Chemistry

Steven S. Zumdahl, Susan A. Zumdahl

Chapter 7

Atomic Structure and Periodicity - all with Video Answers

Educators

Chapter Questions

Problem 1

What does it mean for something to have wavelike properties? Particulate properties? Electromagnetic radiation can be discussed in terms of both particles and waves. Explain the experimental verification for each of these views.

James Irizarry

James Irizarry

Numerade Educator

Problem 1

Defend and criticize Bohr's model. Why was it reasonable that such a model was proposed, and what evidence was there that it "works"? Why do we no longer "believe" in it?

JP

Josiah Piceno

Numerade Educator

Problem 3

The first four ionization energies for the elements $X$ and $Y$ are shown below. The units are not $\mathrm{kJ} / \mathrm{mol}$.
$$
\begin{array}{|lrr|}
\hline & \boldsymbol{X} & \boldsymbol{Y} \\
\hline \text { First } & 170 & 200 \\
\text { Second } & 350 & 400 \\
\text { Third } & 1800 & 3500 \\
\text { Fourth } & 2500 & 5000 \\
\hline
\end{array}
$$
Identify the elements $X$ and $Y$. There may be more than one correct answer, so explain completely.

Joanna Josey

Numerade Educator

Problem 4

Compare the first ionization energy of helium to its second ionization energy, remembering that both electrons come from the $1 s$ orbital. Explain the difference without using actual numbers from the text.

JP

Josiah Piceno

Numerade Educator

Problem 5

Which has the larger second ionization energy, lithium or beryllium? Why?

Audrey Kile

Numerade Educator

Problem 6

Explain why a graph of ionization energy versus atomic number (across a row) is not linear. Where are the exceptions? Why are there exceptions?

James Irizarry

Numerade Educator

Problem 7

Without referring to your text, predict the trend of second ionization energies for the elements sodium through argon. Compare your answer with Table $7.5 .$ Explain any differences.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 8

Account for the fact that the line that separates the metals from the nonmetals on the periodic table is diagonal downward to the right instead of horizontal or vertical.

James Irizarry

Numerade Educator

Problem 9

Explain electron from a quantum mechanical perspective, including a discussion of atomic radii, probabilities, and orbitals.

James Irizarry

Numerade Educator

Problem 10

Choose the best response for the following. The ionization energy for the chlorine atom is equal in magnitude to the electron affinity for
a. the $\mathrm{Cl}$ atom.
b. the $\mathrm{Cl}^{-}$ ion.
c. the $\mathrm{Cl}^{+}$ ion.
d. the $\mathrm{F}$ atom.
e. none of these.
Explain each choice. Justify your choice, and for the choices you did not select, explain what is incorrect about them.

James Irizarry

Numerade Educator

Problem 11

Consider the following statement: "The ionization energy for the potassium atom is negative, because when $\mathrm{K}$ loses an electron to become $\mathrm{K}^{+}$, it achieves a noble gas electron configuration." Indicate everything that is correct in this statement. Indicate everything that is incorrect. Correct the incorrect information and explain.

Audrey Kile

Numerade Educator

Problem 12

In going across a row of the periodic table, electrons are added and ionization energy generally increases. In going down a column of the periodic table, electrons are also being added but ionization energy decreases. Explain.

JP

Josiah Piceno

Numerade Educator

Problem 13

How does probability fit into the description of the atom?

James Irizarry

Numerade Educator

Problem 14

What is meant by an orbital?

JP

Josiah Piceno

Numerade Educator

Problem 15

Explain the difference between the probability density distribution for an orbital and its radial probability.

James Irizarry

Numerade Educator

Problem 16

Is the following statement true or false? The hydrogen atom has a $3 s$ orbital. Explain.

JP

Josiah Piceno

Numerade Educator

Problem 16

We expect the atomic radius to increase going down a group in the periodic table. Can you suggest why the atomic radius of hafnium breaks this rule? (See data below.)

Joanna Josey

Numerade Educator

Problem 17

Which is higher in energy: the $2 s$ or $2 p$ orbital in hydrogen? Is this also true for helium? Explain.

Audrey Kile

Numerade Educator

Problem 18

Prove mathematically that it is more energetically favorable for a fluorine atom to take an electron from a sodium atom than for
a fluorine atom to take an electron from another fluorine atom.

James Irizarry

Numerade Educator

Problem 19

What type of relationship (direct or inverse) exists between wavelength, frequency, and photon energy? What does a photon energy unit of a joule equal?

Audrey Kile

Numerade Educator

Problem 20

What do we mean by the frequency of electromagnetic radiation? Is the frequency the same as the speed of the electromagnetic radiation?

Lottie Adams

Numerade Educator

Problem 21

Explain the photoelectric effect.

James Irizarry

Numerade Educator

Problem 22

Describe briefly why the study of electromagnetic radiation has been important to our understanding of the arrangement of electrons in atoms.

Meghan Hinton

Numerade Educator

Problem 23

How does the wavelength of a fast-pitched baseball compare to the wavelength of an electron traveling at $1 / 10$ the speed of light? What is the significance of this comparison? See Example $7.3$

James Irizarry

Numerade Educator

Problem 24

The Bohr model only works for one electron species. Why do we discuss it in this text (what's good about it)?

Audrey Kile

Numerade Educator

Problem 25

Describe the significance of the radial probability distribution shown in Fig. 7.13(b).

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 26

The periodic table consists of four blocks of elements that correspond to $s, p, d$, and $f$ orbitals being filled. After $f$ orbitals come $g$ and $h$ orbitals. In theory, if a $g$ block and an $h$ block of elements existed, how long would the rows of $g$ and $h$ elements be in this theoretical periodic table?

JP

Josiah Piceno

Numerade Educator

Problem 27

Many times the claim is made that subshells half-filled with electrons are particularly stable. Can you suggest a possible physical basis for this claim?

James Irizarry

Numerade Educator

Problem 28

Diagonal relationships in the periodic table exist as well as the vertical relationships. For example, Be and $\mathrm{Al}$ are similar in some of their properties, as are $\mathrm{B}$ and $\mathrm{Si}$. Rationalize why these diagonal relationships hold for properties such as size, ionization energy, and electron affinity.

James Irizarry

Numerade Educator

Problem 29

Elements with very large ionization energies also tend to have highly exothermic electron affinities. Explain. Which group of elements would you expect to be an exception to this statement?

James Irizarry

Numerade Educator

Problem 30

The changes in electron affinity as one goes down a group in the periodic table are not nearly as large as the variations in ionization energies. Why?

James Irizarry

Numerade Educator

Problem 31

Why is it much harder to explain the line spectra of polyelectronic atoms and ions than it is to explain the line spectra of hydrogen and hydrogenlike ions?

