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Chemical Principles

Peter Atkins, Loretta Jones

Chapter 1

Atoms: The Quantum World - all with Video Answers

Educators

Chapter Questions

01:37

Problem 1

At the time that J. J. Thomson conducted his experiments on cathode rays, the nature of the electron was in doubt. Some considered it to be a form of radiation, like light; others believed the electron to be a particle. Some of the observations made on cathode rays were used to advance one view or the other. Explain how each of the following properties of cathode rays supports either the wave or the particle model of the electron. (a) They pass through metal foils. (b) They travel at speeds slower than that of light. (c) If an object is placed in their path, they cast a shadow. (d) Their path is deflected when they are passed between electrically charged plates.

Dominador Tan
Dominador Tan
Numerade Educator
02:05

Problem 2

J. J. Thomson originally referred to the rays produced in his apparatus (Fig. B.5) as "canal rays." The canal ray is deflected within the region between the poles of a magnet and strikes the phosphor screen. The ratio $Q / m$ (where $Q$ is the charge and $m$ the mass) of the particles making up the canal rays is found to be $2.410 \times 10^{7} \mathrm{C} \cdot \mathrm{kg}^{-1}$. The cathode and anode of the apparatus are made of lithium, and the tube contains helium. Use the information inside the back cover to identify the particles (and their charge) that make up the canal rays. Explain your reasoning.

Nicole Smina
Nicole Smina
Numerade Educator
00:45

Problem 3

Arrange the following types of photons of electromagnetic radiation in order of increasing energy: $y$-rays, visible light, ultraviolet radiation, microwaves, x-rays.

Lottie Adams
Lottie Adams
Numerade Educator
01:49

Problem 4

Arrange the following types of photons of electromagnetic radiation in order of increasing frequency: visible light, radio waves, ultraviolet radiation, infrared radiation.

Kevin Chimex
Kevin Chimex
Numerade Educator
01:12

Problem 5

A college student recently had a busy day. Each of the student's activities on that day (reading, having a dental x-ray, making popcorn in a microwave oven, and getting a suntan) involved radiation from a different part of the electromagnetic spectrum. Complete the following table and match each type of radiation to the appropriate event:

An H
An H
Numerade Educator
01:30

Problem 6

A college student used a variety of types of electromagnetic radiation when going to a restaurant for lunch (watching a red traffic light change, listening to the car radio, being struck by a stray gamma ray from outer space while entering the restaurant, and taking food from a serving table heated with an infrared lamp). Complete the following table and match each type of radiation to the appropriate event:

Katherine Mccandless
Katherine Mccandless
Numerade Educator
04:46

Problem 7

Use the Rydberg formula for atomic hydrogen to calculate the wavelength for the transition from $n=4$ to $n=2$. (b) What is the name given to the spectroscopic series to which this transition belongs? (c) Use Table $1.1$ to determine the region of the spectrum in which the transition takes place. If the change takes place in the visible region of the spectrum, what color will be emitted?

Edward Zhang
Edward Zhang
Numerade Educator
04:46

Problem 8

(a) Use the Rydberg formula for atomic hydrogen to calculate the wavelength for the transition from $n=5$ to $n=1$. (b) What is the name given to the spectroscopic series to which this transition belongs? (c) Use Table $1.1$ to determine the region of the spectrum in which the transition takes place. If the change takes place in the visible region of the spectrum, what color will be emitted?

Edward Zhang
Edward Zhang
Numerade Educator
06:50

Problem 9

In the spectrum of atomic hydrogen, several lines are generally classified together as belonging to a series (for example, Balmer series, Lyman series, Paschen series), as shown in Fig. 1.28. What is common to the lines within a series that makes grouping them together logical?

Guilherme Barros
Guilherme Barros
Numerade Educator
01:32

Problem 10

In the spectrum of atomic hydrogen, a violet line is observed at $434 \mathrm{~nm}$. Determine the beginning and ending energy levels of the electron during the emission of energy that leads to this spectral line.

Ankur S
Ankur S
Numerade Educator
02:09

Problem 11

The energy levels of hydrogenlike one-electron ions of atomic number $Z$ differ from those of hydrogen by a factor of $Z^{2}$. Predict the wavelength of the $2 \mathrm{~s} \rightarrow 1$ s transition in $\mathrm{He}^{+}$.

Lottie Adams
Lottie Adams
Numerade Educator
01:05

Problem 12

Some lasers work by exciting atoms of one element and letting these excited atoms collide with atoms of another element and transfer their excitation energy to those atoms. The transfer is most efficient when the separation of energy levels matches in the two species. Given the information in Exercise 1.11, are there any transitions of $\mathrm{He}^{+}$(including transitions from its excited states) that could be excited by collision with an excited hydrogen atom with the configuration $2 \mathrm{~s}^{1}$ ?

Raj Bala
Raj Bala
Numerade Educator
01:00

Problem 13

Consider the following statements about electromagnetic radiation and decide whether they are true or false. If they are false, correct them. (a) The total intensity of radiation emitted from a black body at absolute temperature $T$ is directly proportional to the temperature. (b) As the temperature of a black body increases, the wavelength at which the maximum intensity is found decreases. (c) Photons of radio-frequency radiation are higher in energy than photons of ultraviolet radiation.

David Collins
David Collins
Numerade Educator
03:59

Problem 14

Consider the following statements about electromagnetic radiation and decide whether they are true or false. If they are false, correct them. (a) Photons of ultraviolet radiation have less energy than photons of infrared radiation. (b) The kinetic energy of an electron ejected from a metal surface when the metal is irradiated with ultraviolet radiation is independent of the frequency of the radiation. (c) The energy of a photon is inversely proportional to the wavelength of the radiation.

Keenan Mintz
Keenan Mintz
University of Miami
01:54

Problem 15

The temperature of molten iron can be estimated by using Wien's law. If the melting point of iron is $1540^{\circ} \mathrm{C}$, what will be the wavelength (in nanometers) corresponding to maximum intensity when a piece of iron melts?

Ajay Singhal
Ajay Singhal
Numerade Educator
01:20

Problem 16

An astronomer discovers a new red star and finds that the maximum intensity is at $\lambda=572 \mathrm{~nm}$. What is the temperature of the surface of the star?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:02

Problem 17

The $\gamma$-ray photons emitted by the nuclear decay of a technetium-99 atom used in radiopharmaceuticals have an energy of $140.511 \mathrm{keV}$. Calculate the wavelength of these $\gamma$-rays.

