Chemistry and Chemical Reactivity

John C. Kotz, Paul M. Treichel, John R. Townsend, David A. Treichel

Chapter 6

The Structure of Atoms - all with Video Answers

Educators

Chapter Questions

Problem 1

Answer the following questions based on Figure 6.2:
(a) Which type of radiation involves less energy, x-rays or microwaves?
(b) Which radiation has the higher frequency, radar or red light?
(c) Which radiation has the longer wavelength, ultraviolet or infrared light?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 2

Consider the colors of the visible spectrum.
(a) Which colors of light involve less energy than green light?
(b) Which color of light has photons of greater energy, yellow or blue?
(c) Which color of light has the higher frequency, blue or green?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 3

Traffic signals are often now made of LEDs (lightemitting diodes). Amber and green ones are pictured here.
(a) The light from an amber signal has a wavelength of $595 \mathrm{nm},$ and that from a green signal has a wavelength of $500 \mathrm{nm}$. Which has the higher frequency?
(b) Calculate the frequency of amber light.
(FIGURE CANNOT COPY)

An H

Numerade Educator

Problem 4

Suppose you are standing $225 \mathrm{m}$ from a radio transmitter. What is your distance from the transmitter in terms of the number of wavelengths if
(a) the station is broadcasting at $1150 \mathrm{kHz}$ (on the AM radio band)? $\left(1 \mathrm{kHz}=1 \times 10^{3} \mathrm{Hz}\right)$
(b) the station is broadcasting at $98.1 \mathrm{MHz}$ (on the FM radio band)? $\left(1 \mathrm{MHz} \times 10^{6} \mathrm{Hz}\right)$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 5

Green light has a wavelength of $5.0 \times 10^{2} \mathrm{nm}$ What is the energy, in joules, of one photon of green light? What is the energy, in joules, of 1.0 mol of photons of green light?

An H

Numerade Educator

Problem 6

Violet light has a wavelength of about $410 \mathrm{nm} .$ What is its frequency? Calculate the energy of one photon of violet light. What is the energy of 1.0 mol of violet photons? Compare the energy of photons of violet light with those of red light. Which is more energetic?

Diana Cruz

Numerade Educator

Problem 7

The most prominent line in the emission spectrum of aluminum is at $396.15 \mathrm{nm}$. What is the frequency of this line? What is the energy of one photon with this wavelength? Of 1.00 mol of these photons?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 8

The most prominent line in the emission spectrum of magnesium is $285.2 \mathrm{nm} .$ Other lines are found at 383.8 and $518.4 \mathrm{nm}$. In what region of the electromagnetic spectrum are these lines found? Which is the most energetic line? What is the energy of $1.00 \mathrm{mol}$ of photons with the wavelength of the most energetic line?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 9

Place the following types of radiation in order of increasing energy per photon:
(a) yellow light from a sodium lamp
(b) x-rays from an instrument in a dentist's office
(c) microwaves in a microwave oven
(d) your favorite FM music station at $91.7 \mathrm{MHz}$

An H

Numerade Educator

Problem 10

Place the following types of radiation in order of increasing energy per photon:
(a) radiation within a microwave oven
(b) your favorite radio station
(c) gamma rays from a nuclear reaction
(d) red light from a neon sign
(e) ultraviolet radiation from a sun lamp

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 11

An energy of $3.3 \times 10^{-19} \mathrm{J} /$ atom is required to cause a cesium atom on a metal surface to lose an electron. Calculate the longest possible wavelength of light that can ionize a cesium atom. In what region of the electromagnetic spectrum is this radiation found?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 12

You are an engineer designing a switch that works by the photoelectric effect. The metal you wish to use in your device requires $6.7 \times 10^{-19} \mathrm{J} /$ atom to remove an electron. Will the switch work if the light falling on the metal has a wavelength of $540 \mathrm{nm}$ or greater? Why or why not?