Audrey Kile

Numerade Educator

Problem 32

Scientists use emission spectra to confirm the presence of an element in materials of unknown composition. Why is this possible?

James Irizarry

Numerade Educator

Problem 33

Does the minimization of electron-electron repulsions correlate with Hund's rule?

Audrey Kile

Numerade Educator

Problem 34

In the hydrogen atom, what is the physical significance of the state for which $n=\infty$ and $E=0$ ?

James Irizarry

Numerade Educator

Problem 35

The work function is the energy required to remove an electron from an atom on the surface of a metal. How does this definition differ from that for ionization energy?

Audrey Kile

Numerade Educator

Problem 36

Many more anhydrous lithium salts are hygroscopic (readily absorb water) than are those of the other alkali metals. Explain.

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 37

The laser in an audio CD player uses light with a wavelength of $7.80 \times 10^{2} \mathrm{~nm} .$ Calculate the frequency of this light.

Audrey Kile

Numerade Educator

Problem 38

An FM radio station broadcasts at $99.5 \mathrm{MHz}$. Calculate the wavelength of the corresponding radio waves.

James Irizarry

Numerade Educator

Problem 39

Microwave radiation has a wavelength on the order of $1.0 \mathrm{~cm}$. Calculate the frequency and the energy of a single photon of this radiation. Calculate the energy of an Avogadro's number of photons (called an einstein) of this radiation.

Crystal Wang

Numerade Educator

Problem 40

A photon of ultraviolet (UV) light possesses enough energy to mutate a strand of human DNA. What is the energy of a single UV photon and a mole of UV photons having a wavelength of $25 \mathrm{~nm} ?$

James Irizarry

Numerade Educator

Problem 41

Consider the following waves representing electromagnetic radiation:
Which wave has the longer wavelength? Calculate the wavelength. Which wave has the higher frequency and larger photon energy? Calculate these values. Which wave has the greater velocity? What type of electromagnetic radiation does each wave represent?

James Irizarry

Numerade Educator

Problem 42

One type of electromagnetic radiation has a frequency of $107.1$ MHz, another type has a wavelength of $2.12 \times 10^{-10} \mathrm{~m}$, and another type of electromagnetic radiation has photons with energy equal to $3.97 \times 10^{-19} \mathrm{~J} /$ photon. Identify each type of electromagnetic radiation and place them in order of increasing photon energy and increasing frequency.

James Irizarry

Numerade Educator

Problem 43

Carbon absorbs energy at a wavelength of $150 . \mathrm{nm}$. The total amount of energy emitted by a carbon sample is $1.98 \times 10^{5} \mathrm{~J}$. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon.

Audrey Kile

Numerade Educator

Problem 44

$\mathrm{X}$ rays have wavelengths on the order of $1 \times 10^{-10} \mathrm{~m} .$ Calculate the energy of $1.0 \times 10^{-10} \mathrm{~m} \mathrm{X}$ rays in units of kilojoules per mole of X rays. AM radio waves have wavelengths on the order of $1 \times$ $10^{4} \mathrm{~m} .$ Calculate the energy of $1.0 \times 10^{4} \mathrm{~m}$ radio waves in units of kilojoules per mole of radio waves. Consider that the bond energy of a carbon-carbon single bond found in organic compounds is $347 \mathrm{~kJ} / \mathrm{mol}$. Would $\mathrm{X}$ rays and/or radio waves be able to disrupt organic compounds by breaking carbon-carbon single bonds?

Crystal Wang

Numerade Educator

Problem 45

The work function of an element is the energy required to remove an electron from the surface of the solid element. The work function for lithium is $279.7 \mathrm{~kJ} / \mathrm{mol}$ (that is, it takes $279.7 \mathrm{~kJ}$ of energy to remove one mole of electrons from one mole of Li atoms on the surface of Li metal). What is the maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 46

It takes $208.4 \mathrm{~kJ}$ of energy to remove 1 mole of electrons from an atom on the surface of rubidium metal. How much energy does it take to remove a single electron from an atom on the surface of solid rubidium? What is the maximum wavelength of light capable of doing this?

James Irizarry

Numerade Educator

Problem 47

It takes $7.21 \times 10^{-19} \mathrm{~J}$ of energy to remove an electron from an iron atom. What is the maximum wavelength of light that can do this?

Audrey Kile

Numerade Educator

Problem 48

Ionization energy is the energy required to remove an electron from an atom in the gas phase. The ionization energy of gold is $890.1 \mathrm{~kJ} / \mathrm{mol}$. Is light with a wavelength of $225 \mathrm{~nm}$ capable of ionizing a gold atom (removing an electron) in the gas phase?

James Irizarry

Numerade Educator

Problem 49

Calculate the de Broglie wavelength for each of the following.
a. an electron with a velocity $10 . \%$ of the speed of light
b. a tennis ball $(55 \mathrm{~g})$ served at $35 \mathrm{~m} / \mathrm{s}(\sim 80 \mathrm{mi} / \mathrm{h})$

Audrey Kile

Numerade Educator

Problem 50

Neutron diffraction is used in determining the structures of molecules.
a. Calculate the de Broglie wavelength of a neutron moving at $1.00 \%$ of the speed of light.
b. Calculate the velocity of a neutron with a wavelength of $75 \mathrm{pm}\left(1 \mathrm{pm}=10^{-12} \mathrm{~m}\right)$

JP

Josiah Piceno

Numerade Educator

Problem 51

A particle has a velocity that is $90 . \%$ of the speed of light. If the wavelength of the particle is $1.5 \times 10^{-15} \mathrm{~m}$, calculate the mass of the particle.

James Irizarry

Numerade Educator

Problem 52

Calculate the velocities of electrons with de Broglie wavelengths of $1.0 \times 10^{2} \mathrm{~nm}$ and $1.0 \mathrm{~nm}$, respectively.

Lottie Adams

Numerade Educator

Problem 53

Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition?
a. $n=3 \rightarrow n=2$
b. $n=4 \rightarrow n=2$
c. $n=2 \rightarrow n=1$

Audrey Kile

Numerade Educator

Problem 54

Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition?
a. $n=4 \rightarrow n=3$
b. $n=5 \rightarrow n=4$
c. $n=5 \rightarrow n=3$

James Irizarry

Numerade Educator

Problem 55

Using vertical lines, indicate the transitions from Exercise 53 on an energy-level diagram for the hydrogen atom (see Fig. 7.9).

James Irizarry

Numerade Educator

Problem 56

Using vertical lines, indicate the transitions from Exercise 54 on an energy-level diagram for the hydrogen atom (see Fig. 7.9).