Crystal Wang
Crystal Wang
Numerade Educator
01:02

Problem 18

A mixture of argon and mercury vapor used in blue advertising signs emits light of wavelength $470 \mathrm{~nm}$. Calculate the energy change resulting from the emission of $1.00$ mol of photons at this wavelength.

Crystal Wang
Crystal Wang
Numerade Educator
01:02

Problem 19

Sodium vapor lamps, used for public lighting, emit yellow light of wavelength $589 \mathrm{~nm}$. How much energy is emitted by (a) an excited sodium atom when it generates a photon; (b) $5.00 \mathrm{mg}$ of sodium atoms emitting light at this wavelength; (c) $1.00 \mathrm{~mol}$ of sodium atoms emitting light at this wavelength?

Raj Bala
Raj Bala
Numerade Educator
01:56

Problem 20

When an electron beam strikes a block of copper, x-rays with a frequency of $1.2 \times 10^{17}$ Hz are emitted. How much energy is emitted at this wavelength by (a) an excited copper atom when it generates an x-ray photon; (b) $2.00$ mol of excited copper atoms; (c) $2.00 \mathrm{~g}$ of copper atoms?

Averell Hause
Averell Hause
Carnegie Mellon University
02:39

Problem 21

A lamp rated at $32 \mathrm{~W}\left(1 \mathrm{~W}=1 \mathrm{~J} \cdot \mathrm{s}^{-1}\right)$ emits violet light of wavelength $420 \mathrm{~nm}$. How many photons of violet light can the lamp generate in $2.0 \mathrm{~s}$ ?

ES
Eugene Schneider
University of Minnesota - Twin Cities
03:02

Problem 22

A lamp rated at $40 \mathrm{~W}\left(1 \mathrm{~W}=1 \mathrm{~J} \cdot \mathrm{s}^{-1}\right)$ emits blue light of wavelength $470 \mathrm{~nm}$. How many photons of blue light can the lamp generate in $2.0 \mathrm{~s}$ ?

Dominique Jan Tan
Dominique Jan Tan
Numerade Educator
01:56

Problem 23

The velocity of an electron that is emitted from a metallic surface by a photon is $3.6 \times 10^{3} \mathrm{~km}^{-\mathrm{s}}^{-1}$. (a) What is the wavelength of the ejected electron? (b) No electrons are emitted from the surface of the metal until the frequency of the radiation reaches $2.50 \times 10^{16} \mathrm{~Hz}$. How much energy is required to remove the electron from the metal surface? (c) What is the wavelength of the radiation that caused photoejection of the electron? (d) What kind of electromagnetic radiation was used?

Averell Hause
Averell Hause
Carnegie Mellon University
01:40

Problem 24

The work function for chromium metal is $4.37 \mathrm{eV}$. What wavelength of radiation must be used to eject electrons with a velocity of $1.5 \times 10^{3} \mathrm{~km} \cdot \mathrm{s}^{-1}$ ?

Narayan Hari
Narayan Hari
Numerade Educator
06:04

Problem 25

A baseball must weigh between $5.00$ and $5.25$ ounces (1 ounce $=28.3 \mathrm{~g}$ ). What is the wavelength of a $5.15$-ounce baseball thrown at $92 \mathrm{mph}$ ?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
01:37

Problem 26

A certain automobile of mass $1645 \mathrm{~kg}$ travels on a German autobahn at $162 \mathrm{~km} \cdot \mathrm{h}^{-1}$. What is the wavelength of the automobile?

Jheremiah Simon
Jheremiah Simon
Numerade Educator
01:21

Problem 27

What is the velocity of a neutron of wavelength $100 . \mathrm{pm} ?$

Nicole Smina
Nicole Smina
Numerade Educator
03:25

Problem 28

The average speed of a helium atom at $25^{\circ} \mathrm{C}$ is $1.23 \times$ $10^{3} \mathrm{~m} \cdot \mathrm{s}^{-1}$. What is the average wavelength of a helium atom at this temperature?

Tim Blackstad
Tim Blackstad
Numerade Educator
01:51

Problem 29

What is the minimum uncertainty in the speed of an electron confined to within the diameter of a lead atom, which has a diameter of $350 . \mathrm{pm}$ ?

Katie Mcalpine
Katie Mcalpine
Numerade Educator
01:33

Problem 30

What is the minimum uncertainty in the position of a hydrogen atom in a particle accelerator given that its speed is known to within $\pm 5.0 \mathrm{~m} \cdot \mathrm{s}^{-1}$ ?

Narayan Hari
Narayan Hari
Numerade Educator
03:10

Problem 31

The energy levels of a particle of mass $m$ in a twodimensional square box of side $L$ are given by $\left(n_{1}^{2}+n_{2}^{2}\right) h^{2} / 8 m L^{2}$. Are any of the levels degenerate? If so, find the values of the quantum numbers $n_{1}$ and $n_{2}$ for which these degeneracies arise for the first three cases.

Zachary Warner
Zachary Warner
Numerade Educator
05:17

Problem 32

Refer to Exercise 1.31. If one side of the box is twice that of the other, the energy levels are given by $\left(n_{1}^{2} / L_{1}{ }^{2}+\right.$ $\left.n_{2}^{2} / L_{2}^{2}\right) \times h^{2} / 8 m$. Are degeneracies allowed? If so, which are the degenerate states of the lowest level that shows degeneracy?

Declan Nell
Declan Nell
Numerade Educator
05:17

Problem 32

Refer to Exercise 1.31. If one side of the box is twice that of the other, the energy levels are given by $\left(n_{1}^{2} / L_{1}{ }^{2}+\right.$ $\left.n_{2}^{2} / L_{2}^{2}\right) \times h^{2} / 8 m$. Are degeneracies allowed? If so, which are the degenerate states of the lowest level that shows degeneracy?

Declan Nell
Declan Nell
Numerade Educator
05:17

Problem 32

Refer to Exercise 1.31. If one side of the box is twice that of the other, the energy levels are given by $\left(n_{1}^{2} / L_{1}{ }^{2}+\right.$ $\left.n_{2}^{2} / L_{2}^{2}\right) \times h^{2} / 8 m$. Are degeneracies allowed? If so, which are the degenerate states of the lowest level that shows degeneracy?