Diana Cruz

Numerade Educator

Problem 13

The most prominent line in the spectrum of mercury is at $253.652 \mathrm{nm}$. Other lines are located at $365.015 \mathrm{nm}, 404.656 \mathrm{nm}, 435.833 \mathrm{nm},$ and $1013.975 \mathrm{nm}$
(a) Which of these lines represents the most energetic light?
(b) What is the frequency of the most prominent line? What is the energy of one photon with this wavelength?
(c) Are any of these lines found in the spectrum of mercury shown in Figure $6.6 ?$ What color or colors are these lines?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 14

The most prominent line in the spectrum of neon is found at $865.438 \mathrm{nm} .$ Other lines are located at $837.761 \mathrm{nm}, 878.062 \mathrm{nm}, 878.375 \mathrm{nm},$ and $885.387 \mathrm{nm}$
(a) In what region of the electromagnetic spectrum are these lines found?
(b) Are any of these lines found in the spectrum of neon shown in Figure $6.6 ?$
(c) Which of these lines represents the most energetic radiation?
(d) What is the frequency of the most prominent line? What is the energy of one photon with this wavelength?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 15

A line in the Balmer series of emission lines of excited H atoms has a wavelength of $410.2 \mathrm{nm}$ (Figure 6.10 ). What color is the light emitted in this transition? What quantum levels are involved in this emission line? That is, what are the values of $n_{\text {initial }}$ and $n_{\text {final }} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 16

What are the wavelength and frequency of the radiation involved in the least energetic emission line in the Lyman series? What are the values of $n_{\text {initial }}$ and $n_{\text {final }} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 17

Consider only transitions involving the $n=1$ through $n=5$ energy levels for the H atom (see Figures 6.7 and 6.10 ).
(a) How many emission lines are possible, considering only the five quantum levels?
(b) Photons of the highest frequency are emitted in a transition from the level with $n=$ _________ to a level with $n=$ __________
(c) The emission line having the longest wavelength corresponds to a transition from the level with n= ___________ to the level with $n=$ __________

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 18

Consider only transitions involving the $n=1$ through $n=4$ energy levels for the hydrogen atom (see Figures 6.7 and 6.10 ).
(a) How many emission lines are possible, considering only the four quantum levels?
(b) Photons of the lowest energy are emitted in a transition from the level with $n=$ __________ level with $n=$ __________
(c) The emission line having the shortest wavelength corresponds to a transition from the level with $n=$ __________ to the level with $n=$ __________

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 19

The energy emitted when an electron moves from a higher energy state to a lower energy state in any atom can be observed as electromagnetic radiation.
(a) Which involves the emission of less energy in the H atom, an electron moving from $n=4$ to $n=2$ or an electron moving from $n=3$ to $n=2 ?$
(b) Which involves the emission of more energy in the H atom, an electron moving from $n=4$ to $n=1$ or an electron moving from $n=5$ to $n=2 ?$ Explain fully.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 20

If energy is absorbed by a hydrogen atom in its ground state, the atom is excited to a higher energy state. For example, the excitation of an electron from $n=1$ to $n=3$ requires radiation with a wavelength of $102.6 \mathrm{nm} .$ Which of the following transitions would require radiation of longer wavelength than this?
(a) $n=2$ to $n=4$
(b) $n=1$ to $n=4$
(c) $n=1$ to $n=5$
(d) $n=3$ to $n=5$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 21

Calculate the wavelength and frequency of light emitted when an electron changes from $n=3$ to $n=1$ in the $\mathrm{H}$ atom. In what region of the spectrum is this radiation found?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 22

Calculate the wavelength and frequency of light emitted when an electron changes from $n=4$ to $n=3$ in the $\mathrm{H}$ atom. In what region of the spectrum is this radiation found?

Diana Cruz

Numerade Educator

Problem 23

An electron moves with a velocity of $2.5 \times 10^{8} \mathrm{cm} / \mathrm{s}$ What is its wavelength?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 24

A beam of electrons $\left(m=9.11 \times 10^{-31} \mathrm{kg} / \text { electron }\right)$ has an average speed of $1.3 \times 10^{8} \mathrm{m} / \mathrm{s}$. What is the wavelength of electrons having this average speed?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 25

Calculate the wavelength, in nanometers, associated with a $46-\mathrm{g}$ golf ball moving at $30 . \mathrm{m} / \mathrm{s}$ (about $67 \mathrm{mph}) .$ At what speed must the ball travel to have a wavelength of $5.6 \times 10^{-3} \mathrm{nm} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 26

A rifle bullet (mass $=1.50 \mathrm{g}$ ) has a velocity of $7.00 \times 10^{2} \mathrm{mph}$ (miles per hour). What is the wavelength associated with this bullet?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 27