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 57

Calculate the longest and shortest wavelengths of light emitted by electrons in the hydrogen atom that begin in the $n=6$ state and then fall to states with smaller values of $n .$

Audrey Kile

Numerade Educator

Problem 58

Assume that a hydrogen atom's electron has been excited to the $n=5$ level. How many different wavelengths of light can be emitted as this excited atom loses energy?

James Irizarry

Numerade Educator

Problem 59

Does a photon of visible light $(\lambda \approx 400$ to $700 \mathrm{~nm}$ ) have sufficient energy to excite an electron in a hydrogen atom from the $n=1$ to the $n=5$ energy state? from the $n=2$ to the $n=6$ energy state?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 60

An electron is excited from the $n=1$ ground state to the $n=3$ state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true.
a. It takes more energy to ionize (completely remove) the electron from $n=3$ than from the ground state.
b. The electron is farther from the nucleus on average in the $n=3$ state than in the $n=1$ state.
c. The wavelength of light emitted if the electron drops from $n=3$ to $n=2$ will be shorter than the wavelength of light emitted if the electron falls from $n=3$ to $n=1$.
d. The wavelength of light emitted when the electron returns to the ground state from $n=3$ will be the same as the wavelength of light absorbed to go from $n=1$ to $n=3$.
e. For $n=3$, the electron is in the first excited state.

James Irizarry

Numerade Educator

Problem 61

Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by $n=1$, by $n=2$.

Audrey Kile

Numerade Educator

Problem 62

Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the $\mathrm{H}$ atom is $1460 \mathrm{~nm} .$ What is the initial excited state for the electron $(n=?) ?$

James Irizarry

Numerade Educator

Problem 63

An excited hydrogen atom with an electron in the $n=5$ state emits light having a frequency of $6.90 \times 10^{14} \mathrm{~s}^{-1}$. Determine the principal quantum level for the final state in this electronic transition.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 64

An excited hydrogen atom emits light with a wavelength of $397.2 \mathrm{~nm}$ to reach the energy level for which $n=2$. In which principal quantum level did the electron begin?

James Irizarry

Numerade Educator

Problem 65

Using the Heisenberg uncertainty principle, calculate $\Delta x$ for each of the following.
a. an electron with $\Delta v=0.100 \mathrm{~m} / \mathrm{s}$
b. a baseball (mass $=145 \mathrm{~g}$ ) with $\Delta v=0.100 \mathrm{~m} / \mathrm{s}$
c. How does the answer in part a compare with the size of a hydrogen atom?
d. How does the answer in part b correspond to the size of a baseball?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 66

The Heisenberg uncertainty principle can be expressed in the form
$$
\Delta E \cdot \Delta t \geq \frac{h}{4 \pi}
$$
where $E$ represents energy and $t$ represents time. Show that the units for this form are the same as the units for the form used in
this chapter:
$$
\Delta x \cdot \Delta(m v) \geq \frac{h}{4 \pi}
$$

James Irizarry

Numerade Educator

Problem 67

What are the possible values for the quantum numbers $n, \ell$, and $m_{\ell} ?$

James Irizarry

Numerade Educator

Problem 68

Which of the following orbital designations are incorrect: $1 s, 1 p$, $7 d, 9 s, 3 f, 4 f, 2 d ?$

James Irizarry

Numerade Educator

Problem 69

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set.
a. $n=3, \ell=2, m_{\ell}=2$
b. $n=4, \ell=3, m_{\ell}=4$
c. $n=0, \ell=0, m_{\ell}=0$
d. $n=2, \ell=-1, m_{\ell}=1$

James Irizarry

Numerade Educator

Problem 70

Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect.
a. $n=3, \ell=3, m_{\ell}=0, m_{s}=-\frac{1}{2}$
b. $n=4, \ell=3, m_{\ell}=2, m_{s}=-\frac{1}{2}$
c. $n=4, \ell=1, m_{\ell}=1, m_{s}=+\frac{1}{2}$
d. $n=2, \ell=1, m_{\ell}=-1, m_{s}=-1$
e. $n=5, \ell=-4, m_{\ell}=2, m_{s}=+\frac{1}{2}$
f. $n=3, \ell=1, m_{\ell}=2, m_{s}=-\frac{1}{2}$

James Irizarry

Numerade Educator

Problem 71

What is the physical significance of the value of $\psi^{2}$ at a particular point in an atomic orbital?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 72

In defining the sizes of orbitals, why must we use an arbitrary value, such as $90 \%$ of the probability of finding an electron in that region?

JP

Josiah Piceno

Numerade Educator

Problem 73

How many orbitals in an atom can have the designation $5 p, 3 d_{z^{2}}$, $4 d, n=5, n=4 ?$

Crystal Wang

Numerade Educator

Problem 74

How many electrons in an atom can have the designation $1 p$, $6 d_{x^{2}-y^{2}}, 4 f, 7 p_{y}, 2 s, n=3 ?$

Lottie Adams

Numerade Educator

Problem 75

Give the maximum number of electrons in an atom that can have these quantum numbers:
a. $n=4$
b. $n=5, m_{\ell}=+1$
c. $n=5, m_{s}=+\frac{1}{2}$
d. $n=3, \ell=2$
e. $n=2, \ell=1$

James Irizarry

Numerade Educator

Problem 76

Give the maximum number of electrons in an atom that can have these quantum numbers:
a. $n=0, \ell=0, m_{\ell}=0$
b. $n=2, \ell=1, m_{\ell}=-1, m_{s}=-\frac{1}{2}$
c. $n=3, m_{s}=+\frac{1}{2}$
d. $n=2, \ell=2$
e. $n=1, \ell=0, m_{\ell}=0$

James Irizarry

Numerade Educator

Problem 77

Draw atomic orbital diagrams representing the ground-state electron configuration for each of the following elements.
a. $\mathrm{Na}$
b. $\mathrm{Co}$
c. $\mathrm{Kr}$
How many unpaired electrons are present in each element?

Audrey Kile

Numerade Educator

Problem 78

For elements $1-36$, there are two exceptions to the filling order as predicted from the periodic table. Draw the atomic orbital diagrams for the two exceptions and indicate how many unpaired electrons are present.

Joanna Josey

Numerade Educator

Problem 79

The elements $\mathrm{Si}$, Ga, As, Ge, Al, $\mathrm{Cd}, \mathrm{S}$, and Se are all used in the manufacture of various semiconductor devices. Write the expected electron configuration for these atoms.

Audrey Kile

Numerade Educator

Problem 80

The elements $\mathrm{Cu}, \mathrm{O}, \mathrm{La}, \mathrm{Y}, \mathrm{Ba}, \mathrm{Tl}$, and $\mathrm{Bi}$ are all found in high-
temperature ceramic superconductors. Write the expected electron configuration for these atoms.

