to reorganize the electrical conduction within the heart before significant damage can occur. In order to understand how the reorganization of electrical pathways occurs, it is important to recall the normal cardiac conduction pathways. The normal cardiac conduction pathway begins with an electrical impulse from the sinoatrial node (SA) located in the right atrium, to the atrial-ventricle node (AV) located between the atrium and ventricles, down the bundle of His branches located within the ventricular septum, to the Purkinje fibers that deliver the electrical impulses to the ventricular myocardium. As the impulses are transmitted through the ventricular myocardium, they activate the contractions of the right and left ventricles.
When a client is experiencing a serious dysrhythmia, the conduction of the electrical impuse has become altered and the SA node is no longer initiating the rhythm. Cardioversion and defibrillation are used to attempt to reset the heart’s normal electrical conduction pathway and put the SA node back in charge.
Cardioversion
Cardioversion involves the use of low-energy electrical shocks to resume the heart’s normal electrical rhythm. It is important to remember that cardioversion is only used for dysrhythmia in which the client has a pulse. The typical rhythms that require cardioversion are paroxysmal supraventricular tachycardia (PSVT), supraventricular or narrow complex tachycardia, rapid atrial fibrillation/flutter, torsades de pointes (with a pulse), and ventricular tachycardia (with a pulse). If the client is hemodynamically stable, a provider may first attempt to convert the rhythm with the use of medications. However, if the client is unstable, immediate cardioversion may be required.
When a client has a heart dysrhythmia but is hemodynamically stable, such as new onset atrial fibrillation or atrial flutter, cardioversion may be a scheduled procedure. In these cases, clients will typically have a transesophageal echocardiogram (TEE) prior to the cardioversion to assess for potential blood clots within the heart, particularly if the rhythm has persisted for greater than 48 hours or the time of rhythm onset is unknown. The TEE procedure involves the use of an ultrasound transducer inserted down into the client’s esophagus via endoscope to examine blood flow within the heart. If there is no sign of clot present, the provider can proceed to cardioversion. If a clot is present, the client may require anticoagulation or a different medical treatment to manage the arrhythmia.
As with any invasive medical procedure, the client must complete informed consent prior to proceeding. The nurse ensures that a signed consent in present in the client’s medical record and the provider has explained the procedure. The nurse provides patient education about the procedure, including reminding the client they will receive sedation during the procedure, which will limit their memory of the cardioversion.When preparing the client for cardioversion, electrode patches are placed on the chest in addition to the cardioversion pads. A cardiac monitor is used to monitor the heart rhythm then synchronizes the shock to the existing electrical activity within the client’s heart. When the monitor is “synced,” it identifies the client’s R waves and administers the electrical shock during the peak of the R wave. See Figure 7.33 [1] for an image of a defibrillator monitor displaying triangles above the R waves of the client’s cardiac rhythm, which indicate the monitor has been synced. This synchronization ensures the shock is delivered at the appropriate time in the electrical cycle and minimizes the risk of developing ventricular fibrillation or asystole.
The majority of cardiac monitors, including automated external defibrillators ( AEDs ), are biphasic. Biphasic monitors deliver current to the client in two directions. In the first phase, current moves from one paddle to the other. In the second phase, it reverses direction. [2] The electrical energy levels are determined by the provider and may be as low as 100 to 200 joules. To maintain a safe environment, everyone must remain clear of the client when delivering the electrical shock. No one should touch the client, and the hospital bed and oxygen equipment should be moved away from the client when the shock is delivered. Because the synced cardiac monitor will deliver the electrical shock at the optimal moment of the client’s existing cardiac electrical activity, there may be a few second delay from the time the shock is implemented to when it is actually delivered.
Defibrillation
Defibrillation is the immediate administration of an electrical current to help restore normal cardiac function. Defibrillation is administered when the client does not have a pulse. The typical rhythms for defibrillation are ventricular fibrillation, torsades de pointes (without a pulse), and ventricular tachycardia (without a pulse). [3] Automated external defibrillators (AEDs) search for these rhythms to determine if a client is experiencing a “shockable rhythm” that may be responsive to an electrical shock.
If a client has a dysrhythmia requiring defibrillation, the nurse must understand that blood is not circulating in the client. Therefore, in addition to the shock, the client requires cardiopulmonary resuscitation (CPR) to circulate blood throughout the body. Because these dysrhythmias are life-threatening and require emergency treatment, informed consent is not obtained. It is imperative for the client to receive the defibrillation shock as rapidly as possible, but high-quality compressions must be administered to maintain perfusion of vital organs until the defibrillator is connected to the client, the rhythm interpreted by the monitor, and shock is advised.
After the defibrillation monitor has arrived near the client, the pads must be placed on the client’s chest as quickly as possible to allow the monitor to analyze the rhythm. During the rhythm analysis process, is important that no one touches or moves the client. Once the monitor determines if a shock is advised, the staff should continue compressions until the monitor is charged and ready to administer shock at the required joules.
The goal of rapid defibrillation is to stop the disorganized rhythm promptly so the heart’s natural pacemaker can hopefully take over with an organized rhythm. Because disorganized rhythms use a tremendous amount of oxygen in already depleted heart tissue, continuing chest compressions for at least two minutes after defibrillation is required to reoxygenate the heart tissue and decrease the risk of the heart going back into ventricular tachycardia or ventricular defibrillation.
Defibrillation does not resolve asystole because an underlying electrical rhythm must be present. During asystole, the heart is in constant polarization and no electrical conduction is occurring.
- “LIFEPAK_20e_Defibrillator_and_Monitor_displaying_synchronization_with_QRS_complexes._(arrowheads).jpg” by StudentDoctorDG is licensed under CC BY-SA 4.0 ↵
- Li, W., Li, J., Wei, L., Wang, J., Peng, L., Wang, J., Yin, C., & Li, Y. (2021). A framework of current based defibrillation improves defibrillation efficacy of biphasic truncated exponential waveform in rabbits. Scientific Reports, 11 (1), 1586-1586. https://doi.org/10.1038/s41598-020-80521-9 ↵
- Choi, H. J., & Noh, H. (2021). Successful defibrillation using double sequence defibrillation: Case reports. Medicine, 100 (10), e24992-e24992. https://doi.org/10.1097/MD.0000000000024992 ↵