Chemistry : structure and properties

Nivaldo J. Tro

Chapter 21 Radioactivity and Nuclear Chemistry - all with Video Answers

Educators

Chapter Questions

01:27

Problem 1

What is radioactivity? Who discovered it? How was it discovered?

Matthew Hurlock

Numerade Educator

02:34

Problem 2

Explain Marie Curie's role in the discovery of radioactivity.

Monica Mame Soma Nyansa

Michigan Technological University

01:08

Problem 3

Define $A, Z$, and $X$ in the notation used to specify a nuclide: $\frac{A}{Z} X$.

Joanna Josey

Numerade Educator

04:34

Problem 4

Use the notation from Question 3 to write symbols for a proton, a neutron, and an electron.

Monica Mame Soma Nyansa

Michigan Technological University

01:20

Problem 5

What is an alpha particle? What happens to the mass number and atomic number of a nuclide that emits an alpha particle?

Matthew Hurlock

Numerade Educator

02:50

Problem 6

What is a beta particle? What happens to the mass number and atomic number of a nuclide that emits a beta particle?

Monica Mame Soma Nyansa

Michigan Technological University

00:53

Problem 7

What is a gamma ray? What happens to the mass number and atomic number of a nuclide that emits a gamma ray?

Matthew Hurlock

Numerade Educator

02:16

Problem 8

What is a positron? What happens to the mass number and atomic number of a nuclide that emits a positron?

Monica Mame Soma Nyansa

Michigan Technological University

01:28

Problem 9

Describe the process of electron capture. What happens to the mass number and atomic number of a nuclide that undergoes electron capture?

Matthew Hurlock

Numerade Educator

04:21

Problem 10

Rank alpha particles, beta particles, positrons, and gamma rays in terms of: (a) increasing ionizing power; (b) increasing penetrating power.

Monica Mame Soma Nyansa

Michigan Technological University

01:26

Explain why the ratio of neutrons to protons $(\mathrm{N} / \mathrm{Z})$ is important in determining nuclear stability. How can you use the $N / Z$ ratio of a nuclide to predict the kind of radioactive decay that it might undergo?

Tiffany Noble

Numerade Educator

03:12

Problem 12

What are magic numbers? How are they important in determining the stability of a nuclide?

Monica Mame Soma Nyansa

Michigan Technological University

02:31

Problem 13

Describe the basic way that each device detects radioactivity:
(a) thermoluminescent dosimeter; (b) Geiger-Müller counter; and (c) scintillation counter.

Brooke Smith

Numerade Educator

04:57

Problem 14

Explain the concept of half-life with respect to radioactive nuclides. What rate law is characteristic of radioactivity?

Monica Mame Soma Nyansa

Michigan Technological University

00:53

Problem 15

Explain the main concepts behind the technique of radiocarbon dating. How is radiocarbon dating corrected for changes in atmospheric concentrations of $\mathrm{C}-14$ ? What range of ages is reliably determined by $\mathrm{C}-14$ dating?

Tiffany Noble

Numerade Educator

04:32

Problem 16

How is the uranium to lead ratio in a rock used to estimate its age? How does this dating technique provide an estimate for Earth's age? How old is Earth according to this dating method?

Monica Mame Soma Nyansa

Michigan Technological University

03:00

Problem 17

Describe fission. Include the concepts of chain reaction and critical mass in your description. How and by whom was fission discovered? Explain how fission is used to generate electricity.

Matthew Hurlock

Numerade Educator

04:13

Problem 18

What was the Manhattan Project? Briefly describe its development and culmination.

Monica Mame Soma Nyansa

Michigan Technological University

02:02

Problem 19

Describe the advantages and disadvantages of using fission to generate electricity.

Matthew Hurlock

Numerade Educator

04:32

Problem 20

The products of a nuclear reaction usually have a different mass than the reactants. Why?

Monica Mame Soma Nyansa

Michigan Technological University

02:12

Problem 21

Explain the concepts of mass defect and nuclear binding energy. At what mass number does the nuclear binding energy per nucleon peak? What is the significance of this?

Matthew Hurlock

Numerade Educator

02:43

Problem 22

What is fusion? Why can fusion and fission both produce energy? Explain.

Monica Mame Soma Nyansa

Michigan Technological University

01:47

Problem 23

What are some of the challenges associated with using fusion to generate electricity?

Matthew Hurlock

Numerade Educator

02:34

Problem 24

Explain transmutation and provide one or two examples.

Monica Mame Soma Nyansa

Michigan Technological University

02:09

Problem 25

How does a linear accelerator work? For what purpose is it used?

Matthew Hurlock

Numerade Educator

02:18

Problem 26

Explain the basic principles of cyclotron function.