JP

Josiah Piceno

Numerade Educator

Problem 81

Write the expected electron configurations for each of the following atoms: $\mathrm{Sc}, \mathrm{Fe}, \mathrm{P}, \mathrm{Cs}$, Eu, $\mathrm{Pt}, \mathrm{Xe}, \mathrm{Br}$.

Nicholas Mogoi

Numerade Educator

Problem 82

Write the expected electron configurations for each of the following atoms: $\mathrm{Cl}, \mathrm{Sb}, \mathrm{Sr}, \mathrm{W}, \mathrm{Pb}, \mathrm{Cf}$.

James Irizarry

Numerade Educator

Problem 83

Write the expected ground-state electron configuration for the following.
a. the element with one unpaired $5 p$ electron that forms a covalent with compound fluorine
b. the (as yet undiscovered) alkaline earth metal after radium
c. the noble gas with electrons occupying $4 f$ orbitals
d. the first-row transition metal with the most unpaired electrons

Joanna Josey

Numerade Educator

Problem 84

Using only the periodic table inside the front cover of the text, write the expected ground-state electron configurations for
a. the third element in Group $5 \mathrm{~A}$.
b. element number 116 .
c. an element with three unpaired $5 d$ electrons.
d. the halogen with electrons in the $6 p$ atomic orbitals.

Joanna Josey

Numerade Educator

Problem 85

Write the expected ground-state electron configuration for each of the following.
a. the lightest halogen atom
b. the alkali metal with only $2 p$ and $3 p$ electrons
c. the Group $3 \mathrm{~A}$ element in the same period as $\mathrm{Sn}$
d. the nonmetallic elements in Group $4 \mathrm{~A}$

Joanna Josey

Numerade Educator

Problem 86

Identify the following elements.
a. An excited state of this element has the electron configuration $1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}$.
b. The ground-state electron configuration is $[\mathrm{Ne}] 3 s^{2} 3 p^{4}$.
c. An excited state of this element has the electron configuration $[\mathrm{Kr}] 5 s^{2} 4 d^{6} 5 p^{2} 6 s^{1}$
d. The ground-state electron configuration contains three unpaired $6 p$ electrons.

Joanna Josey

Numerade Educator

Problem 87

In the ground state of mercury, $\mathrm{Hg}$,
a. how many electrons occupy atomic orbitals with $n=3$ ?
b. how many electrons occupy $d$ atomic orbitals?
c. how many electrons occupy $p_{z}$ atomic orbitals?
d. how many electrons have spin "up" $\left(m_{s}=+\frac{1}{2}\right)$ ?

James Irizarry

Numerade Educator

Problem 88

In the ground state of element 115, Uup,
a. how many electrons have $n=5$ as one of their quantum numbers?
b. how many electrons have $\ell=3$ as one of their quantum numbers?
c. how many electrons have $m_{\ell}=1$ as one of their quantum numbers?
d. how many electrons have $m_{s}=-\frac{1}{2}$ as one of their quantum numbers?

James Irizarry

Numerade Educator

Problem 89

Give a possible set of values of the four quantum numbers for all the electrons in a boron atom and a nitrogen atom if each is in the ground state.

James Irizarry

Numerade Educator

Problem 90

Give a possible set of values of the four quantum numbers for the $4 s$ and $3 d$ electrons in titanium.

Joanna Josey

Numerade Educator

Problem 91

Valence electrons are those electrons in the outermost principal quantum level (highest $n$ level) of an atom in its ground state. Groups $1 \mathrm{~A}$ to $8 \mathrm{~A}$ have from 1 to 8 valence electrons. For each group of the representative elements (1A-8A), give the number of valence electrons, the general valence electron configuration, a sample element in that group, and the specific valence electron configuration for that element.

Joanna Josey

Numerade Educator

Problem 92

How many valence electrons do each of the following elements have, and what are the specific valence electrons for each element?
a. $\mathrm{Ca}$
b. $\mathrm{O}$
c. element 117
d. In
e. Ar
f. $\mathrm{Bi}$

James Irizarry

Numerade Educator

Problem 93

A certain oxygen atom has the electron configuration $1 s^{2} 2 s^{2} 2 p_{x}^{2} 2 p_{y}^{2}$. How many unpaired electrons are present? Is this an excited state of oxygen? In going from this state to the ground state would energy be released or absorbed?

Audrey Kile

Numerade Educator

Problem 94

Which of the following electron configurations correspond to an excited state? Identify the atoms and write the ground-state electron configuration where appropriate.
a. $1 s^{2} 2 s^{2} 3 p^{1}$
b. $1 s^{2} 2 s^{2} 2 p^{6}$
c. $1 s^{2} 2 s^{2} 2 p^{4} 3 s^{1}$
d. $[\mathrm{Ar}] 4 s^{2} 3 d^{5} 4 p^{1}$
How many unpaired electrons are present in each of these species?

Joanna Josey

Numerade Educator

Problem 95

Which of elements 1-36 have two unpaired electrons in the ground state?

Audrey Kile

Numerade Educator

Problem 96

Which of elements 1-36 have one unpaired electron in the ground
state?

Prashant Bana

Numerade Educator

Problem 97

One bit of evidence that the quantum mechanical model is "correct" lies in the magnetic properties of matter. Atoms with unpaired electrons are attracted by magnetic fields and thus are said to exhibit paramagnetism. The degree to which this effect is observed is directly related to the number of unpaired electrons present in the atom. Consider the ground-state electron configurations for $\mathrm{Li}, \mathrm{N}, \mathrm{Ni}, \mathrm{Te}, \mathrm{Ba}$, and $\mathrm{Hg} .$ Which of these atoms would be expected to be paramagnetic, and how many unpaired electrons are present in each paramagnetic atom?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 98

How many unpaired electrons are present in each of the following in the ground state: $\mathrm{O}, \mathrm{O}^{+}, \mathrm{O}^{-}, \mathrm{Os}, \mathrm{Zr}, \mathrm{S}, \mathrm{F}, \mathrm{Ar}$ ?

James Irizarry

Numerade Educator

Problem 99

Arrange the following groups of atoms in order of increasing size.
a. $\mathrm{Te}, \mathrm{S}, \mathrm{Se}$
b. $\mathrm{K}, \mathrm{Br}, \mathrm{Ni}$
c. $\mathrm{Ba}, \mathrm{Si}, \mathrm{F}$

Audrey Kile

Numerade Educator

Problem 100

Arrange the following groups of atoms in order of increasing size.
a. $\mathrm{Rb}, \mathrm{Na}, \mathrm{Be}$
b. $\mathrm{Sr}, \mathrm{Se}, \mathrm{Ne}$
c. $\mathrm{Fe}, \mathrm{P}, \mathrm{O}$

James Irizarry

Numerade Educator

Problem 101

Arrange the atoms in Exercise 99 in order of increasing first ionization energy.