Declan Nell
Declan Nell
Numerade Educator
02:27

Problem 33

(a) Using the particle-in-the-box model for the hydrogen atom and treating the atom as an electron in a one-dimensional box of length $150 .$ pm, predict the wavelength of radiation emitted when the electron falls from the level with $n=3$ to that with $n=2$. (b) Repeat the calculation for the transition from $n=4$ to $n=2$.

Guilherme Barros
Guilherme Barros
Numerade Educator
01:02

Problem 34

(a) What is the highest energy photon that can be absorbed by a ground-state hydrogen atom without causing ionization?
(b) What is the wavelength of this radiation? (c) To what region of the electromagnetic spectrum does this photon belong?

Raj Bala
Raj Bala
Numerade Educator
02:29

Problem 35

(a) Use the Living Graphs on the Web site for this book to plot the particle-in-a-box wavefunction for $n=2$ and $L=1 \mathrm{~m}$. (b) How many nodes does the wavefunction have? Where do these nodes occur? (c) Repeat parts (a) and (b) for $n=3 .$ (d) What general conclusion can you draw about the relation between $n$ and the number of nodes present in a
wavefunction? (e) Convert the $n=2$ plot to a probability density distribution: at what values of $x$ is it most likely to find the particle? (f) Repeat part (e) for $n=3$.

Adriano Chikande
Adriano Chikande
Numerade Educator
02:28

Problem 36

Verify the conclusion in part (d) of Exercise $1.35$ by plotting the wavefunction for $n=4$ and determining the number of nodes.

Keshav Singh
Keshav Singh
Numerade Educator
01:42

Problem 37

The wavefunction for a particle in a one-dimensional box is given in Eq. 9. (a) Confirm that the probability of finding the particle in the left half of the box is $\frac{1}{2}$ regardless of the value of $n$. (b) Does the probability of finding the particle in the left-hand onethird of the box depend on $n$ ? If so, find the probability. Hint: The indefinite integral of $\sin ^{2} a x$ is $\frac{1}{2} x-(1 / 4 a) \sin (2 a x)+$ constant.

Lottie Adams
Lottie Adams
Numerade Educator
08:44

Problem 38

The Humphreys series is a set of spectral lines in the emission spectrum of atomic hydrogen that ends in the fifth excited state. If an atom emits a photon of radiation of wavelength $5910 \mathrm{~nm}$, to which spectral line in the Humphreys series does that photon correspond (i.e., the lowest-energy spectral line, the second-lowestenergy spectral line, the third-lowest-energy spectral line, etc.)? Justify your answer with a calculation.

Amit Srivastava
Amit Srivastava
Numerade Educator
04:18

Problem 39

Evaluate the probability of finding an electron in a small region of a hydrogen 1s-orbital at a distance $0.55 a_{0}$ from the nucleus relative to finding it in the same small region located at the nucleus.

Sheh Lit Chang
Sheh Lit Chang
University of Washington
05:18

Problem 40

Evaluate the probability of finding an electron in a small region of a hydrogen 1s-orbital at a distance $0.65 a_{0}$ from the nucleus relative to finding it in the same small region located at the nucleus.

Zachary Warner
Zachary Warner
Numerade Educator
01:39

Problem 41

Show that the electron distribution is spherically symmetrical for an atom in which an electron occupies each of the three p-orbitals of a given shell.

Daniel Gosser
Daniel Gosser
Numerade Educator
02:34

Problem 42

Show that, if the radial distribution function is defined as $P=r^{2} R^{2}$, then the expression for $P$ for an s-orbital is $P=4 \pi r^{2} \psi^{2} .$

Suzanne W.
Suzanne W.
Numerade Educator
03:47

Problem 43

What is the probability of finding an electron anywhere in a sphere of radius (a) $a_{0}$ or (b) $2 a_{0}$ in the ground state of a hydrogen atom?

João Gabriel Alencar Caribé
João Gabriel Alencar Caribé
Numerade Educator
00:23

Problem 44

At what distance from the nucleus is the electron most likely to be found if it occupies (a) a $3 \mathrm{~d}$-orbital or (b) a 4 s-orbital in a hydrogen atom?

Nicole Smina
Nicole Smina
Numerade Educator
03:48

Problem 45

(a) Sketch the shape of the boundary surfaces corresponding to $1 \mathrm{~s}-2 \mathrm{p}^{-}$, and $3 \mathrm{~d}$-orbitals. (b) What is meant by a node? (c) How many radial nodes and angular nodal surfaces does each orbital have? (d) Predict the number of nodal planes expected for a 4f-orbital.

Kim Trang Nguyen
Kim Trang Nguyen
Numerade Educator
03:47

Problem 46

Locate the positions of the radial nodes of (a) a 3 s-orbital; (b) a 4d-orbital.

Jennifer Hudspeth
Jennifer Hudspeth
Numerade Educator
01:14

Problem 47

Describe the orientation of the lobes of the $\mathrm{p}_{x}^{-}, \mathrm{p}_{y}^{-}$, and $\mathrm{P}_{z}$-orbitals with respect to the reference Cartesian axes.

Kevin Chimex
Kevin Chimex
Numerade Educator
01:28

Problem 48

Describe the difference in orientation of the $\mathrm{d}_{x y^{-}}$and the $d_{x^{2}-y^{2}-\mathrm{orbitals}}$ with respect to the reference Cartesian axes. You may wish to refer to the animation of the atomic orbitals found on the Web site for this text.

Ahmed Ali
Ahmed Ali
Numerade Educator
00:45

Problem 49

How many orbitals are in subshells with $l$ equal to (a) 0 ; (b) $2 ;$ (c) $1 ;$ (d) 3 ?

Nicole Smina
Nicole Smina
Numerade Educator
01:21

Problem 50

(a) How many subshells are there for principal quantum number $n=5$ ? (b) Identify the subshells in the form $5 \mathrm{~s}$, etc. (c) How many orbitals are there in the shell with $n=5$ ?

Sam Limsuwannarot
Sam Limsuwannarot
Numerade Educator
03:23

Problem 51

(a) How many values of the quantum number $l$ are possible when $n=7 ?$ (b) How many values of $m_{l}$ are allowed for an electron in a $6 \mathrm{~d}-\mathrm{subshell}$ ? (c) How many values of $m_{l}$ are allowed for an electron in a $3 \mathrm{p}-\mathrm{subshell}$ ? (d) How many subshells are there in the shell with $n=4$ ?