(a) When $n=4,$ what are the possible values of $\ell ?$
(b) When $\ell$ is $2,$ what are the possible values of $m_{\ell} ?$
(c) For a $4 s$ orbital, what are the possible values of $n, \ell,$ and $m_{\ell} ?$
(d) For a $4 f$ orbital, what are the possible values of $n, \ell,$ and $m_{\ell} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 28

(a) When $n=4, \ell=2,$ and $m_{\ell}=-1,$ to what orbital type does this refer? (Give the orbital label, such as $1 s .$ )
(b) How many orbitals occur in the $n=5$ electron shell? How many subshells? What are the letter labels of the subshells?
(c) How many orbitals occur in an $f$ subshell? What are the values of $m_{\ell} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 29

A possible excited state of the H atom has the electron in a $4 p$ orbital. List all possible sets of quantum numbers $n, \ell,$ and $m_{\ell}$ for this electron.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 30

A possible excited state for the H atom has an electron in a $5 d$ orbital. List all possible sets of quantum numbers $n, \ell,$ and $m_{\ell}$ for this electron.

Abdel Osman

Numerade Educator

Problem 31

How many subshells occur in the electron shell with the principal quantum number $n=4 ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 32

How many subshells occur in the electron shell with the principal quantum number $n=5 ?$

Abdel Osman

Numerade Educator

Problem 33

Explain briefly why each of the following is not a possible set of quantum numbers for an electron in an atom.
(a) $n=2, \ell=2, m_{\ell}=0$
(b) $n=3, \ell=0, m_{\ell}=-2$
(c) $n=6, \ell=0, m_{\ell}=1$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 34

Which of the following represent valid sets of quantum numbers? For a set that is invalid, explain briefly why it is not correct.
(a) $n=3, \ell=3, m_{\ell}=0$
(b) $n=2, \ell=1, m_{\ell}=0$
(c) $n=6, \ell=5, m_{\ell}=-1$
(d) $n=4, \ell=3, m_{\ell}=-4$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 35

What is the maximum number of orbitals that can be identified by each of the following sets of quantum numbers? When "none" is the correct answer, explain your reasoning.
(a) $n=3, \ell=0, m_{\ell}=+1$
(b) $n=5, \ell=1$
(c) $n=7, \ell=5$
(d) $n=4, \ell=2, m_{\ell}=-2$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 36

What is the maximum number of orbitals that can be identified by each of the following sets of quantum numbers? When "none" is the correct answer, explain your reasoning.
(a) $n=4, \ell=3$
(b) $n=5$
(c) $n=2, \ell=2$
(d) $n=3, \ell=1, m_{\ell}=-1$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 37

Explain briefly why each of the following is not a possible set of quantum numbers for an electron in an atom. In each case, change the incorrect value (or values) to make the set valid.
(a) $n=4, \ell=2, m_{\ell}=0, m_{\mathrm{s}}=0$
(b) $n=3, \ell=1, m_{\ell}=-3, m_{\mathrm{s}}=-1 / 2$
(c) $n=3, \ell=3, m_{\ell}=-1, m_{\mathrm{s}}=+1 / 2$

Sam Limsuwannarot

Sam Limsuwannarot

Numerade Educator

Problem 38

Explain briefly why each of the following is not a possible set of quantum numbers for an electron in an atom. In each case, change the incorrect value (or values) to make the set valid.
(a) $n=2, \ell=2, m_{\ell}=0, m_{\mathrm{s}}=+1 / 2$
(b) $n=2, \ell=1, m_{\ell}=-1, m_{\mathrm{s}}=0$
(c) $n=3, \ell=1, m_{\ell}=-2, m_{\mathrm{s}}=+1 / 2$

Sam Limsuwannarot

Sam Limsuwannarot

Numerade Educator

Problem 39

State which of the following orbitals cannot exist according to the quantum theory: $2 s, 2 d, 3 p, 3 f, 4 f$ and $5 s .$ Briefly explain your answers.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 40

State which of the following orbitals cannot exist according to the quantum theory: $3 p, 4 s, 2 f,$ and 1p. Briefly explain your answers.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 41

Write a complete set of quantum numbers $(n, \ell,$ and $m_{\ell}$ ) that quantum theory allows for each of the following orbitals: (a) $2 p,$ (b) $3 d,$ and (c) $4 f$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 42

Write a complete set of quantum numbers $(n, \ell,$ and $m_{\ell}$ ) for each of the following orbitals: (a) $5 f$
(b) $4 d,$ and $(c) 2 s$