Joanna Josey

Numerade Educator

Problem 102

Arrange the atoms in Exercise 100 in order of increasing first ionization energy.

Anand Jangid

Numerade Educator

Problem 103

In each of the following sets, which atom or ion has the smallest radius?
a. $\mathrm{H}, \mathrm{He}$
b. $\mathrm{Cl}$, In, Se
c. element 120 , element 119 , element 116
d. $\mathrm{Nb}, \mathrm{Zn}, \mathrm{Si}$
e. $\mathrm{Na}^{-}, \mathrm{Na}, \mathrm{Na}^{+}$

Audrey Kile

Numerade Educator

Problem 104

In each of the following sets, which atom or ion has the smallest ionization energy?
a. $\mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba}$
b. $\mathrm{K}, \mathrm{Mn}, \mathrm{Ga}$
c. $\mathrm{N}, \mathrm{O}, \mathrm{F}$
d. $\mathrm{S}^{2-}, \mathrm{S}, \mathrm{S}^{2+}$
e. $\mathrm{Cs}$, Ge, Ar

James Irizarry

Numerade Educator

Problem 105

Element 106 has been named seaborgium, $\mathrm{Sg}$, in honor of Glenn Seaborg, discoverer of the first transuranium element.
a. Write the expected electron configuration for element 106 .
b. What other element would be most like element 106 in its properties?
c. Write the formula for a possible oxide and a possible oxyanion of element 106 .

Anand Jangid

Numerade Educator

Problem 106

Predict some of the properties of element 117 (the symbol is Uus, following conventions proposed by the International Union of Pure and Applied Chemistry, or IUPAC).
a. What will be its electron configuration?
b. What element will it most resemble chemically?
c. What will be the formula of the neutral binary compounds it forms with sodium, magnesium, carbon, and oxygen?
d. What oxyanions would you expect Uus to form?

James Irizarry

Numerade Educator

Problem 107

The first ionization energies of As and Se are $0.947$ and $0.941$ $\mathrm{MJ} / \mathrm{mol}$, respectively. Rationalize these values in terms of electron configurations.

James Irizarry

Numerade Educator

Problem 108

Rank the elements $\mathrm{Be}, \mathrm{B}, \mathrm{C}, \mathrm{N}$, and $\mathrm{O}$ in order of increasing first ionization energy. Explain your reasoning.

James Irizarry

Numerade Educator

Problem 109

For each of the following pairs of elements
$(\mathrm{C}$ and $\mathrm{N}) \quad(\mathrm{Ar}$ and $\mathrm{Br})$
pick the atom with
a. more favorable (exothermic) electron affinity.
b. higher ionization energy.
c. larger size.

James Irizarry

Numerade Educator

Problem 110

For each of the following pairs of elements
$(\mathrm{Mg}$ and $\mathrm{K}) \quad(\mathrm{F}$ and $\mathrm{Cl})$
pick the atom with
a. more favorable (exothermic) electron affinity.
b. higher ionization energy.
c. larger size.

James Irizarry

Numerade Educator

Problem 111

The electron affinities of the elements from aluminum to chlorine are $-44,-120,-74,-200.4$, and $-384.7 \mathrm{~kJ} / \mathrm{mol}$, respectively. Rationalize the trend in these values.

Audrey Kile

Numerade Educator

Problem 112

In the second row of the periodic table, $\mathrm{Be}, \mathrm{N}$, and $\mathrm{Ne}$ all have endothermic (unfavorable) electron affinities, whereas the other second-row elements have exothermic (favorable) electron affinities. Rationalize why Be, $\mathrm{N}$, and Ne have unfavorable electron affinities.

James Irizarry

Numerade Educator

Problem 113

Order the atoms in each of the following sets from the least exothermic electron affinity to the most.
a. $\mathrm{S}, \mathrm{Se}$
b. $\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}$

James Irizarry

Numerade Educator

Problem 114

Order the atoms in each of the following sets from the least exothermic electron affinity to the most.
a. $\mathrm{N}, \mathrm{O}, \mathrm{F}$
b. $\mathrm{Al}, \mathrm{Si}, \mathrm{P}$

James Irizarry

Numerade Educator

Problem 115

The electron affinity for sulfur is more exothermic than that for oxygen. How do you account for this?

James Irizarry

Numerade Educator

Problem 116

Which has the more negative electron affinity, the oxygen atom or the $\mathrm{O}^{-}$ ion? Explain your answer.

James Irizarry

Numerade Educator

Problem 117

Write equations corresponding to the following.
a. the fourth ionization energy of Se
b. the electron affinity of $\mathrm{S}^{-}$
c. the electron affinity of $\mathrm{Fe}^{3+}$
d. the ionization energy of $\mathrm{Mg}$

Audrey Kile

Numerade Educator

Problem 118

Using data from the text, determine the following values (justify your answer):
a. the electron affinity of $\mathrm{Mg}^{2+}$
b. the ionization energy of $\mathrm{Cl}^{-}$
c. the electron affinity of $\mathrm{Cl}^{+}$
d. the ionization energy of $\mathrm{Mg}^{-}$ (Electron affinity of $\mathrm{Mg}=$ $230 \mathrm{~kJ} / \mathrm{mol}$ )

Joanna Josey

Numerade Educator

Problem 119

An ionic compound of potassium and oxygen has the empirical formula KO. Would you expect this compound to be potassium(II) oxide or potassium peroxide? Explain.

James Irizarry

Numerade Educator

Problem 120

Give the name and formula of each of the binary compounds formed from the following elements.
a. $\mathrm{Li}$ and $\mathrm{N}$
b. $\mathrm{Na}$ and $\mathrm{Br}$
c. $\mathrm{K}$ and $\mathrm{S}$

James Irizarry

Numerade Educator

Problem 121

Cesium was discovered in natural mineral waters in 1860 by R. W. Bunsen and G. R. Kirchhoff using the spectroscope they invented in $1859 .$ The name came from the Latin caesius ("sky blue") because of the prominent blue line observed for this element at $455.5 \mathrm{~nm} .$ Calculate the frequency and energy of a photon of this light.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 122

The bright yellow light emitted by a sodium vapor lamp consists of two emission lines at $589.0$ and $589.6 \mathrm{~nm}$. What are the frequency and the energy of a photon of light at each of these wavelengths? What are the energies in $\mathrm{kJ} / \mathrm{mol}$ ?

