Chemistry and Chemical Reactivity

John C. Kotz, Paul M. Treichel, Gabriela C. Weaver

Chapter 7

Atomic Structure - all with Video Answers

Educators

+ 1 more educators

Chapter Questions

Problem 1

Answer the following questions based on Figure 7.3 :
(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?

An H

An H

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 greater frequency, blue or green?

Diana Cruz

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 wavelength of 500 nm. Which has the higher frequency?
(b) Calculate the frequency of amber light.
(FIGURE CAN'T 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)? ( $1 \mathrm{kHZ}=1 \times 10^{3} \mathrm{~Hz}$ or 1000 cycles per second.)
(b) The station is broadcasting at $98.1 \mathrm{MHz}$ (on the FM radio band)? ( $1 \mathrm{MHz}=10^{6} \mathrm{~Hz}$, or cycles per second.)

Diana Cruz

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 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?

Ronald Prasad

Numerade Educator

Problem 8

The most prominent line in the 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 mol of photons with the wavelength of the most energetic line?

Diana Cruz

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) radar signals
(b) radiation within a microwave oven
(c) gamma rays from a nuclear reaction
(d) red light from a neon sign
(c) ultraviolet radiation from a sun lamp

Diana Cruz

Numerade Educator

Problem 11

An energy of $2.0 \times 10^{2} \mathrm{kJ} / \mathrm{mol}$ 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?

An H

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 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 $7.9 ?$ What color or colors are these lines?

An H

Numerade Educator

Problem 14

The most prominent line in the spectrum of neon is found at 865.438 nm. Other lines are located at $837.761 \mathrm{nm}, 878.062 \mathrm{nm}, 878.375 \mathrm{nm},$ and $1885.387 \mathrm{nm}$
(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 $7.9 ?$
(c) Which of these lines represents the most energetic light?
(d) What is the frequency of the most prominent line? What is the energy of one photon with this wavelength?

Diana Cruz

Numerade Educator

Problem 15

A line in the Balmer series of emission lines of excited $\mathrm{H}$ atoms has a wavelength of $410.2 \mathrm{nm} \text { (Figure } 7.12) .$ What color is the light emitted in this transition? What quantum levels are involved in this emission line? 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 quantum levels are involved in this emission line? What are the values of $n_{\text {initial }}$ and $n_{\text {final }} ?$

Diana Cruz

Numerade Educator

Problem 17

Consider only transitions involving the $n=1$ through $n=5$ energy levels for the H atom (where the energy level spacings below are not to scale).
$$\begin{aligned}
&\begin{aligned}
& n=5 \\
& n=4 \\
& n=3 \\
& n=2
\end{aligned}\\
&7\\
&n=1
\end{aligned}$$
(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 $n=\quad$ to a level with $n=$
(c) The emission line having the longest wavelength corresponds to a transition from the level with $n=\ldots$ to the level with $n=$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 18

Consider only transitions involving the $n=1$ through $n=4$ energy levels for the hydrogen atom (using the diagram in Study Question 17 ).
(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 $n=\ldots$ to a level with
$n=$
(c) The emission line having the shortest wavelength corresponds to a transition from the level with
$n=\quad$ to the level with $n=$

Diana Cruz

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 $\mathrm{H}$ 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 $\mathrm{H}$ 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 the level with $n=1$ to the level with $n=3$ 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 $n=4$
(c) $n=1$ to $n=5$
(b) $n=1$ to $n=4$
(d) $n=3$ to $n=5$

Diana Cruz

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 $H$ atom. In what region of the spectrum is this radiation found?

Diana Cruz

Numerade Educator

Problem 23

An electron moves with a velocity of $2.5 \times 10^{8} \mathrm{cm} \cdot \mathrm{s}^{-1}$ What is its wavelength?

Rashmi Sinha

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 $1.3 \times 10^{8} \mathrm{m} \cdot \mathrm{s}^{-1} .$ What is the wavelength of electrons having this average speed?