Abdel Osman

Numerade Educator

Problem 43

A particular orbital has $n=4$ and $\ell=2 .$ What must this orbital be: $(a) 3 p,(b) 4 p,(c) 5 d,$ or (d) $4 d ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 44

A given orbital has a magnetic quantum number of $m_{\ell}=-1 .$ This could not be a(n)
(a) $f$ orbital
(c) $p$ orbital
(b) $d$ orbital
(d) $s$ orbital

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 45

How many nodal surfaces through the nucleus (planar nodes) are associated with each of the following orbitals?
(a) $2 s$
(b) $5 d$
(c) $5 f$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 46

How many nodal surfaces through the nucleus (planar nodes) are associated with each of the following atomic orbitals?
(a) $4 f$
(b) $2 p$
(c) $6 s$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 47

Which of the following are applicable when explaining the photoelectric effect? Correct any statements that are wrong.
(a) Light is electromagnetic radiation.
(b) The intensity of a light beam is related to its frequency.
(c) Light can be thought of as consisting of mass less particles whose energy is given by Planck's equation, $E=h v$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 48

In what region of the electromagnetic spectrum for hydrogen is the Lyman series of lines found? The Balmer series?

Diana Cruz

Numerade Educator

Problem 49

Give the number of nodal surfaces through the nucleus (planar nodes) for each orbital type: $s, p, d$ and $f$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 50

What is the maximum number of $s$ orbitals found in a given electron shell? The maximum number of
$p$ orbitals? Of $d$ orbitals? Of $f$ orbitals?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 51

Match the values of $\ell$ shown in the table with orbital type $(s, p, d, \text { or } f)$
(TABLE CANNOT COPY)

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 52

Sketch a picture of the $90 \%$ boundary surface of an $s$ orbital and the $p_{x}$ orbital. Be sure the latter drawing shows why the $p$ orbital is labeled $p_{x}$ and not $p_{y},$ for example.

Abdel Osman

Numerade Educator

Problem 53

Complete the following table.
(TABLE CANNOT COPY)

John Connell

Numerade Educator

Problem 54

Excited H atoms have many emission lines. One series of lines, called the Pfund series, occurs in the infrared region. It results when an electron changes from higher energy levels to a level with $n=5 .$ Calculate the wavelength and frequency of the lowest energy line of this series.

Abdel Osman

Numerade Educator

Problem 55

An advertising sign gives off red light and green light.
(a) Which light has higher-energy photons?
(b) One of the colors has a wavelength of $680 \mathrm{nm}$ and the other has a wavelength of $500 \mathrm{nm}$. Which color has which wavelength?
(c) Which light has the higher frequency?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 56

Radiation in the ultraviolet region of the electromagnetic spectrum is quite energetic. It is this radiation that causes dyes to fade and your skin to develop a sunburn. If you are bombarded with 1.00 mol of photons with a wavelength of $375 \mathrm{nm}$ what amount of energy, in kilojoules per mole of photons, are you being subjected to?

Diana Cruz

Numerade Educator

Problem 57

A cell phone sends signals at about $850 \mathrm{MHz}$ (where $1 \mathrm{MHz}=1 \times 10^{6} \mathrm{Hz}$ or cycles per second).
(a) What is the wavelength of this radiation?
(b) What is the energy of 1.0 mol of photons with a frequency of $850 \mathrm{MHz} ?$
(c) Compare the energy in part (b) with the energy of a mole of photons of violet light $(420 \mathrm{nm})$
(d) Comment on the difference in energy between $850 \mathrm{MHz}$ radiation and violet light.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 58

Assume your eyes receive a signal consisting of blue light, $\lambda=470 \mathrm{nm} .$ The energy of the signal is $2.50 \times 10^{-14} \mathrm{J} .$ How many photons reach your eyes?

Diana Cruz

Numerade Educator

Problem 59

If sufficient energy is absorbed by an atom, an electron can be lost by the atom and a positive ion formed. The amount of energy required is called the ionization energy. In the H atom, the ionization energy is that required to change the electron from $n=1$ to $n=$ infinity. Calculate the ionization energy for the He $^{+}$ ion. Is the ionization energy of the He $^{+}$ more or less than that of H? (Bohr's theory applies to He $^{+}$ because it, like the H atom, has a single electron. The electron energy, however, is now given by $E=-Z^{2} R h c / n^{2},$ where $Z$ is the atomic number of helium.)