James Irizarry

Numerade Educator

Problem 123

Does the information on alkali metals in Table $7.8$ of the text
confirm the general periodic trends in ionization energy and atomic radius? Explain.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 124

Predict the atomic number of the next alkali metal after francium and give its ground-state electron configuration.

James Irizarry

Numerade Educator

Problem 125

Complete and balance the equations for the following reactions.
a. $\mathrm{Li}(s)+\mathrm{N}_{2}(g) \rightarrow$
b. $\mathrm{Rb}(s)+\mathrm{S}(s) \rightarrow$

James Irizarry

Numerade Educator

Problem 126

Complete and balance the equations for the following reactions.
a. $\mathrm{Cs}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow$
b. $\mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \rightarrow$

James Irizarry

Numerade Educator

Problem 127

Photosynthesis uses $660-\mathrm{nm}$ light to convert $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ into glucose and $\mathrm{O}_{2}$. Calculate the frequency of this light.

James Irizarry

Numerade Educator

Problem 128

Octyl methoxycinnamate and oxybenzone are common ingredients in sunscreen applications. These compounds work by absorbing ultraviolet (UV) B light (wavelength $280-320 \mathrm{~nm}$ ), the UV light most associated with sunburn symptoms. What frequency range of light do these compounds absorb?

Audrey Kile

Numerade Educator

Problem 129

A carbon-oxygen double bond in a certain organic molecule absorbs radiation that has a frequency of $6.0 \times 10^{13} \mathrm{~s}^{-1}$.
a. What is the wavelength of this radiation?
b. To what region of the spectrum does this radiation belong?
c. What is the energy of this radiation per photon? per mole of photons?
d. A carbon-oxygen bond in a different molecule absorbs radiation with frequency equal to $5.4 \times 10^{13} \mathrm{~s}^{-1}$. Is this radiation more or less energetic?

James Irizarry

Numerade Educator

Problem 130

Human color vision is "produced" by the nervous system based on how three different cone receptors interact with photons of light in the eye. These three different types of cones interact with photons of different frequency light, as indicated in the following chart:
$$
\begin{array}{|lc|}
\hline \text { Cone Type } & \begin{array}{c}
\text { Range of Light } \\
\text { Frequency Detected }
\end{array} \\
\hline \mathrm{S} & 6.00-7.49 \times 10^{14} \mathrm{~s}^{-1} \\
\mathrm{M} & 4.76-6.62 \times 10^{14} \mathrm{~s}^{-1} \\
\mathrm{~L} & 4.28-6.00 \times 10^{14} \mathrm{~s}^{-1} \\
\hline
\end{array}
$$
What wavelength ranges (and corresponding colors) do the three types of cones detect?

Urvashi Arora

Numerade Educator

Problem 131

The four most abundant elements by mass in the human body are oxygen, carbon, hydrogen, and nitrogen. These four elements make up about $96 \%$ of the human body. The next four most abundant elements are calcium, phosphorus, magnesium, and potassium. Write the expected ground-state electron configurations for these eight most abundant elements in the human body.

Audrey Kile

Numerade Educator

Problem 132

The first-row transition metals from chromium through zinc all have some biologic function in the human body. How many unpaired electrons are present in each of these first-row transition metals in the ground state?

Joanna Josey

Numerade Educator

Problem 133

Consider the eight most abundant elements in the human body, as outlined in Exercise 131 . Excluding hydrogen, which of these elements would have the smallest size? largest size? smallest first ionization energy? largest first ionization energy?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 134

"Lithium" is often prescribed as a mood stabilizing drug. Do you think the "lithium" prescribed is in the elemental form? What is the more likely form of lithium to be prescribed as a drug?

Audrey Kile

Numerade Educator

Problem 135

Photogray lenses incorporate small amounts of silver chloride in the glass of the lens. When light hits the AgCl particles, the following reaction occurs:
$$
\mathrm{AgCl} \stackrel{h v}{\longrightarrow} \mathrm{Ag}+\mathrm{Cl}
$$
The silver metal that is formed causes the lenses to darken. The enthalpy change for this reaction is $3.10 \times 10^{2} \mathrm{~kJ} / \mathrm{mol}$. Assuming all this energy must be supplied by light, what is the maximum wavelength of light that can cause this reaction?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 136

A certain microwave oven delivers $750 .$ watts $(\mathrm{J} / \mathrm{s})$ of power to a coffee cup containing $50.0 \mathrm{~g}$ water at $25.0^{\circ} \mathrm{C}$. If the wavelength of microwaves in the oven is $9.75 \mathrm{~cm}$, how long does it take, and how many photons must be absorbed, to make the water boil? The specific heat capacity of water is $4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}$ and assume only the water absorbs the energy of the microwaves.

Crystal Wang

Numerade Educator

Problem 137

Mars is roughly 60 million $\mathrm{km}$ from earth. How long does it take for a radio signal originating from earth to reach Mars?

James Irizarry

Numerade Educator

Problem 138

Consider the following approximate visible light spectrum:
Barium emits light in the visible region of the spectrum. If each photon of light emitted from barium has an energy of $3.59 \times$ $10^{-19} \mathrm{~J}$, what color of visible light is emitted?

James Irizarry

Numerade Educator

Problem 139

One of the visible lines in the hydrogen emission spectrum corresponds to the $n=6$ to $n=2$ electronic transition. What color light is this transition? See Exercise 138 .

Joanna Josey

Numerade Educator

Problem 140

Using Fig. $7.29$, list the elements (ignore the lanthanides and actinides) that have ground-state electron configurations that differ from those we would expect from their positions in the periodic table.

James Irizarry

Numerade Educator

Problem 141

Are the following statements true for the hydrogen atom only, true for all atoms, or not true for any atoms?
a. The principal quantum number completely determines the energy of a given electron.
b. The angular momentum quantum number, $\ell$, determines the shapes of the atomic orbitals.
c. The magnetic quantum number, $m_{\ell}$, determines the direction that the atomic orbitals point in space.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 142

Although no currently known elements contain electrons in $g$ orbitals in the ground state, it is possible that these elements will be found or that electrons in excited states of known elements could be in $g$ orbitals. For $g$ orbitals, the value of $\ell$ is $4 .$ What is the lowest value of $n$ for which $g$ orbitals could exist? What are the possible values of $m_{\ell} ?$ How many electrons could a set of $g$ orbitals hold?

James Irizarry

Numerade Educator

Problem 143

Consider the representations of the $p$ and $d$ atomic orbitals in Figs. $7.15$ and $7.17 .$ What do the $+$ and $-$ signs indicate?