Diana Cruz

Numerade Educator

Problem 25

Calculate the wavelength, in nanometers, associated with a $1.0 \times 10^{2}-\mathrm{g}$ golf ball moving at $30 . \mathrm{m} \cdot \mathrm{s}^{-1}$ (about $67 \mathrm{mph}$ ).
How fast must the ball travel to have a wavelength of $5.6 \times$ $10^{-3} \mathrm{nm} ?$

Rashmi Sinha

Numerade Educator

Problem 26

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

Diana Cruz

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 $m_{e} ?$
(d) For a 4 forbital, what are the possible values of $n, \ell$ and $m_{e} ?$

Rashmi Sinha

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) If a subshell is labeled $f$, how many orbitals occur in the subshell? What are the values of $m_{\ell} ?$

Abdel Osman

Numerade Educator

Problem 29

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

Rashmi Sinha

Numerade Educator

Problem 30

A possible excited state for the $\mathrm{H}$ 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 bricfly 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) $n=6, \ell=0, m_{\ell}=1$

Rashmi Sinha

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) $n=3, \ell=3, m_{\ell}=0$
(c) $n=6, \ell=5, m_{\ell}=-1$
(b) $n=2, \ell=1, m_{\ell}=0$
(d) $n=4, \ell=3, m_{\ell}=-4$

Abdel Osman

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.
(c) $n=7, \ell=5$
(a) $n=3, \ell=0, m_{\ell}=+1$
(b) $n=5, \ell=1$
(d) $n=4, \ell=2, m_{\ell}=-2$

Rashmi Sinha

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) $n=4, \ell=3$
(c) $n=2, \ell=2$
(b) $n=5$
(d) $n=3, \ell=1, m_{\ell}=-1$

Abdel Osman

Numerade Educator

Problem 37

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 38

State which of the following are incorrect designations for orbitals according to the quantum theory: $3 p, 4 s, 2 f$ and $1 p .$ Briefly explain your answers.

Abdel Osman

Numerade Educator

Problem 39

Write a complete set of quantum numbers $\left(n, \ell, \text { and } m_{\ell}\right)$ 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 40

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

Abdel Osman

Numerade Educator

Problem 41

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 42

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

Abdel Osman

Numerade Educator

Problem 43

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

Rashmi Sinha

Numerade Educator

Problem 44

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

Abdel Osman

Numerade Educator

Problem 45

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 massless particles whose energy is given by Planck's equation, $E=h v$

Rashmi Sinha

Numerade Educator

Problem 46

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

Diana Cruz

Numerade Educator

Problem 47

Give the number of nodal surfaces for each orbital type: $s$
$p, d,$ and $f$

Rashmi Sinha

Numerade Educator

Problem 48

What is the maximum number of sorbitals found in a given electron shell? The maximum number of porbitals? Of $d$ orbitals? Of forbitals?

Abdel Osman

Numerade Educator

Problem 49

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

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 50

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 51

Complete the following table.
(TABLE CAN'T COPY)

John Connell

Numerade Educator

Problem 52

Excited $\mathrm{H}$ 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 53

An advertising sign gives off red light and green light.
(a) Which light has the 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 54

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 nm, what amount of energy, in kilojoules per mole of photons, are you being subjected to?

Diana Cruz

Numerade Educator

Problem 55

A cell phone sends signals at about $850 \mathrm{MHz}$ ( $1 \mathrm{MHz}=$
$1 \times 10^{6} \mathrm{Hz}$ 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 blue light $(420 \mathrm{nm})$
(d) Comment on the difference in energy between 850 MHz radiation and blue light.

Rashmi Sinha

Numerade Educator

Problem 56

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 57

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. (See "A Closer Look: Experimental Evidence for Bohr's Theory," page $313 .$ ) Calculate the ionization energy for $\mathrm{He}^{+}$ 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 $\mathrm{H}$ atom, has a single electron. The electron energy, however,

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 58

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

Abdel Osman

Numerade Educator

Problem 59

Rank the following orbitals in the $\mathrm{H}$ 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 60

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

Abdel Osman

Numerade Educator

Problem 61

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 MeV. (1 MeV = 1 million electron-volts and 1 $\mathrm{eV}=$ $9.6485 \times 10^{4} \mathrm{J} / \mathrm{mol} .$. What are the wavelength and frequency of a $\gamma$ -ray photon with an energy of $1.173 \mathrm{MeV} ?$

Rashmi Sinha

Numerade Educator

Problem 62

A Exposure to high doses of microwaves can cause 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 $4.0 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}$

Abdel Osman

Numerade Educator

Problem 63

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

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 64

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 $425.4 \mathrm{nm} ?$

Abdel Osman

Numerade Educator

Problem 65

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 (less or 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 $m_{e}=-2$ is
(f) Label each of the following orbital pictures with the appropriate letter:
(FIGURE CAN'T 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 66