Cheryl Glor
Cheryl Glor
Numerade Educator
03:23

Problem 52

(a) How many values of the quantum number $l$ are possible when $n=6$ ? (b) How many values of $m_{l}$ are allowed for an electron in a $5 \mathrm{f}$-subshell? (c) How many values of $m_{l}$ are allowed for an electron in a $2 \mathrm{~s}-\mathrm{subshell}$ ? (d) How many subshells are there in the shell with $n=3$ ?

Cheryl Glor
Cheryl Glor
Numerade Educator
01:21

Problem 53

What are the principal and orbital angular momentum quantum numbers for each of the following orbitals: (a) 6p; (b) $3 \mathrm{~d} ;$ (c) $2 \mathrm{p} ;$ (d) $5 \mathrm{f}$ ?

Sam Limsuwannarot
Sam Limsuwannarot
Numerade Educator
01:21

Problem 54

What are the principal and orbital angular momentum quantum numbers for each of the following orbitals: (a) $2 \mathrm{~s}$; (b) 6 f; (c) $4 \mathrm{~d}$; (d) $5 \mathrm{p}$ ?

Sam Limsuwannarot
Sam Limsuwannarot
Numerade Educator
01:28

Problem 55

For each orbital listed in Exercise 1.53, give the possible values for the magnetic quantum number.

Nathan Silvano
Nathan Silvano
Numerade Educator
01:28

Problem 56

For each orbital listed in Exercise 1.54, give the possible values for the magnetic quantum number.

Nathan Silvano
Nathan Silvano
Numerade Educator
02:27

Problem 57

How many electrons can occupy (a) the 4p-orbitals?
(b) the $3 \mathrm{~d}$-orbitals? (c) the $1 \mathrm{~s}$-orbital? (d) the $4 \mathrm{f}$-orbitals?

Kim Trang Nguyen
Kim Trang Nguyen
Numerade Educator
03:54

Problem 58

How many electrons can occupy a subshell with $l=$ (a) 0 ; (b) $1 ;$ (c) $2 ;$ (d) 3 ?

Yaqub Khan
Yaqub Khan
Numerade Educator
01:13

Problem 59

Write the subshell notation ( $3 \mathrm{~d}$, for instance) and the number of orbitals having the following quantum numbers: (a) $n=5$, $l=2 ;$ (b) $n=1, l=0 ;$ (c) $n=6, l=3 ;$ (d) $n=2, l=1$.

Sima Sarker
Sima Sarker
Numerade Educator
02:06

Problem 60

Write the subshell notation ( $3 \mathrm{~d}$, for instance) and the number of electrons that can have the following quantum numbers if all the orbitals of that subshell are filled: (a) $n=4, l=1 ;$ (b) $n=5$, $l=0 ;$; (c) $n=6, l=2$; (d) $n=7, l=3$.

Jasmine Haskell
Jasmine Haskell
Numerade Educator
04:01

Problem 61

How many electrons can have the following quantum numbers in an atom: (a) $n=2, l=1$; (b) $n=4, l=2, m_{l}=-2$; (c) $n=2 ;$ (d) $n=3, l=2, m_{l}=+1$ ?

Shalini Tyagi
Shalini Tyagi
Numerade Educator
01:07

Problem 62

How many electrons can have the following quantum
numbers in an atom: (a) $n=3, l=1$; (b) $n=5, l=3, m_{l}=-1$;
(c) $n=2, l=1, m_{l}=0$; (d) $n=7$ ?

Ajay Singhal
Ajay Singhal
Numerade Educator
00:57

Problem 63

Which of the following subshells cannot exist in an atom:
(a) $2 \mathrm{~d}$; (b) $4 \mathrm{~d}$; (c) $4 \mathrm{~g}$; (d) $6 \mathrm{f}$ ?

Kevin Chimex
Kevin Chimex
Numerade Educator
02:37

Problem 64

Which of the following subshells cannot exist in an atom:
(a) $4 \mathrm{f} ;$ (b) $3 \mathrm{f} ;$ (c) $5 \mathrm{~g} ;$ (d) $6 \mathrm{~h}$ ?

Rabia Shuaib
Rabia Shuaib
Numerade Educator
09:26

Problem 65

(a) Write an expression for the total coulombic potential energy for a lithium atom. (b) What does each individual term represent?

Yaqub Khan
Yaqub Khan
Numerade Educator
00:45

Problem 66

(a) Write an expression for the total coulombic potential energy for a beryllium atom. (b) If $Z$ denotes the number of electrons present in an atom, write a general expression to represent the total number of terms that will be present in the total coulombic potential energy equation.

Mayukh Banik
Mayukh Banik
Numerade Educator
01:17

Problem 67

Which of the following statements are true for many-electron atoms? If false, explain why. (a) The effective nuclear charge $Z_{\text {eff }}$ is independent of the number of electrons present in an atom.
(b) Electrons in an s-orbital are more effective than those in other orbitals at shielding other electrons from the nuclear charge because an electron in an $s$-orbital can penetrate to the nucleus of the atom. (c) Electrons having $l=2$ are better at shielding than electrons having $l=1$. (d) $Z_{\text {eff }}$ for an electron in a p-orbital is lower than for an electron in an $s$-orbital in the same shell.

Lottie Adams
Lottie Adams
Numerade Educator
01:17

Problem 68

For the electrons on a carbon atom in the ground state, decide which of the following statements are true. If false, explain why. (a) $Z_{\text {eff }}$ for an electron in a 1s-orbital is the same as $Z_{\text {eff }}$ for an electron in a $2 \mathrm{~s}$-orbital. (b) $Z_{\mathrm{eff}}$ for an electron in a $2 \mathrm{~s}$-orbital is the same as $Z_{\text {eff }}$ for an electron in a 2 p-orbital. (c) An electron in the $2 \mathrm{~s}$-orbital has the same energy as an electron in the $2 \mathrm{p}$-orbital.
(d) The electrons in the $2 \mathrm{p}$-orbitals have spin quantum numbers $m_{s}$ of opposite sign. (e) The electrons in the $2 \mathrm{~s}$-orbital have the same value of the quantum number $m_{s}$.

Lottie Adams
Lottie Adams
Numerade Educator
00:59

Problem 69

Determine whether each of the following electron configurations represents the ground state or an excited state of the atom given.

Lottie Adams
Lottie Adams
Numerade Educator
06:24

Problem 70

Each of the following valence-shell configurations is possible for a neutral atom of a certain element. What is the element and which configuration represents the ground state?

Jennifer Hudspeth
Jennifer Hudspeth
Numerade Educator
01:25

Problem 71

Of the following sets of four quantum numbers $\left\{n, l, m_{l}, m_{s}\right\}$, identify the ones that are forbidden for an electron in an atom and explain why they are invalid:
(a) $\left\{4,2,-1,+\frac{1}{2}\right\} ;$ (b) $\left\{5,0,-1,+\frac{1}{2}\right\} ;$ (c) $\left\{4,4,-1,+\frac{1}{2}\right\}$.

Suzanne W.
Suzanne W.
Numerade Educator
03:45

Problem 72

Of the following sets of four quantum numbers $\left\{n, l, m_{l}, m_{s}\right\}$, identify the ones that are forbidden for an electron in an atom and explain why they are invalid:
(a) $\left\{2,2,-1,+\frac{1}{2}\right\} ;$ (b) $\left\{6,6,0,+\frac{1}{2}\right\} ;$ (c) $\left\{5,4,+5,+\frac{1}{2}\right\}$

Ronald Prasad
Ronald Prasad
Numerade Educator
08:40

Problem 73

What is the ground-state electron configuration expected for each of the following elements: (a) silver; (b) beryllium; (c) antimony; (d) gallium; (e) tungsten; (f) iodine?

Jennifer Hudspeth
Jennifer Hudspeth
Numerade Educator
08:19

Problem 74

What is the ground-state electron configuration expected for each of the following elements: (a) arsenic; (b) strontium; (c) tin; (d) platinum; (e) osmium; (f) molybdenum?

Jennifer Hudspeth
Jennifer Hudspeth
Numerade Educator
01:27

Problem 75

Which elements are predicted to have the following groundstate electron configurations: (a) $[\mathrm{Kr}] 4 \mathrm{~d}^{10} 5 \mathrm{~s}^{2} 5 \mathrm{p}^{4} ;$ (b) $[\mathrm{Ar}] 3 \mathrm{~d}^{3} 4 \mathrm{~s}^{2}$ (c) $[\mathrm{He}] 2 \mathrm{~s}^{2} 2 \mathrm{p}^{2} ;$ (d) $[\mathrm{Rn}] 7 \mathrm{~s}^{2} 6 \mathrm{~d}^{2} ?$

Morgan Sizemore
Morgan Sizemore
Numerade Educator
01:27

Problem 76

Which elements are predicted to have the following groundstate electron configurations: (a) $[\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^{2} 4 \mathrm{p}^{1} ;$ (b) $[\mathrm{Ne}] 3 \mathrm{~s}^{1} ;$
(c) $[\mathrm{Kr}] 5 \mathrm{~s}^{2} ;$ (d) [Xe] $4 \mathrm{f}^{7} 6 \mathrm{~s}^{2}$ ?

Morgan Sizemore
Morgan Sizemore
Numerade Educator
02:16

Problem 77

For each of the following ground-state atoms, predict the type of orbital (1s, 2p, 3d, 4f, etc.) from which an electron will be removed to form the $+1$ ion: (a) Ge; (b) Mn; (c) Ba; (d) Au.

Devon Burke
Devon Burke
Numerade Educator
01:10

Problem 78

For each of the following ground-state atoms, predict the type of orbital (1s, 2p, 3d, 4f, etc.) from which an electron will be removed to form the $+1$ ion: (a) $\mathrm{Zn}$; (b) Cl; (c) Al; (d) Cu.

Shveta Prithiani
Shveta Prithiani
Numerade Educator
02:27

Problem 79

Predict the number of valence electrons present in each of the following atoms (include the outermost d-electrons: (a) N; (b) Ag; (c) $\mathrm{Nb}$; (d) W.

David Collins
David Collins
Numerade Educator
02:27

Problem 80

Predict the number of valence electrons present in each of the following atoms (include the outermost d-electrons): (a) Bi; (b) Ba; (c) Mn; (d) Zn.

David Collins
David Collins
Numerade Educator
01:38

Problem 81

How many unpaired electrons are predicted for the groundstate configuration of each of the following atoms: (a) Bi; (b) Si; (c) $\mathrm{Ta} ;$ (d) Ni?

Morgan Sizemore
Morgan Sizemore
Numerade Educator
01:38

Problem 82

How many unpaired electrons are predicted for the groundstate configuration of each of the following atoms: (a) $\mathrm{Pb}$; (b) Ir; (c) $Y$; (d) Cd?

Morgan Sizemore
Morgan Sizemore
Numerade Educator
03:38

Problem 83

The elements Ga, Ge, As, Se, and Br lie in the same period in the periodic table. Write the electron configuration expected for the ground-state atoms of these elements and predict how many unpaired electrons, if any, each atom has.

Keenan Mintz
Keenan Mintz
University of Miami
01:47

Problem 84

The elements $\mathrm{N}, \mathrm{P}, \mathrm{As}, \mathrm{Sb}$, and Bi belong to the same group in the periodic table. Write the electron configuration expected for the ground-state atoms of these elements and predict how many unpaired electrons, if any, each atom has.

Tracy Tourville
Tracy Tourville
Numerade Educator
01:25

Problem 85

Give the notation for the valence-shell configuration (including the outermost d-electrons) of (a) the alkali metals;
(b) Group 15/V elements; (c) Group 5 transition metals;
(d) "coinage" metals (Cu, Ag, Au).

Nicole Smina
Nicole Smina
Numerade Educator
01:15

Problem 86

Give the notation for the valence-shell configuration (including the outermost d-electrons) of (a) the halogens; (b) the chalcogens (the Group 16/VI elements); (c) the transition metals in Group 5 ; (d) the Group 14/IV elements.

Nicole Smina
Nicole Smina
Numerade Educator
02:03

Problem 87

Arrange the elements in each of the following sets in order of decreasing atomic radius: (a) sulfur, chlorine, silicon; (b) cobalt,
titanium, chromium; (c) zinc, mercury, cadmium; (d) antimony, bismuth, phosphorus.

Shveta Prithiani
Shveta Prithiani
Numerade Educator
02:03

Problem 88

Arrange the elements in each of the following sets in order of decreasing atomic radius: (a) bromine, chlorine, iodine;
(b) gallium, selenium, arsenic; (c) calcium, potassium, zinc;
(d) barium, calcium, strontium.

Shveta Prithiani
Shveta Prithiani
Numerade Educator
00:19

Problem 89

Place the following ions in order of increasing ionic radius: $\mathrm{S}^{2-}, \mathrm{Cl}^{-}, \mathrm{P}^{3-}$

Sam Limsuwannarot
Sam Limsuwannarot
Numerade Educator
00:38

Problem 90

Which ion of each of the following pairs has the larger radius:
(a) $\mathrm{Ca}^{2+}, \mathrm{Ba}^{2+} ;$ (b) $\mathrm{As}^{3-}, \mathrm{Se}^{2-} ;$ (c) $\mathrm{Sn}^{2+}, \mathrm{Sn}^{4+}$ ?

Lottie Adams
Lottie Adams
Numerade Educator
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Problem 91

Which member of each pair has the smaller first ionization energy: (a) $\mathrm{Ca}$ or $\mathrm{Mg}$; (b) $\mathrm{Mg}$ or $\mathrm{Na}$; (c) $\mathrm{Al}$ or $\mathrm{Na}$ ?

David Collins
David Collins
Numerade Educator
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Problem 92

Which member of each pair is likely to have the smaller second ionization energy: (a) Ca or Mg; (b) Mg or Na; (c) Al or Na?

David Collins
David Collins
Numerade Educator
03:08

Problem 93

Place each of the following sets of elements in order of decreasing ionization energy. Explain your choices. (a) Selenium, oxygen, tellurium; (b) gold, tantalum, osmium; (c) lead, barium, cesium.

Lottie Adams
Lottie Adams
Numerade Educator
04:40

Problem 94

(a) Generally, the first ionization energies for elements in the same period increase on going to higher atomic number. Why?
(b) Examine the data for the p-block elements given in Fig. $1.50$.
Note any exceptions to the rule given in part (a). How are these exceptions explained?

HC
Hashim Choudhry
Numerade Educator
03:23

Problem 95

Which element of each of the following pairs has the higher electron affinity: (a) oxygen or fluorine; (b) nitrogen or carbon; (c) chlorine or bromine; (d) lithium or sodium?

Ronald Prasad
Ronald Prasad
Numerade Educator
06:07

Problem 96

Which element of each of the following pairs has the higher electron affinity: (a) aluminum or indium; (b) bismuth or antimony; (c) silicon or lead?

Niamat Khuda
Niamat Khuda
Numerade Educator
01:48

Problem 97

(a) What is the inert-pair effect? (b) Why is the inert-pair effect observed only for heavy elements?

Adriano Chikande
Adriano Chikande
Numerade Educator
View

Problem 98

Identify which of the following elements experience the inertpair effect and write the formulas for the ions that they form: (a) $\mathrm{Sb}$; (b) $\mathrm{As}$; (c) $\mathrm{Tl}$; (d) $\mathrm{Ba}$.

Ronald Prasad
Ronald Prasad
Numerade Educator
01:47

Problem 99

(a) What is a diagonal relationship? (b) How does it arise?
(c) Give two examples to illustrate the concept.

RC
Ryan Carlson
Numerade Educator
02:16

Problem 100

Use Appendix 2D to find the values for the atomic radii of germanium and antimony as well as the ionic radii for $\mathrm{Ge}^{2+}$ and $\mathrm{Sb}^{3+}$. What do these values suggest about the chemical properties of these two ions?

Nicole Smina
Nicole Smina
Numerade Educator
01:05

Problem 101

Which of the following pairs of elements exhibit a diagonal relationship: (a) $\mathrm{Li}$ and $\mathrm{Mg}$; (b) $\mathrm{Ca}$ and $\mathrm{Al}$; (c) $\mathrm{F}$ and $\mathrm{S}$ ?

Hitendra Singh
Hitendra Singh
Numerade Educator
01:47

Problem 102

Which of the following pairs of elements do not exhibit a diagonal relationship: (a) Be and Al; (b) As and Sn; (c) Ga and $\mathrm{Sn}$ ?

RC
Ryan Carlson
Numerade Educator
01:58

Problem 103

Why are s-block metals more reactive than p-block metals?

HC
Hashim Choudhry
Numerade Educator
00:29

Problem 104

Which of the following elements are transition metals:
(a) radium; (b) radon; (c) hafnium; (d) niobium?

Emily Himsel
Emily Himsel
Numerade Educator
00:45

Problem 105

Identify the following elements as metals, nonmetals, or metalloids: (a) lead; (b) sulfur; (c) zinc; (d) silicon; (e) antimony; (f) cadmium.

Aadit Sharma
Aadit Sharma
Numerade Educator
02:31

Problem 106

Identify the following elements as metals, nonmetals, or metalloids: (a) aluminum; (b) carbon; (c) germanium; (d) arsenic; (e) selenium; (f) tellurium.

Bhumika Jayee
Bhumika Jayee
Numerade Educator
01:36

Problem 107

Photoelectron spectroscopy (PES, see Section $1.4$ and
Box 3.3) can be used to determine the energies of atomic orbitals by measuring the energies required to remove electrons from them. The following peaks were observed in the PES spectra for two elements. Identify the elements, write their electron configurations, and explain your reasoning:
(a) $7.30 \mathrm{MJ} \cdot \mathrm{mol}^{-1}$ and $0.52 \mathrm{MJ} \cdot \mathrm{mol}^{-1}$
(b) $11.5 \mathrm{MJ} \cdot \mathrm{mol}^{-1}$ and $0.90 \mathrm{MJ} \cdot \mathrm{mol}^{-1}$

David Collins
David Collins
Numerade Educator
02:59

Problem 108

The following peaks were observed in the PES spectra for two elements (see Exercise 1.107). Identify the elements, write their electron configurations, and explain your reasoning:
(a) $21 \mathrm{MJ} \cdot \mathrm{mol}^{-1}, 2.4 \mathrm{MJ} \cdot \mathrm{mol}^{-1}$, and $0.80 \mathrm{MJ} \cdot \mathrm{mol}^{-1}$
(b) $29 \mathrm{MJ} \cdot \mathrm{mol}^{-1}, 4.6 \mathrm{MJ} \cdot \mathrm{mol}^{-1}$, and $1.10 \mathrm{MJ} \cdot \mathrm{mol}^{-1}$

Keenan Mintz
Keenan Mintz
University of Miami
02:26

Problem 109

Infrared spectroscopy is an important tool for studying vibrations of molecules. Just as an atom can absorb a photon of suitable energy to move an electron from one electronic state to another, a molecule can absorb a photon of electromagnetic radiation in the infrared region to move from one vibrational energy level to another. In infrared spectroscopy, it is common to express energy in terms of $v / c$, with the units $\mathrm{cm}^{-1}(\mathrm{read}$ as reciprocal centimeters). (a) If an absorption occurs in the infrared spectrum at $3600 \mathrm{~cm}^{-1}$, what is the frequency of radiation that corresponds to that absorption? (b) What is the energy, in joules $(J)$, of that absorption? (c) How much energy would be absorbed by $1.00$ mol of molecules absorbing at $3600 \mathrm{~cm}^{-1}$ ?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
04:47

Problem 110

Diffraction of electromagnetic radiation by atoms and molecules occurs when the wavelength of the electromagnetic radiation is similar to the size of the particle that causes the diffraction-in this case, atoms or molecules. (a) Using $2.0 \times$ $10^{2} \mathrm{pm}$ as the diameter of an atom, decide what type(s) of electromagnetic radiation would give rise to diffraction when passed through a sample of atoms or molecules. Beams of electrons and neutrons can also be used in diffraction experiments because of their high speeds and the de Broglie relation. Calculate the speed of (b) an electron and (c) a neutron that would be necessary to generate wavelengths comparable to the diameter of an atom.

Bettina Hanlon
Bettina Hanlon
Numerade Educator
03:35

Problem 111

Ionization energies usually increase on going from left to right across the periodic table. The ionization energy for oxygen, however, is lower than that of either nitrogen or fluorine. Explain this anomaly.

Adriano Chikande
Adriano Chikande
Numerade Educator
01:54

Problem 112

Thallium is the heaviest member of Group 13/III. Aluminum is also a member of that group, and its chemical properties are dominated by the $+3$ oxidation state.
Thallium, however, is found most usually in the $+1$ oxidation state. Examine this difference by plotting the first, second, and third ionization energies for the Group 13/III elements against atomic number (see Appendix $2 \mathrm{D}$ or the periodic-table data found on the Web site for this text). Explain the trends you observe.

Lottie Adams
Lottie Adams
Numerade Educator
01:54

Problem 113

The German physicist Lothar Meyer observed a periodicity in the physical properties of the elements at about the same time that Mendeleev was working on their chemical properties. Some of Meyer's observations can be reproduced by examining the molar volume for the solid element as a function of atomic number. Calculate the molar volumes for the elements in Periods 2 and 3 from the densities of the elements found in Appendix $2 \mathrm{D}$ and the following solid densities $\left(\mathrm{g} \cdot \mathrm{cm}^{-3}\right)$ :

Nicole Smina
Nicole Smina
Numerade Educator
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Problem 114

In the spectroscopic technique known as photoelectron spectroscopy (PES), ultraviolet radiation is directed at an atom or a molecule. Electrons are ejected from the valence shell, and their kinetic energies are measured. Because the energy of the incoming ultraviolet photon is known and the kinetic energy of the outgoing electron is measured, the ionization energy, $I$, can be deduced from the fact that the total energy is conserved. (a) Show that the speed $v$ of the ejected electron and the frequency $\nu$ of the incoming radiation are related by
$$
h v=I+\frac{1}{2} m_{\mathrm{e}} \nu^{2}
$$
(b) Use this relation to calculate the ionization energy of a rubidium atom, given that radiation of wavelength $58.4 \mathrm{~nm}$ produces electrons with a speed of $2450 \mathrm{~km} \cdot \mathrm{s}^{-1}$; recall that $1 \mathrm{~J}=1 \mathrm{~kg} \cdot \mathrm{m}^{2} \cdot \mathrm{s}^{-2}$.
1.115 In the heavier transition-metal elements, especially the lanthanoids and actinoids, there are numerous exceptions to the regular order of orbital occupation predicted by the building-up principle. Suggest why more exceptions would be noted for these elements.

Jean Gephart
Jean Gephart
Numerade Educator
05:19

Problem 115

In the heavier transition-metal elements, especially the lanthanoids and actinoids, there are numerous exceptions to the regular order of orbital occupation predicted by the building-up principle. Suggest why more exceptions would be noted for these elements.

Crystal Wang
Crystal Wang
Numerade Educator
01:04

Problem 116

Modern periodic tables sometimes differ in which elements are placed immediately to the right of barium and radium. In some cases, the elements are lanthanum and actinium, whereas others place lutetium and lawrencium there. Why? Justify each selection.

Rachel Shi
Rachel Shi
Numerade Educator
01:17

Problem 117

Wavefunctions corresponding to states of different energy of particle in a box are mutually "orthogonal" in the sense that, if he two wavefunctions are multiplied together and then integrated fver the length of the box, then the outcome is zero. (a) Confirm hat the wavefunctions for $n=1$ and $n=2$ are orthogonal.
b) Demonstrate, without doing a calculation, that all wavefunctions with even $n$ are orthogonal to all wavefunctions with odd $n$. Hint: Think about the area under the product of any two such functions.

Lottie Adams
Lottie Adams
Numerade Educator
01:31

Problem 118

Wavefunctions are "normalized" to 1 . This term means that the total probability of finding an electron in the system is 1 . Verify this statement for a particle-in-the-box wavefunction (Eq. 10).

Nicole Krahulik
Nicole Krahulik
Numerade Educator
02:13

Problem 119

The intensity of a transition between the states $n$ and $n^{\prime}$ of a particle in a box is proportional to the square of the integral $I$, where
$$
I_{n n^{\prime}}=\int_{0}^{L} \psi_{n} \psi_{n^{\prime}} \mathrm{d} x
$$
(a) Can there be a transition between states with quantum numbers 3 and 1? (b) Consider the transition between states with quantum numbers 2 and 1 . Does the intensity decrease or increase as the box lengthens?

Chai Santi
Chai Santi
Numerade Educator
01:06

Problem 120

Millikan measured the charge of the electron in electrostatic units, esu. The data that he collected included the following series of charges found on oil drops: $9.60 \times 10^{-10}$ esu, $1.92 \times 10^{-9}$ esu, $2.40 \times 10^{-9}$ esu, $2.88 \times 10^{-9}$ esu, and $4.80 \times 10^{-9}$ esu. (a) From this series find the likely charge on the electron in electrostatic units. (b) Predict the number of electrons on an oil drop with the charge $6.72 \times 10^{-9}$ esu.

David Collins
David Collins
Numerade Educator
03:49

Problem 121

Atomic orbitals may be combined to form molecular orbitals. In such orbitals, there is a nonzero probability of finding
an electron on any of the atoms that contribute to that molecular orbital. Consider an electron that is confined in a molecular orbital that extends over two adjacent carbon atoms. The electron can move freely between the two atoms. The $\mathrm{C}-\mathrm{C}$ distance is $139 \mathrm{pm}$. (a) Using the one-dimensional particle-in-the-box model, calculate the energy required to promote an electron from the $n=1$ to the $n=2$ level, assuming that the length of the box is determined by the distance between two carbon atoms. (b) To what wavelength of radiation does this correspond? (c) Repeat the calculation for a linear chain of 1000 carbon atoms. (d) What can you conclude about the energy separation between energy levels as the size of the atom chain increases?

Jenna Nikles
Jenna Nikles
Numerade Educator
02:21

Problem 122

The energy required to break a $\mathrm{C}-\mathrm{C}$ bond in a molecule is $348 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$. Will visible light be able to break this bond? If yes, what is the color of that light? If not, what type of electromagnetic radiation will be suitable?

Crystal Wang
Crystal Wang
Numerade Educator
06:03

Problem 123

Apparent anomalies in the filling of electron orbitals in atoms occur in chromium and copper. In these elements an electron expected to occupy an s-orbital occupies a d-orbital instead. (a) Explain why these anomalies occur. (b) Similar anomalies are known to occur in seven other elements. Using Appendix $2 \mathrm{C}$, identify those elements and indicate for which ones the explanation used to rationalize the chromium and copper electron configurations is valid. (c) Explain why there are no elements in which electrons fill $(n+1)$ s-orbitals instead of $n$ p-orbitals.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
05:40

Problem 124

The electron in a hydrogen atom is excited to a 4d-orbital. Calculate the energy of the photon released if the electron were then to move to each of the following orbitals: (a) $1 \mathrm{~s} ;$ (b) $2 \mathrm{p} ;$ (c) $2 \mathrm{~s}$; (d) $4 \mathrm{~s}$. (e) If the outermost electron in a potassium atom were excited to a 4d-orbital and then fell to the same orbitals, describe qualitatively how the emission spectrum would differ from that of hydrogen (do not do any calculations). Explain your answer.

Julia Fontana
Julia Fontana
Numerade Educator
01:58

Problem 125

The following properties are observed for an unknown element. Identify the element from its properties. (a) The neutral atom has two unpaired electrons. (b) One of the valence electrons in the ground state atom has $m_{l}=+1$. (c) The most common oxidation state is $+4$. (d) If an electron in a hydrogen atom were excited to the same principal quantum level, $n$, as the valence electrons in an atom of this element, and fell to the $n-1$ quantum level, the photon emitted would have an energy of $4.9 \times 10^{-20} \mathrm{~J} .$

Shveta Prithiani
Shveta Prithiani
Numerade Educator
02:24

Problem 126

The electron affinity of thulium has been measured by laser photodetachment electron spectroscopy. In this technique a gaseous beam of the anions of an element is bombarded with photons from a laser. The photons eject electrons from some of the anions and the energies of the ejected electrons are detected. The photons had a wavelength of $1064 \mathrm{~nm}$ and the ejected electrons had an energy of $0.137 \mathrm{eV}$. Although the analysis is somewhat more complicated, we can obtain a rough estimate of the electron affinity as the difference in energy between the photons and the energy of the ejected electrons. What is the electron affinity of thulium in $\mathrm{kJ} \cdot \mathrm{mol}^{-1}$ ?

Lottie Adams
Lottie Adams
Numerade Educator
00:34

Problem 127

Francium is thought to be the most reactive of the alkali metals. Because it is radioactive and available in only very small amounts it is difficult to study. However, we can predict its properties based on its location in Group 1 of the periodic table. Estimate the following properties of francium: (a) atomic radius; (b) ionic radius of the $+1$ cation; (c) ionization energy.

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:40

Problem 128

Below is pictured the reaction between an atom of magnesium and an atom of oxygen. Identify each element and the ions formed and explain your reasoning.

Mehrnaz Siavoshi
Mehrnaz Siavoshi
Numerade Educator
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Problem 129

Below is pictured the reaction between an atom of sodium and an atom of chlorine. Identify each element and the ions formed and explain your reasoning.

Nicole Basile
Nicole Basile
Numerade Educator
02:23

Problem 130

This plot shows the radial distribution function of the 3 s- and 3 p-orbitals of a hydrogen atom. Identify each curve and explain how you made your decision.

Nidhi Singhi
Nidhi Singhi
Numerade Educator
20:21

Problem 131

Green chemistry methods, which use nontoxic chemicals, are replacing elemental chlorine for the bleaching of paper pulp. Chlorine causes problems because it is a strong oxidizing agent that reacts with organic compounds to form toxic by-products such as furan and dioxins. (a) Write the electron configuration of a chlorine atom in its ground state. How many unpaired electrons are present in the atom? Write the electron configuration you expect a chloride ion to have. The electron configuration of the chloride ion is identical to that of a neutral atom of what other element?
(b) When a chlorine atom is excited by heat or light, one of its valence electrons may be promoted to a higher energy level. Predict the most likely electron configuration for the lowest possible excited state for an excited chlorine atom.
(c) Estimate the wavelength (in nm) of the energy that needs to be absorbed for the electron to reach the excited state in part (b). To make this estimate, use Eq. 20 and take the effective nuclear charge from Fig. $1.45$.
(d) What is the value of the energy required in part (c) in kilojoules per mole and electronvolts?
(e) The proportion of ${ }^{37} \mathrm{Cl}$ in a typical sample is $75.77 \%$, with the remainder being ${ }^{35} \mathrm{Cl}$. What would the molar mass of a sample of chlorine atoms be if the proportion of ${ }^{37} \mathrm{Cl}$ were reduced to half its current value? The mass of an atom of ${ }^{35} \mathrm{Cl}$ is $5.807 \times 10^{-23} \mathrm{~g}$ and that of an atom of ${ }^{37} \mathrm{Cl}$ is $6.139 \times 10^{-23} \mathrm{~g}$.
(f) What are the oxidation numbers of chlorine in the bleaching agents $\mathrm{ClO}_{2}$ and $\mathrm{NaClO}$ ?
(g) What are the oxidation numbers of chlorine in the oxidizing agents $\mathrm{KClO}_{3}$ and $\mathrm{NaClO}_{4}$ ?
(h) Write the names of the compounds in parts (f) and (g).

Susan Hallstrom
Susan Hallstrom
Numerade Educator