James Irizarry

Numerade Educator

Problem 144

Total radial probability distributions for the helium, neon, and argon atoms are shown in the following graph. How can one interpret the shapes of these curves in terms of electron configurations, quantum numbers, and nuclear charges?

James Irizarry

Numerade Educator

Problem 145

The following graph plots the first, second, and third ionization energies for $\mathrm{Mg}, \mathrm{Al}$, and $\mathrm{Si}$.
Without referencing the text, which plot corresponds to which element? In one of the plots, there is a huge jump in energy between $I_{2}$ and $I_{3}$, unlike in the other two plots. Explain this phenomenon.

James Irizarry

Numerade Educator

Problem 146

An ion having a $4+$ charge and a mass of $49.9$ amu has 2 electrons with principal quantum number $n=1,8$ electrons with $n=2$, and 10 electrons with $n=3 .$ Supply as many of the properties for the ion as possible from the information given. (Hint:
In forming ions for this species, the $4 s$ electrons are lost before the $3 d$ electrons.)
a. the atomic number
b. total number of $s$ electrons
c. total number of $p$ electrons
d. total number of $d$ electrons
e. the number of neutrons in the nucleus
f. the ground-state electron configuration of the neutral atom

Nicole Smina

Numerade Educator

Problem 147

The successive ionization energies for an unknown element are $I_{1}=896 \mathrm{~kJ} / \mathrm{mol}$
$I_{2}=1752 \mathrm{~kJ} / \mathrm{mol}$
$I_{3}=14,807 \mathrm{~kJ} / \mathrm{mol}$
$I_{4}=17,948 \mathrm{~kJ} / \mathrm{mol}$
To which family in the periodic table does the unknown element most likely belong?

Audrey Kile

Numerade Educator

Problem 148

An unknown element is a nonmetal and has a valence electron configuration of $n s^{2} n p^{4}$.
a. How many valence electrons does this element have?
b. What are some possible identities for this element?
c. What is the formula of the compound this element would form with potassium?
d. Would this element have a larger or smaller radius than barium?
e. Would this element have a greater or smaller ionization energy than fluorine?

James Irizarry

Numerade Educator

Problem 149

Using data from this chapter, calculate the change in energy expected for each of the following processes.
a. $\mathrm{Na}(g)+\mathrm{Cl}(g) \rightarrow \mathrm{Na}^{+}(g)+\mathrm{Cl}^{-}(g)$
b. $\mathrm{Mg}(g)+\mathrm{F}(g) \rightarrow \mathrm{Mg}^{+}(g)+\mathrm{F}^{-}(g)$
c. $\mathrm{Mg}^{+}(g)+\mathrm{F}(g) \rightarrow \mathrm{Mg}^{2+}(g)+\mathrm{F}^{-}(g)$
d. $\mathrm{Mg}(g)+2 \mathrm{~F}(\mathrm{~g}) \rightarrow \mathrm{Mg}^{2+}(g)+2 \mathrm{~F}^{-}(g)$

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 150

Three elements have the electron configurations $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}$, $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}$, and $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}$. The first ionization energies of these elements (not in the same order) are $0.419,0.735$, and $1.527 \mathrm{MJ} / \mathrm{mol}$. The atomic radii are $1.60,0.98$, and $2.35 \AA$. Identify the three elements, and match the appropriate values of ionization energy and atomic radius to each configuration.

Madi Sousa

Numerade Educator

Problem 151

An atom moving at its root mean square velocity at $100 .{ }^{\circ} \mathrm{C}$ has a wavelength of $2.31 \times 10^{-11} \mathrm{~m}$. Which atom is it?

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 152

One of the emission spectral lines for $\mathrm{Be}^{3+}$ has a wavelength of $253.4 \mathrm{~nm}$ for an electronic transition that begins in the state with $n=5 .$ What is the principal quantum number of the lowerenergy state corresponding to this emission? (Hint: The Bohr model can be applied to one-electron ions. Don't forget the $Z$ factor: $Z=$ nuclear charge $=$ atomic number. $)$

James Irizarry

Numerade Educator

Problem 153

The figure below represents part of the emission spectrum for a one-electron ion in the gas phase. All the lines result from electronic transitions from excited states to the $n=3$ state. (See Exercise 152.)
a. What electronic transitions correspond to lines $A$ and $B$ ?
b. If the wavelength of line $B$ is $142.5 \mathrm{~nm}$, calculate the wavelength of line $A$.

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 154

When the excited electron in a hydrogen atom falls from $n=5$ to $n=2$, a photon of blue light is emitted. If an excited electron in $\mathrm{He}^{+}$ falls from $n=4$, to which energy level must it fall so that a similar blue light (as with the hydrogen) is emitted? Prove it. (See Exercise 152.)

James Irizarry

Numerade Educator

Problem 155

The ground state ionization energy for the one electron ion $\mathrm{X}^{m+}$ is $4.72 \times 10^{4} \mathrm{~kJ} / \mathrm{mol}$. Identify $\mathrm{X}$ and $m$. (See Exercise $152 .$ )

Katherine Mccandless

Katherine Mccandless

Numerade Educator

Problem 156

For hydrogen atoms, the wave function for the state $n=3$, $\ell=0, m_{\ell}=0$ is
$$
\psi_{300}=\frac{1}{81 \sqrt{3 \pi}}\left(\frac{1}{a_{0}}\right)^{3 / 2}\left(27-18 \sigma+2 \sigma^{2}\right) e^{-\sigma / 3}
$$
where $\sigma=r / a_{0}$ and $a_{0}$ is the Bohr radius $\left(5.29 \times 10^{-11} \mathrm{~m}\right)$. Calculate the position of the nodes for this wave function.

Madi Sousa

Numerade Educator

Problem 157

The wave function for the $2 p_{z}$ orbital in the hydrogen atom is
$$
\psi_{2 p_{z}}=\frac{1}{4 \sqrt{2 \pi}}\left(\frac{Z}{a_{0}}\right)^{3 / 2} \sigma \mathrm{e}^{-\sigma / 2} \cos \theta
$$
where $a_{0}$ is the value for the radius of the first Bohr orbit in meters $\left(5.29 \times 10^{-11}\right), \sigma$ is $Z\left(r / a_{0}\right), r$ is the value for the distance from the nucleus in meters, and $\theta$ is an angle. Calculate the value of $\psi_{2 p_{p}}^{2}$ at $r=a_{0}$ for $\theta=0^{\circ}\left(z\right.$ axis) and for $\theta=90^{\circ}(x y$ plane).