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 60

Suppose hydrogen atoms absorb energy so that electrons are excited to the $n=7$ energy level. Electrons then undergo these transitions, among others:
(a) $n=7 \rightarrow n=1 ;$ (b) $n=7 \rightarrow n=6 ;$ and (c) $n=2 \rightarrow n=1 .$ Which of these transitions produces a photon with (i) the smallest energy, (ii) the highest frequency, and (iii) the shortest wavelength?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 61

Rank the following orbitals in the H atom in order of increasing energy: $3 s, 2 s, 2 p, 4 s, 3 p, 1 s,$ and $3 d$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 62

How many orbitals correspond to each of the following designations?
(a) $3 p$
(b) $4 p$
(c) $4 p_{x}$
(d) $6 d$
(e) $5 d$
(f) $5 f$
(g) $n=5$
(h) $7 s$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 63

Cobalt-60 is a radioactive isotope used in medicine for the treatment of certain cancers. It produces $\beta$ particles and $\gamma$ rays, the latter having energies of 1.173 and $1.332 \mathrm{MeV} .\left(1 \mathrm{MeV}=10^{6}$ electron-volts \right. and $\left.1 \mathrm{eV}=1.6022 \times 10^{-19} \mathrm{J} .\right)$ What are the wavelength and frequency of a $\gamma$ -ray photon with an energy of $1.173 \mathrm{MeV} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 64

Exposure to high doses of microwaves can cause tissue damage. Estimate how many photons, with $\lambda=12 \mathrm{cm},$ must be absorbed to raise the temperature of your eye by $3.0^{\circ} \mathrm{C}$. Assume the mass of an eye is $11 \mathrm{g}$ and its specific heat capacity is $4.0 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 65

When the Sojourner spacecraft landed on Mars in $1997,$ the planet was approximately $7.8 \times 10^{7} \mathrm{km}$ from Earth. How long did it take for the television picture signal to reach Earth from Mars?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 66

$.$ The most prominent line in the emission spectrum of chromium is found at $425.4 \mathrm{nm} .$ Other lines in the chromium spectrum are found at $357.9 \mathrm{nm}$ $359.3 \mathrm{nm}, 360.5 \mathrm{nm}, 427.5 \mathrm{nm}, 429.0 \mathrm{nm},$ and $520.8 \mathrm{nm}$
(a) Which of these lines represents the most energetic light?
(b) What color is light of wavelength $425.4 \mathrm{nm} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 67

Answer the following questions as a summary quiz on the chapter.
(a) The quantum number $n$ describes the __________ of an atomic orbital.
(b) The shape of an atomic orbital is given by the quantum number __________.
(c) A photon of green light has ___________ more) energy than a photon of orange light.
(d) The maximum number of orbitals that may be associated with the set of quantum numbers $n=4$ and $\ell=3$ is __________.
(e) The maximum number of orbitals that may be associated with the quantum number set $n=$ $3, \ell=2,$ and $m_{\ell}=-2$ is __________.
(f) Label each of the following orbital pictures with the appropriate letter:
(FIGURE CANNOT COPY)
(g) When $n=5,$ the possible values of $\ell$ are __________.
(h) The number of orbitals in the $n=4$ shell is __________.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 68

Answer the following questions as a summary quiz on this chapter.
(a) The quantum number $n$ describes the __________ of an atomic orbital, and the quantum number
$\ell$ describes its __________.
(b) When $n=3,$ the possible values of $\ell$ are __________.
(c) What type of orbital corresponds to $\ell=3 ?$ __________
(d) For a $4 d$ orbital, the value of $n$ is __________, the value of $\ell$ is __________, and a possible value of $m_{\ell}$ is __________.
(e) Each of the following drawings represents a type of atomic orbital. Give the letter designation for the orbital, give its value of $\ell,$ and specify the number of planar nodes.
(FIGURE CANNOT COPY)
Letter $=$ ________ __________
$\ell$ value $=$ __________ __________
Planar nodes $=$ __________ __________
(f) An atomic orbital with three planar nodes through the nucleus is a(n) __________ orbital.
(g) Which of the following orbitals cannot exist according to modern quantum theory: $2 s, 3 p$ $2 d, 3 f, 5 p, 6 p ?$
(h) Which of the following is not a valid set of quantum numbers?
(TABLE CANNOT COPY)
(i) What is the maximum number of orbitals that can be associated with each of the following sets of quantum numbers? (One possible answer is "none."
(i) $\quad n=2$ and $\ell=1$
(ii) $\quad n=3$
(iii) $n=3$ and $\ell=3$
(iv) $n=2, \ell=1,$ and $m_{\ell}=0$

Tom Comey

Numerade Educator

Problem 69

For an electron in a hydrogen atom, calculate the energy of the photon emitted when an electron falls in energy from the $n=5$ level to the $n=2$ state. What are the frequency and wavelength of this electromagnetic radiation?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 70

A solution of $\mathrm{KMnO}_{4}$ absorbs light at $540 \mathrm{nm}$ (page 206 ). What is the frequency of the light absorbed? What is the energy of one mole of photons with $\lambda=540 \mathrm{nm} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 71

A large pickle is attached to two electrodes, which are then attached to a 110 -V power supply. As the voltage is increased across the pickle, it begins to glow with a yellow color. Knowing that pickles are made by soaking the vegetable in a concentrated salt solution, describe why the pickle might emit light when electrical energy is added.
(FIGURE CANNOT COPY)

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 72

The spectrum shown here is for aspirin. The vertical axis is the amount of light absorbed, and the horizontal axis is the wavelength of incident light (in $\mathrm{nm}$ ). (For more on spectrophotometry, see Section 4.9.)
(FIGURE CANNOT COPY)
What is the frequency of light with a wavelength of $278 \mathrm{nm} ?$ What is the energy of one mole of photons with $\lambda=278 \mathrm{nm}$ ? What region of the electromagnetic spectrum is covered by the spectrum above? Knowing that aspirin only absorbs light in the region depicted by this spectrum, what is the color of aspirin?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 73

The infrared spectrum for methanol, $\mathrm{CH}_{3} \mathrm{OH},$ is illustrated below. It shows the amount of light in the infrared region that methanol transmits as a function of wavelength. The vertical axis is the amount of light transmitted. At points near the top of the graph, most of the incident light is being transmitted by the sample (or, conversely, little light is absorbed). Therefore, the "peaks" or "bands" that descend from the top indicate light absorbed; the longer the band, the more light is being absorbed. The horizontal scale is in units of "wave numbers," abbreviated cm $^{-1}$. The energy of light is given by Planck's law as $E=h c / \lambda ;$ that is, $E$ is proportional to $1 / \lambda .$ Therefore, the horizontal scale is in units of $1 / \lambda$ and reflects the energy of the light incident on the sample.
(FIGURE CANNOT COPY)
(a) One point on the horizontal axis is marked as $2000 \mathrm{cm}^{-1} .$ What is the wavelength of light at this point?
(b) Which is the low energy end of this spectrum (left or right), and which is the high energy end?
(c) The broad absorption at about $3300-3400 \mathrm{cm}^{-1}$ indicates that infrared radiation is interacting with the OH group of the methanol molecule. The narrower absorptions around $2800-3000 \mathrm{cm}^{-1}$ are for interactions with C-H bonds. Which interaction requires more energy, with $\mathrm{O}-\mathrm{H}$ or with $\mathrm{C}-\mathrm{H} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 74

Bohr pictured the electrons of the atom as being located in definite orbits about the nucleus, just as the planets orbit the Sun. Criticize this model.

Abdel Osman

Numerade Educator

Problem 75

Light is given off by a sodium- or mercury-containing streetlight when the atoms are excited. The light you see arises for which of the following reasons?
(a) Electrons are moving from a given energy level to one of higher energy.
(b) Electrons are being removed from the atom, thereby creating a metal cation.
(c) Electrons are moving from a given energy level to one of lower energy.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 76

How do we interpret the physical meaning of the square of the wavefunction? What are the units of $4 \pi r^{2} \psi^{2} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 77

What does "wave-particle duality" mean? What are its implications in our modern view of atomic structure?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 78

Which of these are observable?
(a) position of an electron in an $\mathrm{H}$ atom
(b) frequency of radiation emitted by $\mathrm{H}$ atoms
(c) path of an electron in an $\mathrm{H}$ atom
(d) wave motion of electrons
(e) diffraction patterns produced by electrons
(f) diffraction patterns produced by light
(g) energy required to remove electrons from $\mathrm{H}$ atoms
(h) an atom
(i) a molecule
(j) a water wave

Tom Comey

Numerade Educator

Problem 79

In principle, which of the following can be determined?
(a) the energy of an electron in the H atom with high precision and accuracy
(b) the position of a high-speed electron with high precision and accuracy
(c) at the same time, both the position and the energy of a high-speed electron with high precision and accuracy

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 80

Suppose you live in a different universe where a different set of quantum numbers is required to describe the atoms of that universe. These quantum numbers have the following rules:
$N,$ principal $\quad 1,2,3, \ldots, \infty$
$L,$ orbital $\quad=N$
$M,$ magnetic $\quad-1,0,+1$
How many orbitals are there altogether in the first three electron shells?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 81

A photon with a wavelength of $93.8 \mathrm{nm}$ strikes a hydrogen atom, and light is emitted by the atom. How many emission lines would be observed? At what wavelengths? Explain briefly (see Figure 6.10 ).

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 82

Explain why you could or could not measure the wavelength of a golf ball in flight.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 83

The radioactive element technetium is not found naturally on Earth; it must be synthesized in the laboratory. It is a valuable element, however, because it has medical uses. For example, the element in the form of sodium pertechnetate $\left(\mathrm{NaTcO}_{4}\right)$ is used in imaging studies of the brain, thyroid, and salivary glands and in renal blood flow studies, among other things.
(a) In what group and period of the periodic table is the element found?
(b) The valence electrons of technetium are found in the $5 s$ and $4 d$ subshells. What is a set of quantum numbers $\left(n, \ell, \text { and } m_{\ell}\right)$ for one of the electrons of the $5 s$ subshell?
(c) Technetium emits a $\gamma$ -ray with an energy of $0.141 \mathrm{MeV} .\left(1 \mathrm{MeV}=10^{6}\right.$ electron-volts, where quantum numbers $\left(n, \ell, \text { and } m_{\ell}\right)$ for one of the electrons of the $5 s$ subshell?
(d) To make $\mathrm{NaTcO}_{4}$, the metal is dissolved in nitric acid.
\begin{aligned}
&7 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{Tc}(\mathrm{s}) \rightarrow\\
&&\mathrm{HTcO}_{4}(\mathrm{aq})+7 \mathrm{NO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell)
\end{aligned}
and the product, $\mathrm{HTcO}_{4}$ , is treated with $\mathrm{NaOH}$ to make $\mathrm{NaTcO}_{4}$
(i) Write a balanced equation for the reaction of (i) Write a balanced equation for the reaction of $\mathrm{HTCO}_{4}$ with $\mathrm{NaOH}$.
(ii) If you begin with $4.5 \mathrm{mg}$ of Tc metal, what mass of $\mathrm{NaTcO}_{4}$ can be made? What mass of $\mathrm{NaOH}$, in grams, is required to convert all of the $\mathrm{HTcO}_{4}$ into $\mathrm{NaTcO}_{4} ?$

Victor Salazar

Numerade Educator

Problem 84

Figure $6.12 \mathrm{b}$ shows the probability of finding a hydrogen $1 s$ electron at various distances from the nucleus. To create the graph in this figure, the electron cloud is first divided into a series of thin concentric shells about the nucleus and then the probability of finding the electron in each shell is evaluated. The volume of each shell is given by the equation $V=4 \pi r^{2}(d),$ where $d$ is the thickness of the shell and $r$ is the distance of the shell from the nucleus. The probability of finding the electron in each shell is
$$\text { Probability }=4 \pi r^{2} \psi^{2}(d)$$
where $\psi$ is the $1 s$ wavefunction for hydrogen $(a_{o}$ in this equation is $52.9 \mathrm{pm}$ ).
$$\psi=\frac{1}{\left(\pi a_{0}^{3}\right)^{1 / 2}} e^{-r / a_{0}}$$
(a) The most probable distance for a 1 s electron in the hydrogen atom is at $52.9 \mathrm{pm} .$ Evaluate the probability of finding the electron in a concentric shell $1.0 \mathrm{pm}$ thick at this distance from the nucleus.
(b) Calculate the probability of finding the electron in a shell $1.0 \mathrm{pm}$ thick at distances from the nucleus of $0.50 \mathrm{a}_{\mathrm{o}}$ and $4 \mathrm{a}_{\mathrm{o}} .$ Compare the results with the probabilities at a . Are these probabilities in accord with the surface density plot shown in Figure $6.12 \mathrm{b} ?$

Katherine Mccandless

Katherine Mccandless

Numerade Educator