Monica Mame Soma Nyansa

Michigan Technological University

01:43

Problem 27

How does radiation affect living organisms?

Matthew Hurlock

Numerade Educator

02:35

Problem 28

Explain why different kinds of radiation affect biological tissues differently, even though the amount of radiation exposure may be the same.

Monica Mame Soma Nyansa

Michigan Technological University

01:43

Problem 29

Explain the significance of the biological effectiveness factor in measuring radiation exposure. What types of radiation would you expect to have the highest biological effectiveness factor?

Matthew Hurlock

Numerade Educator

02:44

Problem 30

Describe some of the medical uses of radioactivity in both the diagnosis and treatment of disease.

Monica Mame Soma Nyansa

Michigan Technological University

02:59

Problem 31

Write a nuclear equation for the indicated decay of each nuclide.
a. U-234 (alpha)
b. Th-230 (alpha)
c. $\mathrm{Pb}-214$ (beta)
d. $\mathrm{N}-13$ (positron emission)
e. Cr-51 (electron capture)

Matthew Hurlock

Numerade Educator

04:34

Problem 32

Write a nuclear equation for the indicated decay of each nuclide.
a. Po-210 (alpha)
b. Ac-227 (beta)
c. $\mathrm{Tl}-207$ (beta)
d. O-15 (positron emission)
e. Pd-103 (electron capture)

Monica Mame Soma Nyansa

Michigan Technological University

02:14

Problem 33

Write a partial decay series for Th-232 undergoing the sequential decays: $\alpha, \beta, \beta, \alpha$.

Grigoriy Sereda

Numerade Educator

04:24

Problem 34

Write a partial decay series for $\mathrm{Rn}-220$ undergoing the sequential decays: $\alpha, \alpha, \beta, \beta$.

Ryan Johnson

Numerade Educator

01:23

Problem 35

Fill in the missing particle in each nuclear equation.
a. $\qquad$
b. ${ }_{94}^{241} \mathrm{Pu} \longrightarrow{ }_{95}^{241} \mathrm{Am}+$ $\qquad$
c. ${ }_{11}^{19} \mathrm{Na} \longrightarrow{ }_{10}^{19} \mathrm{Ne}+$ $\qquad$
d. ${ }_3^{79} \mathrm{Se}+$ $\qquad$ $\longrightarrow{ }_{33}^{73} \mathrm{As}$

Nicole Mabante

Numerade Educator

01:23

Problem 36

Fill in the missing particle in each nuclear equation.
a. ${ }_{95}^{24} \mathrm{Am} \longrightarrow{ }_{93}^{237} \mathrm{~Np}+$ $\qquad$
b. $\qquad$ $\longrightarrow{ }_{92}^{233} \mathrm{U}+{ }_{-1}^0 \mathrm{e}$
c. ${ }_{93}^{237} \mathrm{~Np} \longrightarrow$ $\qquad$ $+{ }_2^4 \mathrm{He}$
d. ${ }_{35}^{75} \mathrm{Br} \longrightarrow \longrightarrow+{ }_{+1}^0 \mathrm{e}$

Nicole Mabante

Numerade Educator

02:37

Problem 37

Determine whether or not each nuclide is likely to be stable. State your reasons.
a. $\mathrm{Mg}-26$
b. $\mathrm{Ne}-25$
c. Co-51
d. Te-124

Matthew Hurlock

Numerade Educator

03:47

Problem 38

Determine whether or not each nuclide is likely to be stable. State your reasons.
a. $\mathrm{Ti}-48$
b. $\mathrm{Cr}-63$
c. Sn-102
d. Y-88

Monica Mame Soma Nyansa

Michigan Technological University

00:16

Problem 39

The first six elements of the first transition series have the following number of stable isotopes:
(TABLE CAN'T COPY)
Explain why Sc, V, and Mn each has only one stable isotope while the other elements have several.

Tiffany Noble

Numerade Educator

03:37

Problem 40

Neon and magnesium each have three stable isotopes, while sodium and aluminum each have only one. Explain why this might be so.

Monica Mame Soma Nyansa

Michigan Technological University

03:32

Problem 41

Predict a likely mode of decay for each unstable nuclide.
a. Mo-109
b. Ru-90
c. P-27
d. $\mathrm{Sn}-100$

Matthew Hurlock

Numerade Educator

04:33

Problem 42

Predict a likely mode of decay for each unstable nuclide.
a. $\mathrm{Sb}-132$
b. Te-139
c. Fr-202
d. Ba-123

Monica Mame Soma Nyansa

Michigan Technological University

00:34

Problem 43

Which nuclide of each pair would you expect to have the longer half-life?
a. Cs-113 or C5-125
b. $\mathrm{Fe}-62$ or $\mathrm{Fe}-70$

Tiffany Noble

Numerade Educator

04:39

Problem 44

Which one of each pair of nuclides would you expect to have the longer half-life?
a. Cs-149 or C5-139
b. $\mathrm{Fe}-45$ or $\mathrm{Fe}-52$

Monica Mame Soma Nyansa

Michigan Technological University

01:47

Problem 45

One of the nuclides in spent nuclear fuel is U-235, an alpha emitter with a half-life of 703 million years. How long will it take for the amount of U-235 to reach $10.0 \%$ of its initial amount?

Tiffany Noble

Numerade Educator

01:53

Problem 46

A patient is given $0.050 \mathrm{mg}$ of technetium $-99 \mathrm{~m}$, a radioactive isotope with a half-life of about 6.0 hours. How long does it take for the radioactive isotope to decay to $1.0 \times 10^{-3} \mathrm{mg}$ ?

Adriano Chikande

Numerade Educator

05:11

Problem 47

A radioactive sample contains $1.55 \mathrm{~g}$ of an isotope with a half-life of 3.8 days. What mass of the tsotope remains after 5.5 days?

Evelyn Clay

Numerade Educator

04:56

Problem 48

At $8: 00$ A.M., a patient receives a $1.5-\mu \mathrm{g}$ dose of $1-131$ to treat thyroid cancer. If the nuclide has a half-life of eight days, what mass of the nuclide remains in the patient at 5:00 P.M. the next day? (Assume no excretion of the nuclide from the body.)

Ryan Johnson

Numerade Educator

05:21

Problem 49

A sample of F-18 has an initial decay rate of $1.5 \times 10^5 \mathrm{dis} / \mathrm{s}$. How long will it take for the decay rate to fall to $2.5 \times 10^3 \mathrm{dis} / \mathrm{s}$ ? (F-18 has a half-life of 1.83 hours.)

Evelyn Clay

Numerade Educator

02:59

Problem 50

A sample of T1-201 has an initial decay rate of $5.88 \times 10^4 \mathrm{dis} / \mathrm{s}$. How long will it take for the decay rate to fall to 287 dis/s? (T1-201 has a half-life of 3.042 days.)

Joanna Josey

Numerade Educator

01:16

Problem 51

A wooden boat discovered just south of the Great Pyramid in Egypt has a carbon-14/carbon-12 ratio that is $72.5 \%$ of that found in living organisms. How old is the boat?

Tiffany Noble

Numerade Educator

03:21

Problem 52

A layer of peat beneath the glacial sediments of the last ice age has a carbon-14/carbon-12 ratio that is $22.8 \%$ of that found in living organisms. How long ago was this ice age?

Ryan Johnson

Numerade Educator

03:23

Problem 53

An ancient skull has a carbon- 14 decay rate of 0.85 disintegrations per minute per gram of carbon ( $0.85 \mathrm{dis} / \mathrm{min} \cdot \mathrm{gC}$ ). How old is the skull? (Assume that living organisms have a carbon-14 decay rate of $15.3 \mathrm{dis} / \mathrm{min} \cdot \mathrm{gC}$ and that carbon- 14 has a half-life of $5715 \mathrm{yr}$ )

Brooke Smith

Numerade Educator

03:37

Problem 54

A mammoth skeleton has a carbon-14 decay rate of 0.48 disintegrations per minute per gram of carbon $(0.48 \mathrm{dis} / \mathrm{min} \cdot \mathrm{gC}$ ). When did the mammoth live? (Assume that living organisms have a carbon- 14 decay rate of $15.3 \mathrm{dis} / \mathrm{min} \cdot \mathrm{gC}$ and that carbon- 14 has a half-life of $5715 \mathrm{yr}$ )

Brooke Smith

Numerade Educator

05:25

Problem 55

A rock from Australia contains $0.438 \mathrm{~g}$ of $\mathrm{Pb}-206$ to every $1.00 \mathrm{~g}$ of U-238. Assuming that the rock did not contain any $\mathrm{Pb}-206$ at the time of its formation, how old is the rock?

Brooke Smith

Numerade Educator

05:57

Problem 56

A meteor has a $\mathrm{Pb}-206 \mathrm{U}-238$ mass ratio of $0.855-1.00$. What is the age of the meteor?

Ryan Johnson

Numerade Educator

01:49

Problem 57

Write the nuclear reaction for the neutron-induced fission of U-235 to form Xe-144 and Sr-90. How many neutrons are produced in the reaction?

Matthew Hurlock

Numerade Educator

03:31

Problem 58

Write the nuclear reaction for the neutron-induced fission of U-235 to produce Te-137 and Zr-97. How many neutrons are produced in the reaction?

Monica Mame Soma Nyansa

Michigan Technological University

01:01

Problem 59

Write the nuclear equation for the fusion of two $\mathrm{H}-2$ atoms to form $\mathrm{He}-3$ and one neutron.

Tiffany Noble

Numerade Educator

00:55

Problem 60

Write the nuclear equation for the fusion of $\mathrm{H}-3$ with $\mathrm{H}-1$ to form $\mathrm{He}-4$.

Ryan Johnson

Numerade Educator

00:56

Problem 61

A breeder nuclear reactor is a reactor in which nonfissionable (nonfissile) U-238 is converted into fissionable (fissile) Pu-239. The process involves bombardment of $\mathrm{U}-238$ by neutrons to form $\mathrm{U}-239$, which then undergoes two sequential beta decays. Write nuclear equations for this process.

Tiffany Noble

Numerade Educator

02:40

Problem 62

Write the series of nuclear equations to represent the bombardment of $\mathrm{Al}-27$ with a neutron to form a product that subsequently undergoes a beta decay.

Monica Mame Soma Nyansa

Michigan Technological University

01:04

Problem 63

Rutherfordium-257 was synthesized by bombarding Cf-249 with C-12. Write the nuclear equation for this reaction.

Matthew Hurlock

Numerade Educator

03:33

Problem 64

Element 107, now named bohrium, was synthesized by German researchers by colliding bismuth-209 with chromium-54 to form a bohrium isotope and one neutron. Write the nuclear equation to represent this reaction.

Monica Mame Soma Nyansa

Michigan Technological University

02:22

Problem 65

If $1.0 \mathrm{~g}$ of matter is converted to energy, how much energy is formed?

Evelyn Clay

Numerade Educator

05:08

Problem 66

A typical home uses approximately $1.0 \times 10^3 \mathrm{kWh}$ of energy per month. If the energy came from a nuclear reaction, what mass would have to be converted to energy per year to meet the energy needs of the home?

Ryan Johnson

Numerade Educator

05:37

Problem 67

Calculate the mass defect and nuclear binding energy per nucleon of each nuclide.
a. $\mathrm{O}-16$ (atomic mass $=15.994915 \mathrm{amu})$
b. Ni-58 (atomic mass $=57.935346 \mathrm{amu})$
c. Xe-129 (atomic mass $=128.904780 \mathrm{amu}$ )

Matthew Hurlock

Numerade Educator

15:17

Problem 68

Calculate the mass defect and nuclear binding energy per nucleon of each nuclide.
a. $\mathrm{Li}-7$ (atomic mass $=7.016003 \mathrm{amu})$
b. Ti-48 (atomic mass $=47.947947 \mathrm{amu}$ )
c. Ag-107 (atomic mass $=106.905092 \mathrm{amu}$ )

Monica Mame Soma Nyansa

Michigan Technological University

06:24

Problem 69

Calculate the quantity of energy produced per gram of U-235 (atomic mass $=235.043922 \mathrm{amu}$ ) for the neutron-induced fission of U-235 to form Xe-144 (atomic mass $=143.9385 \mathrm{amu}$ ) and Sr-90 (atomic mass $=89.907738 \mathrm{amu})($ discussed in Problem 57).

Matthew Hurlock

Numerade Educator

07:00

Problem 70

Calculate the quantity of energy produced per mole of U-235 (atomic mass $=235.043922 \mathrm{amu}$ ) for the neutron-induced fission of U-235 to produce Te-137 (atomic mass $=136.9253 \mathrm{amu}$ ) and $\mathrm{Zr}-97$ (atomic mass $=96.910950 \mathrm{amu})($ discussed in Problem 58).

Ryan Johnson

Numerade Educator

07:40

Problem 71

Calculate the quantity of energy produced per gram of reactant for the fusion of two H-2 (atomic mass = $2.014102 \mathrm{amu}$ ) atoms to form He-3 (atomic mass $=3.016029 \mathrm{amu})$ and one neutron (discussed in Problem 59).

Rachel Hochberg

Numerade Educator

11:10

Problem 72

Calculate the quantity of energy produced per gram of reactant for the fusion of $\mathrm{H}-3$ (atomic mass $=3.016049 \mathrm{amu}$ ) with $\mathrm{H}-1$ (atomic mass $=1.007825 \mathrm{amu})$ to form He-4 (atomic mass $=4.002603 \mathrm{amu}$ ) (discussed in Problem 60).

Monica Mame Soma Nyansa

Michigan Technological University

01:53

Problem 73

A $75-\mathrm{kg}$ man has a dose of $32.8 \mathrm{rad}$ of radiation. How much energy is absorbed by his body? Compare this energy to the amount of energy absorbed by his body if he jumps from a chair to the floor (assume that the chair is $0.50 \mathrm{~m}$ from the ground and that the man absorbs all of the energy from the fall).

Matthew Hurlock

Numerade Educator

01:30

Problem 74

If a $55-\mathrm{g}$ laboratory mouse has a dose of $20.5 \mathrm{rad}$ of radiation, how much energy is absorbed by the mouse's body?

Adriano Chikande

Numerade Educator

01:44

Problem 75

PET studies require fluorine-18, which is produced in a cyclotron and decays with a half-life of 1.83 hours. Assuming that the F-18 can be transported at 60.0 miles/hour, how close must the hospital be to the cyclotron if $65 \%$ of the F-18 produced makes it to the hospital?

Tiffany Noble

Numerade Educator

07:30

Problem 76

Suppose a patient is given $155 \mu \mathrm{g}$ of $1-131$, a beta emitter with a half-life of 8.0 days. Assuming that none of the $1-131$ is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in $\mathrm{Ci}$ ) during those first four hours?

Joanna Josey

Numerade Educator

08:36

Problem 77

Complete each nuclear equation and calculate the energy change (in $\mathrm{J} / \mathrm{mol}$ of reactant) associated with each. $(\mathrm{Be}-9=9.012182 \mathrm{amu}$, Bi-209 $=208.980384 \mathrm{amu}, \mathrm{He}-4=4.002603 \mathrm{amu}$, Li-6 $=6.015122 \mathrm{amu}, \mathrm{Ni}-64=63.927969 \mathrm{amu}$, $\mathrm{Rg}-272=272.1535 \mathrm{amu}, \mathrm{Ta}-179=178.94593 \mathrm{amu}$, and $\mathrm{W}-179=178.94707 \mathrm{amu})$.
a. $\qquad$ $+{ }_4^9 \mathrm{Be} \longrightarrow{ }_3^6 \mathrm{Li}+{ }_2^{+} \mathrm{He}$
b. ${ }_{83}^{209} \mathrm{Bi}+{ }_{28}^{\mathrm{CH}} \mathrm{Ni} \longrightarrow{ }_{111}^{272} \mathrm{Rg}+$ $\qquad$
c. ${ }_7^{17} \mathrm{~W}+$ $\qquad$ $\longrightarrow{ }_{73}^{179} \mathrm{Ta}$

Adriano Chikande

Numerade Educator

08:14

Problem 78

Complete each nuclear equation and calculate the energy change (in $\mathrm{J} / \mathrm{mol}$ of reactant) associated with each. (Al-27 $=26.981538 \mathrm{amu}$, Am-241 $=241.056822 \mathrm{amu}, \mathrm{He}-4=4.002603 \mathrm{amu}$, $\mathrm{Np}-237=237.048166 \mathrm{amu}, \mathrm{P}-30=29.981801 \mathrm{amu}$, S-32 $=31.972071 \mathrm{amu}$, and Si-29 = $28.976495 \mathrm{amu})$.
a. ${ }_{13}^{27} \mathrm{Al}+{ }_2^4 \mathrm{He} \longrightarrow{ }_{15}^{30} \mathrm{P}+$ $\qquad$
b. ${ }_{10}^{32} \mathrm{~S}+\longrightarrow \longrightarrow{ }_{14}^{29} \mathrm{Si}+{ }_2^4 \mathrm{He}$
c. ${ }_{63}^{241} \mathrm{Am} \longrightarrow{ }_{63}^{237} \mathrm{~Np}+$ $\qquad$

Adriano Chikande

Numerade Educator

02:38

Problem 79

Write the nuclear equation for the most likely mode of decay for each unstable nuclide.
a. Ru-114
b. Ra-216
c. $\mathrm{Zn}-58$
d. $\mathrm{Ne}-31$

Matthew Hurlock

Numerade Educator

03:46

Problem 80

Write the nuclear equation for the most likely mode of decay for each unstable nuclide.
a. $\mathrm{Kr}-74$
b. Th-221
c. Ar-44
d. $\mathrm{Nb}-85$

Monica Mame Soma Nyansa

Michigan Technological University

02:15

Problem 81

Bismuth-210 is a beta emitter with a half-life of 5.0 days. If a sample contains $1.2 \mathrm{~g}$ of Bi-210 (atomic mass $=209.984105 \mathrm{amu}$ ), how many beta emissions occur in 13.5 days? If a person's body intercepts $5.5 \%$ of those emissions, to what amount of radiation (in $\mathrm{Ci}$ ) is the person exposed?

Tiffany Noble

Numerade Educator

11:01

Problem 82

Polonium-218 is an alpha emitter with a half-life of 3.0 minutes. If a sample contains $55 \mathrm{mg}$ of Po-218 (atomic mass = $218.008965 \mathrm{amu}$ ), how many alpha emissions occur in 25.0 minutes? If the polonium is ingested by a person, to what amount of radiation (in $\mathrm{Ci}$ ) is the person exposed?

Monica Mame Soma Nyansa

Michigan Technological University

01:48

Problem 83

Radium-226 (atomic mass $=226.025402 \mathrm{amu}$ ) decays to radon-224 (a radioactive gas) with a half-life of $1.6 \times 10^3$ years. What volume of radon gas (at $25.0^{\circ} \mathrm{C}$ and $1.0 \mathrm{~atm}$ ) does $25.0 \mathrm{~g}$ of radium produce in 5.0 days? (Report your answer to two significant digits.)

Tiffany Noble

Numerade Educator

03:49

Problem 84

In one of the neutron-induced fission reactions of U-235 (atomic mass $=235.043922 \mathrm{amu}$ ), the products are Ba-140 and Kr-93 (a radioactive gas). What volume of $\mathrm{Kr}-93$ (at $25.0^{\circ} \mathrm{C}$ and $1.0 \mathrm{~atm}$ ) is produced when $1.00 \mathrm{~g}$ of $\mathrm{U}-235$ undergoes this fission reaction?

Joanna Josey

Numerade Educator

01:05

Problem 85

When a positron and an electron annihilate one another, the resulting mass is completely converted to energy. Calculate the energy associated with this process in $\mathrm{kJ} / \mathrm{mol}$.

Tiffany Noble

Numerade Educator

03:43

Problem 86

A typical nuclear reactor produces about $1.0 \mathrm{MW}$ of power per day. What is the minimum rate of mass loss required to produce this much energy?

Monica Mame Soma Nyansa

Michigan Technological University

03:32

Problem 87

Find the binding energy in an atom of ${ }^3 \mathrm{He}$, which has a mass of $3.016030 \mathrm{amu}$.

Dindi Voils

Numerade Educator

04:12

Problem 88

The overall hydrogen burning reaction in stars can be represented as the conversion of four protons to one $\alpha$ particle. Use the data for the mass of $\mathrm{H}-1$ and $\mathrm{He}-4$ to calculate the energy released by this process.

Joanna Josey

Numerade Educator

00:58

Problem 89

The nuclide ${ }^{247}$ Es is made by bombardment of ${ }^{238} \mathrm{U}$ in a reaction that emits five neutrons. Identify the bombarding particle.

Tiffany Noble

Numerade Educator

01:03

Problem 90

The nuclide ${ }^6 \mathrm{Li}$ reacts with ${ }^2 \mathrm{H}$ to form two identical particles. Identify the particles.

Jenna Nikles

Numerade Educator

05:54

Problem 91

The half-life of ${ }^{238} \mathrm{U}$ is $4.5 \times 10^9 \mathrm{yr}$. A sample of rock of mass $1.6 \mathrm{~g}$ produces $29 \mathrm{dis} / \mathrm{s}$. Assuming all the radioactivity is due to ${ }^{238} \mathrm{U}$, find the percent by mass of ${ }^{239} \mathrm{U}$ in the rock.

Rashmi Sinha

Numerade Educator

05:47

Problem 92

The half-life of ${ }^{232} \mathrm{Th}$ is $1.4 \times 10^{10} \mathrm{yr}$. Find the number of disintegrations per hour emitted by $1.0 \mathrm{~mol}$ of ${ }^{232} \mathrm{Th}$.

Rashmi Sinha

Numerade Educator

07:25

Problem 93

A $1.50-\mathrm{L}$ gas sample at $745 \mathrm{~mm} \mathrm{Hg}$ and $25.0^{\circ} \mathrm{C}$ contains $3.55 \%$ radon-220 by volume. Radon- 220 is an alpha emitter with a halflife of $55.6 \mathrm{~s}$. How many alpha particles are emitted by the gas sample in 5.00 minutes?

Joanna Josey

Numerade Educator

07:51

Problem 94

A 228-mL sample of an aqueous solution contains $2.35 \% \mathrm{MgCl}_2$ by mass. Exactly half of the magnesium ions are $\mathrm{Mg}-28$, a beta emitter with a half-life of 21 hours. What is the decay rate of $\mathrm{Mg}-28$ in the solution after 4.00 days? (Assume a density of $1.02 \mathrm{~g} / \mathrm{mL}$ for the solution.)

Joanna Josey

Numerade Educator

02:39

Problem 95

When a positron and an electron collide and annihilate each other, two photons of equal energy are produced. Find the wavelength of these photons.

Matthew Hurlock

Numerade Educator

04:05

Problem 96

The half-life of ${ }^{235} \mathrm{U}$, an alpha emitter, is $7.1 \times 10^8 \mathrm{yr}$. Calculate the number of alpha particles emitted by $1.0 \mathrm{mg}$ of this nuclide in 1.0 minute.

Joanna Josey

Numerade Educator

03:33

Problem 97

Given that the energy released in the fusion of two deuterium atoms to ${ }^3 \mathrm{He}$ and a neutron is $3.3 \mathrm{MeV}$, and in the fusion to tritium and a proton it is $4.0 \mathrm{MeV}$. Calculate the energy change for the process ${ }^3 \mathrm{He}+{ }^1 \mathrm{n} \longrightarrow{ }^3 \mathrm{H}+{ }^1 \mathrm{p}$. Suggest an explanation for why this process occurs at much lower temperatures than either of the first two.

Joanna Josey

Numerade Educator

03:04

Problem 98

The nuclide ${ }^{18} \mathrm{~F}$ decays by both electron capture and $\beta^{+}$decay. Find the difference in the energy released by these two processes. The atomic masses are ${ }^{18} \mathrm{~F}=18.000950$ and ${ }^{18} \mathrm{O}=17.9991598$.

Jenna Nikles

Numerade Educator

07:19

Problem 99

The space shuttle carries about $72,500 \mathrm{~kg}$ of solid aluminum fuel, which is oxidized with ammonium perchlorate according to the reaction shown here:
$$
\begin{aligned}
& 10 \mathrm{Al}(\mathrm{s})+6 \mathrm{NH}_4 \mathrm{ClO}_4(\mathrm{~s}) \longrightarrow \\
& 4 \mathrm{Al}_2 \mathrm{O}_3(\mathrm{~s})+2 \mathrm{AlCl}_3(\mathrm{~s})+12 \mathrm{H}_2 \mathrm{O}(\mathrm{g})+3 \mathrm{~N}_2(\mathrm{~g})
\end{aligned}
$$
The space shuttle also carries about $608,000 \mathrm{~kg}$ of oxygen (which reacts with hydrogen to form gaseous water).
a. Assuming that aluminum and oxygen are the limiting reactants, determine the total energy produced by these fuels. ( $\Delta H_{\mathrm{f}}^{\mathrm{f}}$ for solid ammonium perchlorate is $-295 \mathrm{~kJ} / \mathrm{mol}$.)
b. Suppose that a future space shuttle is powered by matterantimatter annihilation. The matter is normal hydrogen (containing a proton and an electron), and the antimatter is antihydrogen (containing an antiproton and a positron). What mass of antimatter is required to produce the energy equivalent of the aluminum and oxygen fuel currently carried on the space shuttle?

Jenna Nikles

Numerade Educator

13:50

Problem 100

Suppose that an $85.0 \mathrm{~g}$ laboratory animal ingests $10.0 \mathrm{mg}$ of a substance that contained $2.55 \%$ by mass $\mathrm{Pu}-239$, an alpha emitter with a half-life of 24,110 years.
a. What is the animal's initial radiation exposure in curies?
b. If all of the energy from the emitted alpha particles is absorbed by the animal's tissues and if the energy of each emission is $7.77 \times 10^{-12} \mathrm{~J}$, what is the dose in rads to the animal in the first 4.0 hours following the ingestion of the radioactive material? Assuming a biological effectiveness factor of 20 , what is the 4.0 -hour dose in rems?

Joanna Josey

Numerade Educator

04:38

Problem 101

In addition to the natural radioactive decay series that begins with U-238 and ends with Pb-206, there are natural radioactive decay series that begin with U-235 and Th-232. Both of these series end with nuclides of $\mathrm{Pb}$. Predict the likely end product of each series and the number of a decay steps that occur.

Matthew Hurlock

Numerade Educator

03:06

Problem 102

The hydride of an unstable nuclide of a Group IIA metal, $\mathrm{MH}_2(s)$, decays by alpha emission. A $0.025-\mathrm{mol}$ sample of the hydride is placed in an evacuated 2.0-L container at $298 \mathrm{~K}$. After 82 minutes, the pressure in the container is $0.55 \mathrm{~atm}$. Find the halflife of the nuclide.

Joanna Josey

Numerade Educator

04:58

Problem 103

The nuclide ${ }^{38} \mathrm{Cl}$ decays by beta emission with a half-life of $37.2 \mathrm{~min}$. A sample of $0.40 \mathrm{~mol}$ of $\mathrm{H}^{38} \mathrm{Cl}$ is placed in a $6.24-\mathrm{L}$ container. After $74.4 \mathrm{~min}$, the pressure is $1650 \mathrm{mmHg}$. What is the temperature of the container?

Joanna Josey

Numerade Educator

03:40

Problem 104

When $\mathrm{BF}_3$ is bombarded with neutrons, the boron undergoes an $\alpha$ decay, but the $\mathrm{F}$ is unaffected. $\mathrm{A} 0.20$-mol sample of $\mathrm{BF}_3$ contained in a $3.0-\mathrm{L}$ container at $298 \mathrm{~K}$ is bombarded with neutrons until half of the $\mathrm{BF}_3$ has reacted. What is the pressure in the container at $298 \mathrm{~K}$ ?

Adriano Chikande

Numerade Educator

01:13

Problem 105

Closely examine the diagram representing the beta decay of fluorine- 21 and draw in the missing nucleus.
(FIGURE CAN'T COPY)

Matthew Hurlock

Numerade Educator

01:39

Problem 106

Approximately how many half-lives must pass for the amount of radioactivity in a substance to decrease to below $1 \%$ of its initial level?

Joanna Josey

Numerade Educator

00:48

Problem 107

A person is exposed for 3 days to identical amounts of two different nuclides that emit positrons of roughly equal energy. The half-life of nuclide $\mathrm{A}$ is 18.5 days, and the half-life of nuclide $B$ is 255 days. Which of the two nuclides poses the greater health risk?

Matthew Hurlock

Numerade Educator

04:00

Problem 108

Identical amounts of two different nuclides, an alpha emitter and a gamma emitter, with roughly equal half-lives are spilled in a building adjacent to your bedroom. Which of the two nuclides poses the greater health threat to you while you sleep in your bed? If you accidentally wander into the building and ingest equal amounts of the two nuclides, which one poses the greater health threat?

Monica Mame Soma Nyansa

Michigan Technological University

00:32

Problem 109

Drugstores in many areas now carry tablets, under such trade names as losat and NoRad, to be taken in the event of an accident at a nuclear power plant or a terrorist attack that releases radioactive material. These tablets contain potassium iodide (K1). Can you explain the nature of the protection that they provide?
(FIGURE CAN'T COPY)

Tiffany Noble

Numerade Educator

03:25

Problem 110

Complete the table of particles involved in radioactive decay.
(TABLE CAN'T COPY)

Audrey Fong

Numerade Educator

02:17

Problem 111

Have each group member study a different mode of radioactive decay (alpha, beta, gamma, positron emission, or electron capture) and present it to the group. Each presentation should include a description of the process, a description of how the atomic and mass numbers change, and at least one specific example. Presentations should also address the questions: What do all types of nuclear reactions have in common, and how do they differ from each other?

Matthew Hurlock

Numerade Educator

03:24

Problem 112

Two students were discussing whether or not the total mass changes during a nuclear reaction. The first student insists that mass is conserved. The second student says that mass is converted into energy. Explain the context in which each student is correct and how that fact is applied to solve problems.

Monica Mame Soma Nyansa

Michigan Technological University

01:23

Problem 113

Write all the balanced nuclear equations for each step of the nuclear decay sequence that starts with U-238 and ends with U-234. Refer to Figure 20.6 for the decay processes involved.

Matthew Hurlock

Numerade Educator

01:08

Problem 114

Radon-220 undergoes alpha decay with a half-life of 55.6 s. Assume there are 16,000 atoms present initially and make a table showing how many atoms will be present at $0 \mathrm{~s}, 55.6 \mathrm{~s}, 111.2 \mathrm{~s}, 166.8 \mathrm{~s}$, $222.4 \mathrm{~s}$, and $278.0 \mathrm{~s}$ (all multiples of the half-life). Now calculate how many atoms will be present at $50 \mathrm{~s}, 100 \mathrm{~s}$, and $200 \mathrm{~s}$ (not multiples of the half-life). Make a graph with the number of atoms present on the $y$-axis and total time on the $x$-axis.

Monica Mame Soma Nyansa

Michigan Technological University

02:41

Problem 115

A common isotope used in medical imaging is technetium $-99 \mathrm{~m}$, which emits gamma rays.
$$
{ }_{43}^{90 \mathrm{~m}} \mathrm{Tc} \longrightarrow{ }_{43}^9 \mathrm{Tc}+{ }_0^9 \gamma
$$
A sample initially containing $0.500 \mathrm{mg}$ of technetium- $99 \mathrm{~m}$ is monitored as a function of time. Based on its rate of gamma ray emission, a graph, showing the mass of active technetium $-99 \mathrm{~m}$ as a function of time, is prepared. Study the graph and answer the questions that follow.
(GRAPH CAN'T COPY)
a. What is the mass of technetium- $99 \mathrm{~m}$ present at 200 minutes? At 400 minutes?
b. What is the half-life of technetium- $99 \mathrm{~m}$ in minutes? In hours?
c. If a patient is given a $2.0-\mu \mathrm{g}$ dose of technetium $-99 \mathrm{~m}$, how much of it is left in the patient's body after 10 hours?

Matthew Hurlock

Numerade Educator