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 $\quad$ 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 nodal surfaces.
(FIGURE CAN'T COPY)
Letter $=$ ___________
$\ell$ value $=$ _________
Nodal surfaces $=$ _________
(f) An atomic orbital with three nodal surfaces is
(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?
$$\begin{array}{lll}
n & \ell & m_{\ell} \\
\hline 3 & 2 & 1 \\
2 & 1 & 2 \\
4 & 3 & 0
\end{array}$$
(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) $n=2$ and $\ell=1$
(ii) $n=3$
(iii) $n=3$ and $\ell=3$
(iv) $n=2, \ell=1,$ and $m_{\ell}=0$

Abdel Osman

Numerade Educator

Problem 67

What are two major assumptions of Bohr's theory of atomic structure?

Rashmi Sinha

Numerade Educator

Problem 68

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 69

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 $n$
(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 $n$

Rashmi Sinha

Numerade Educator

Problem 70

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

Abdel Osman

Numerade Educator

Problem 71

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

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 72

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
(c) diffraction patterns produced by electrons
(f) diffraction patterns produced by light
(g) energy required to remove electrons from H atoms
(h) an atom
(i) a molecule
(j) a water wave

Abdel Osman

Numerade Educator

Problem 73

In principle, which of the following can be determined?
(a) the energy of an electron in the $\mathrm{H}$ 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 74

A 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 $1,2,3, \ldots, \infty$
$I_{7}$ orbital $\quad=N$
$M,$ magnetic -1,0,+1
How many orbitals are there altogether in the first three electron shells?

Abdel Osman

Numerade Educator

Problem 75

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 $7.12 .)$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 76

A Technetium is not found naturally on earth; it must be synthesized in the laboratory. Nonetheless, because it is radioactive it has valuable medical uses. For example, the element in the form of sodium pertechnetate (NaTcO $_{4}$ ) 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 5s and $4 d$ subshells. What is a set of quantum numbers (n, $\ell$, and $m_{\ell}$ ) for one of the electrons of the 5 s subshell?
(c) Technetium emits a $\gamma$ -ray with an energy of $0.141 \mathrm{MeV} .(1 \mathrm{MeV}=1$ million electron-volts, where
$\left.1 \mathrm{eV}=9.6485 \times 10^{4} \mathrm{J} / \mathrm{mol} .\right)$ What are the wavelength
and frequency of a $\gamma$ -ray photon with an energy of $0.141 \mathrm{MeV} ?$
(d) To make NaTcO, the metal is dissolved in nitric acid.
$$\begin{aligned}
7 \mathrm{HNO}_{3}(\mathrm{aq})+& \mathrm{Tc}(\mathrm{s}) \longrightarrow \\
& \mathrm{HTcO}_{4}(\mathrm{aq})+7 \mathrm{NO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell)
\end{aligned}$$
and the product, HTcO, is treated with NaOH to make NaTcO,
(i) Write a balanced equation for the reaction of $\mathrm{HTcO}_{4}$ with $\mathrm{NaOH}$
(ii) If you begin with 4.5 mg of Te metal, how much NaTcO, can be made? What mass of $\mathrm{NaOH}$, in grams, is required to convert all of the HTcO, into $\mathrm{NaTcO}_{4} ?$

Victor Salazar

Numerade Educator

Problem 77

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

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 78

See the General ChemistryNow CD-ROM or website, Screen 7.1 Chemical Puzeler. This screen shows that light of different colors can come from a "neon" sign or from certain salts when they are placed in a burning organic liquid. ("Neon" signs are glass tubes filled with neon, argon, and other gases, and the gases are excited by an electric current. They are very similar in this regard to common fluorescent lights, although the light in fluorescent tubes comes from the phosphor that coats the inside of the tube.) What do these two sources of light have in common? How is the light generated in each case?

Edward Zhang

Numerade Educator

Problem 79

A large pickle is attached to two electrodes, which are then attached to a $110-\mathrm{V}$ power supply (see the problem on Screen 7.7 of the General ChemistryNow CD-ROM or website). 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 CAN'T COPY)

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 80

See the General ChemistryNow CD-ROM or website, Screen 7.7 Bohr's Model of the Hydrogen Atom, Simulation. A photon with a wavelength of $97.3 \mathrm{nm}$ is fired at a hydrogen atom and leads to the emission of light. How many emission lines are emitted? Explain why more than one line is emitted.

Katherine Mccandless

Katherine Mccandless

Numerade Educator