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 158

Answer the following questions assuming that $m_{s}$ could have three values rather than two and that the rules for $n, \ell$, and $m_{\ell}$ are the normal ones.
a. How many electrons would an orbital be able to hold?
b. How many elements would the first and second periods in the periodic table contain?
c. How many elements would be contained in the first transition metal series?
d. How many electrons would the set of 4 forbitals be able to hold?

Joanna Josey

Numerade Educator

Problem 159

Assume that we are in another universe with different physical laws. Electrons in this universe are described by four quantum numbers with meanings similar to those we use. We will call these quantum numbers $p, q, r$, and $s .$ The rules for these quantum numbers are as follows:
$p=1,2,3,4,5, \ldots$
$q$ takes on positive odd integers and $q \leq p$ $r$ takes on all even integer values from $-q$ to $+q$. (Zero is considered an even number.) $s=+\frac{1}{2}$ or $-\frac{1}{2}$
a. Sketch what the first four periods of the periodic table will look like in this universe.
b. Wh?t are the atomic numbers of the first four elements you would expect to be least reactive?
c. Give an example, using elements in the forst four rows, of ionic compounds with the formulas $\mathrm{XY}, \mathrm{XY}_{2}, \mathrm{X}_{2} \mathrm{Y}, \mathrm{XY}_{3}$,
and $\mathrm{X}_{2} \mathrm{Y}_{3}$
d. How many electrons can have $p=4, q=3 ?$
e. How many electrons can have $p=3, q=0, r=0 ?$
f. How many electrons can have $p=6$ ?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 160

Without looking at data in the text, sketch a qualitative graph of the third ionization energy versus atomic number for the elements Na through Ar, and explain your graph.

James Irizarry

Numerade Educator

Problem 161

The following numbers are the ratios of second ionization energy to first ionization energy:
Na: $9.2$
Mg: $2.0$ Al: $\quad 3.1$
Si: $\quad 2.0$
P: $\quad 1.8$
$\begin{array}{ll}\mathrm{S}: & 2.3\end{array}$
$\begin{array}{ll}\mathrm{Cl}: & 1.8\end{array}$
$\begin{array}{ll}\text { Ar: } & 1.8\end{array}$
Explain these relative numbers.

Audrey Kile

Numerade Educator

Problem 163

Consider the following ionization energies for aluminum:
$$
\begin{aligned}
\mathrm{Al}(g) \longrightarrow \mathrm{Al}^{+}(g)+\mathrm{e}^{-} & I_{1}=580 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{Al}^{+}(g) \longrightarrow \mathrm{Al}^{2+}(g)+\mathrm{e}^{-} & I_{2}=1815 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$
$$
\begin{array}{ll}
\mathrm{Al}^{2+}(g) \longrightarrow \mathrm{Al}^{3+}(g)+\mathrm{e}^{-} & I_{3}=2740 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{Al}^{3+}(g) \longrightarrow \mathrm{Al}^{4+}(g)+\mathrm{e}^{-} & I_{4}=11,600 \mathrm{~kJ} / \mathrm{mol}
\end{array}
$$
a. Account for the trend in the values of the ionization energies.
b. Explain the large increase between $I_{3}$ and $I_{4}$.
c. Which one of the four ions has the greatest electron affinity? Explain.
d. List the four aluminum ions given in order of increasing size, and explain your ordering. (Hint: Remember that most of the size of an atom or ion is due to its electrons.)

Julian Taurozzi

Julian Taurozzi

Numerade Educator

Problem 164

While Mendeleev predicted the existence of several undiscovered elements, he did not predict the existence of the noble gases, the lanthanides, or the actinides. Propose reasons why Mendeleev was not able to predict the existence of the noble gases.

Joanna Josey

Numerade Educator

Problem 165

An atom of a particular element is traveling at $1.00 \%$ of the speed of light. The de Broglie wavelength is found to be $3.31 \times 10^{-3}$ pm. Which element is this? Prove it.

James Irizarry

Numerade Educator

Problem 166

As the weapons officer aboard the Starship Chemistry, it is your duty to configure a photon torpedo to remove an electron from the outer hull of an enemy vessel. You know that the work function (the binding energy of the electron) of the hull of the enemy ship is $7.52 \times 10^{-19} \mathrm{~J}$.
a. What wavelength does your photon torpedo need to be to eject an electron?
b. You find an extra photon torpedo with a wavelength of 259 $\mathrm{nm}$ and fire it at the enemy vessel. Does this photon torpedo do any damage to the ship (does it eject an electron)?
c. If the hull of the enemy vessel is made of the element with an electron configuration of $[\mathrm{Ar}] 4 s^{1} 3 d^{10}$, what metal is this?

James Irizarry

Numerade Educator

Problem 167

Francium, Fr, is a radioactive element found in some uranium minerals and is formed as a result of the decay of actinium.
a. What are the electron configurations of francium and its predicted most common ion?
b. It has been estimated that at any one time, there is only one (1.0) ounce of francium on earth. Assuming this is true, what number of francium atoms exist on earth?
c. The longest-lived isotope of francium is ${ }^{223} \mathrm{Fr}$. What is the total mass in grams of the neutrons in one atom of this isotope?

James Irizarry

Numerade Educator

Problem 168

Answer the following questions based on the given electron configurations and identify the elements.
a. Arrange these atoms in order of increasing size:
$[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{6} ;[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{1} ;[\mathrm{Kr}] 5 s^{2} 4 d^{10} 5 p^{3}$
b. Arrange these atoms in order of decreasing first ionization energy: $[\mathrm{Ne}] 3 s^{2} 3 p^{5} ;[\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{3} ;[\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{5}$

James Irizarry

Numerade Educator

Problem 169

From the information below, identify element $\mathrm{X}$.
a. The wavelength of the radio waves sent by an FM station broadcasting at $97.1 \mathrm{MHz}$ is $30.0$ million $\left(3.00 \times 10^{7}\right)$ times greater than the wavelength corresponding to the energy difference between a particular excited state of the hydrogen atom and the ground state.
b. Let $V$ represent the principal quantum number for the valence shell of element $X$. If an electron in the hydrogen atom falls from shell $V$ to the inner shell corresponding to the excited state mentioned above in part a, the wavelength of light emitted is the same as the wavelength of an electron moving at a speed of $570 . \mathrm{m} / \mathrm{s}$
c. The number of unpaired electrons for element $\mathrm{X}$ in the ground state is the same as the maximum number of electrons in an atom that can have the quantum number designations $n=2$, $m_{\ell}=-1$, and $m_{s}=-\frac{1}{2}$
d. Let $A$ equal the charge of the stable ion that would form when the undiscovered element 120 forms ionic compounds. This value of $A$ also represents the angular momentum quantum number for the subshell containing the unpaired electron(s) for element $\mathrm{X}$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator