Chemistry A Molecular Approach

Nivaldo J. Tro

Chapter 20 Radioactivity and Nuclear Chemistry - all with Video Answers

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Chapter Questions

01:01

Problem 1

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

Tiffany Noble

Numerade Educator

00:59

Problem 2

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

Ryan Johnson

Numerade Educator

00:33

Problem 3

Define $A, Z,$ and $X$ in the following notation used to specify a nuclide: $\frac{A}{2} \mathrm{X}$ .

Tiffany Noble

Numerade Educator

01:11

Problem 4

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

Ryan Johnson

Numerade Educator

00:41

Problem 5

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

Tiffany Noble

Numerade Educator

00:49

Problem 6

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

Ryan Johnson

Numerade Educator

01:05

Problem 7

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

Tiffany Noble

Numerade Educator

00:49

Problem 8

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

Ryan Johnson

Numerade Educator

00:23

Problem 9

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

Tiffany Noble

Numerade Educator

01:34

Problem 10

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

Ryan Johnson

Numerade Educator

01:26

Explain why the ratio of neutrons to protons $(N / Z)$ 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

00:16

Problem 12

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

Ryan Johnson

Numerade Educator

00:57

Problem 13

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

Tiffany Noble

Numerade Educator

01:34

Problem 14

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

Ryan Johnson

Numerade Educator

00:53

Problem 15

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

Tiffany Noble

Numerade Educator

01:47

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?

Ryan Johnson

Numerade Educator

00:56

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 can be used to generate electricity.

Tiffany Noble

Numerade Educator

01:23

Problem 18

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

Ryan Johnson

Numerade Educator

00:30

Problem 19

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

Tiffany Noble

Numerade Educator

00:38

Problem 20

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

Ryan Johnson

Numerade Educator

00:47

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?

Tiffany Noble

Numerade Educator

00:27

Problem 22

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

Ryan Johnson

Numerade Educator

00:25

Problem 23

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

Tiffany Noble

Numerade Educator

00:42

Problem 24

Explain transmutation and provide one or two examples.

Ryan Johnson

Numerade Educator

00:28

Problem 25

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

Tiffany Noble

Numerade Educator

00:44

Problem 26

Explain the basic principles of cyclotron function.

Ryan Johnson

Numerade Educator

00:14

Problem 27

How does radiation affect living organisms?

Tiffany Noble

Numerade Educator

00:25

Problem 28

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

Ryan Johnson

Numerade Educator

00:28

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?

Tiffany Noble

Numerade Educator

01:25

Problem 30

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

Ryan Johnson

Numerade Educator

03:28

Problem 31

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

Tiffany Noble

Numerade Educator

07:15

Problem 32

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

Ryan Johnson

Numerade Educator

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

01:28

Problem 35

Fill in the missing particles in each nuclear equation.

Tiffany Noble

Numerade Educator

03:24

Problem 36

Fill in the missing particles in each nuclear equation.

Ryan Johnson

Numerade Educator

00:45

Problem 37

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

Tiffany Noble

Numerade Educator

02:51

Problem 38

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

Ryan Johnson

Numerade Educator

00:16

Problem 39

The first six elements of the first transition series have the following number of stable isotopes:
Explain why Sc, V, and Mn each have only one stable isotope while the other elements have several.

Tiffany Noble

Numerade Educator

01:18

Problem 40

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

Ryan Johnson

Numerade Educator

01:32

Problem 41

Predict a likely mode of decay for each unstable nuclide.
$$
\begin{array}{ll}{\text { a. } \operatorname{Mo-} 109} & {\text { b. } \operatorname{Ru}-90} \\ {\text { c. } \mathrm{P}-27} & {\text { d. } \operatorname{sn}-100}\end{array}
$$

Tiffany Noble

Numerade Educator

02:44

Problem 42

Predict a likely mode of decay for each unstable nuclide.
$$
\begin{array}{ll}{\text { a. } S b-132} & {\text { b. Te- } 139} \\ {\text { c. Fr-202 }} & {\text { d. } B a-123}\end{array}
$$

Ryan Johnson

Numerade Educator

00:34

Problem 43

Which nuclide in each pair would you expect to have the longer half-life?
$$
\begin{array}{l}{\text { a. } \mathrm{Cs}-113 \text { or } \mathrm{Cs}-125} \\ {\text { b. } \mathrm{Fe}-62 \text { or } \mathrm{Fe}-70}\end{array}
$$

Tiffany Noble

Numerade Educator

01:27

Problem 44

Which nuclide in each pair would you expect to have the longer half-life?
$$
\begin{array}{l}{\text { a. } \mathrm{Cs}-149 \text { or } \mathrm{Cs}-139} \\ {\text { b. } \mathrm{Fe}-45 \text { or } \mathrm{Fe}-52}\end{array}
$$

Ryan Johnson

Numerade Educator

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

03:48

Problem 46

A patient is given 0.050$\mu \mathrm{g}$ 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 $1.0 \times 10^{-3} \mu \mathrm{g}$ ? (Assume no excretion of the nuclide from the body.)

Ryan Johnson

Numerade Educator

00:57

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 isotope remains after 5.5 days?

Tiffany Noble

Numerade Educator

04:56

Problem 48

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

Ryan Johnson

Numerade Educator

01:55

Problem 49

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

Tiffany Noble

Numerade Educator

04:21

Problem 50

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

Ryan Johnson

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

01:16

Problem 53

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

Tiffany Noble

Numerade Educator

03:29

Problem 54

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

Ryan Johnson

Numerade Educator

02:32

Problem 55

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

Magnus Legemah

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? (Assume that the meteor did not contain any $\mathrm{Pb}-206$ at the time of its formation.)

Ryan Johnson

Numerade Educator

00:50

Problem 57

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

Tiffany Noble

Numerade Educator

02:08

Problem 58

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

Ryan Johnson

Numerade Educator

01:01

Problem 59

Write the nuclear equation for the fusion of two H-2 atoms to form 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 He- $.$

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 U- $239,$ which then undergoes two sequential beta decays. Write nuclear equations for this process.

Tiffany Noble

Numerade Educator

01:55

Problem 62

Write the series of nuclear equations to represent the bombardment of $A 1-27$ with a neutron to form a product that subsequently undergoes a beta decay.

Ryan Johnson

Numerade Educator

01:01

Problem 63

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

Tiffany Noble

Numerade Educator

01:50

Problem 64

Element $107,$ now named bohrium, was synthesized by German researchers by colliding bismuth-209 with chromium-s4 to form a bohrium isotope and one neutron. Write the nuclear equation to represent this reaction.

Ryan Johnson

Numerade Educator

00:41

Problem 65

If 1.0 g of matter is converted to energy, how much energy is formed?

Tiffany Noble

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

03:43

Problem 67

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

Tiffany Noble

Numerade Educator

09:31

Problem 68

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

Ryan Johnson

Numerade Educator

06:24

Problem 69

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

Matthew Hurlock

Numerade Educator

07:00

Problem 70

Calculate the quantity of energy produced per mole of $\mathrm{U}-235$ (atomic mass $-235.043922$ amu) for the neutron-induced fission of $\mathrm{U}-235$ to produce Te-137 (atomic mass $=136.9253$ amu) and $\mathrm{Zr-97}$ (atomic mass $=96.910950$ 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 $\mathrm{H}-2$ (atomic mass $=2.014102$ amu) atoms to form He-3 (atomic mass $=3.016029$ 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 $=3.016049$ amu) with $\mathrm{H}-1$ (atomic mass $=1.007825$ amu) to form He-4 (atomic mass $=4.002603$ amu) (discussed in Problem 60).

Monica Mame Soma Nyansa

Michigan Technological University

01:16

Problem 73

A 75 -kg human has a dose of 32.8 rad of radiation. How much energy is absorbed by the person's body? Compare this energy to the amount of energy absorbed by the person's body if he or she jumped from a chair to the floor (assume that the chair is 0.50 m from the ground and that all of the energy from the fall
is absorbed by the person).

Tiffany Noble

Numerade Educator

00:59

Problem 74

If a 55 -gram laboratory mouse has a dose of 20.5 rad of radiation, how much energy is absorbed by the mouse's body?

Rashmi Sinha

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

10:20

Problem 76

Suppose a patient is given 1.55$\mu \mathrm{g}$ of $1-131,$ a beta emitter with a half-life of 8.0 days. Assuming that none of the I-131 is eliminated from the person's body in the first 4.0 hours of treatment,
what is the exposure (in Ci) during those first four hours?

Monica Mame Soma Nyansa

Michigan Technological University

03:56

Problem 77

Complete each nuclear equation and calculate the energy change $\quad($ in $\mathrm{J} / \mathrm{mol}$ of reactant) associated with each $(\mathrm{Be}-9=9.012182$ amu, $\quad \mathrm{Bi}-209=208.980384$ amu, $\quad$ He- $4=$ 4.002603 amu, $\quad$ Li-6 $=6.015122$ amu, $\quad$ Ni-64 $=$ 63.927969 amu, $\quad \operatorname{Rg}-272=272.1535$ amu, $\quad$ Ta-1 $79=$ 178.94593 amu, and $\mathrm{W}-179=178.94707$ amu).

Tiffany Noble

Numerade Educator

18:49

Problem 78

Complete each nuclear equation and calculate the energy change (in $\mathrm{J} / \mathrm{mol}$ of reactant) associated with each $(\mathrm{Al}-27=$ 26.981538 amu, $\quad A m-241=241.056822$ amu, $\quad$ He $-4=$ 4.002603 amu, $\quad \mathrm{Np}-237=237.048166 \mathrm{amu}, \quad \mathrm{P}-30=$ 29.981801 amu, $\quad S-32=31.972071$ amu, $\quad$ and $\quad$ Si- $29=$
28.976495 amu).

Monica Mame Soma Nyansa

Michigan Technological University

01:54

Problem 79

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

Tiffany Noble

Numerade Educator

06:23

Problem 80

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

Ryan Johnson

Numerade Educator

02:15

Problem 81

Bismuth-210 is a beta emitter with a half-life of 5.0 days. If a sample contains 1.2 g of $B i-210$ (atomic mass $=$ 209.984105 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 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 mg of Po-218 (atomic mass = 218.008965 amu), how many alpha emissions occur in 25.0 minutes? If the polonium is ingested by a person, to what amount of radiation (in Ci) is the person exposed?

Monica Mame Soma Nyansa

Michigan Technological University

01:48

Problem 83

Radium-226 (atomic mass $=226.025402$ 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

01:45

Problem 84

In one of the neutron-induced fission reactions of $\mathrm{U}-235$ (atomic mass $=235.043922$ amu), the products are Ba-140 and $\mathrm{Kr}-93$ (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 fis- sion reaction?

Grigoriy Sereda

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 kJ/mol.

Tiffany Noble

Numerade Educator

00:41

Problem 86

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

Grigoriy Sereda

Numerade Educator

03:17

Problem 87

Find the binding energy in an atom of $^{3} \mathrm{He},$ which has a mass of 3.016030 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 $^{247}$ can be made by bombardment of $^{238} \mathrm{U}$ in a reaction that emits five neutrons. Identify the bombarding particle.

Tiffany Noble

Numerade Educator

01:29

Problem 90

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

Ryan Johnson

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 dis/s. Assuming all the radioactivity is due to $238 \mathrm{U},$ find the percent by mass of $^{238} \mathrm{U}$ 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

01:56

Problem 93

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

Tiffany Noble

Numerade Educator

07:51

Problem 94

A 228 -mL sample of an aqueous solution contains 2.35$\% \mathrm{MgCl}_{2}$ by mass. Exactly one-half of the magnesium ions are $\mathrm{Mg}-28, \mathrm{a}$ 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

01:16

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.

Tiffany Noble

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

01:32

Problem 97

Given that the energy released in the fusion of two deuterons to $\mathrm{a}^{3}$ 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.

Grigoriy Sereda

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

Jenna Nikles

Numerade Educator

26:54

Problem 100

Suppose that an 85.0 -gram 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.
$$
\begin{array}{l}{\text { a. What is the animal's initial radiation exposure in curies? }} \\ {\text { b. If all of the energy from the emitted alpha particles is }} \\ {\text { absorbed by the animal's tissues, and if the energy of each }} \\ {\text { emission is } 7.77 \times 10^{-12} \mathrm{J}, \text { what is the dose in rads to the animal }} \\ {\text { in the first } 4.0 \text { hours following the ingestion of the }}\\{\text { radioactive material? Assuming a biological effectiveness }} \\ {\text { factor of } 20, \text { what is the } 4.0 \text { -hour dose in rems? }}\end{array}
$$

Monica Mame Soma Nyansa

Michigan Technological University

02:32

Problem 101

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

Grigoriy Sereda

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. $\mathrm{A} 0.025$ -mol sample of the hydride is placed in an evacuated 2.0 $\mathrm{L}$ container at 298 $\mathrm{K}$ . After 82 minutes, the pressure in the container is 0.55 atm. Find the
half-life 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 min. A sample of 0.40 mol of $\mathrm{H}^{38} \mathrm{Cl}$ is placed in a 6.24 -L container. After 74.4 min the pressure is 1650 $\mathrm{mmHg}$ . What is the temperature of the container?

Joanna Josey

Numerade Educator

03:40

Problem 104

When $^{10} \mathrm{BF}_{3}$ is bombarded with neutrons, the boron-10 under-goes an $\alpha$ decay, but the $\mathrm{F}$ is unaffected. A 0.20 -mol sample of $^{10}\mathrm{BF}_{3}$ contained in a $3.0-\mathrm{L}$ container at 298 $\mathrm{K}$ is bombarded with neutrons until half of the $^{10} \mathrm{BF}_{3}$ has reacted. What is the pressure in the container at 298 $\mathrm{K} ?$

Adriano Chikande

Numerade Educator

00:32

Problem 105

Closely examine the diagram representing the beta decay of fluorine- 21 and draw in the missing nucleus.

Tiffany Noble

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

01:07

Problem 107

A person is exposed for three days to identical amounts of two different nuclides that emit positrons of roughly equal energy. The half-life of nuclide 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?

Brooke Smith

Numerade Educator

01:44

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 is likely to pose 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 of the two is likely to pose the greater health threat?

Grigoriy Sereda

Numerade Educator

00:32

Problem 109

Drugstores in many areas now carry tablets, under such trade names as losat and NoRad, designed 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 $(\mathrm{KI}) .$ Can you explain the nature of the protection that they provide? (Hint: see the label in the photo.)

Tiffany Noble

Numerade Educator

01:37

Problem 110

Complete the table of particles involved in radioactive decay.

Grigoriy Sereda

Numerade Educator

01:27

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 nuclear reactions have in common and how do they differ from each other?

Tiffany Noble

Numerade Educator

01:11

Problem 112

Two students are 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.

Grigoriy Sereda

Numerade Educator

01:23

Problem 113

Write all the balanced nuclear equation for each step of the nuclear decay sequence that starts with $\mathrm{U}-238$ and ends with $\mathrm{U}-234$ . Refer to Figure 20.6 for the decay processes involved.

Matthew Hurlock

Numerade Educator

03:36

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 s, $55.6 \mathrm{s},$ 11.2 s, $166.8 \mathrm{s}, 222.4 \mathrm{s},$ and 278.0 s (all multiples of the half-life). Now calculate how many atoms will be present at $50 \mathrm{s}, 100 \mathrm{s},$ and 200 s (not multiples of the half-life). Make a graph with number of atoms present on the $y$ -axis and total time on the $x$ -axis.

Monica Mame Soma Nyansa

Michigan Technological University

02:17

Problem 115

Radioisotopes are useful for medical diagnosis because once ingested the isotopes accumulate in various organs such as the liver, lungs, lymph nodes, and bones. The energy emitted from the decay of the isotopes provides a way to image an organ or bone.
The radioactive isotope Technetium-99 ("m" means metastable) is prepared by bombarding Molybdenum-99 with deuterons:
$$
\stackrel{99}{42} \mathrm{Mo}+\text { deuterons } \longrightarrow_{43}^{99 \mathrm{m}} \mathrm{Tc}+_{-1}^{0} \beta
$$
Once formed, 99 $\mathrm{m}$ Tc decays to $\frac{99}{43} \mathrm{Tc}$ by a release of gamma rays:
$$
_{43}^{99 \mathrm{m}} \mathrm{Tc} \longrightarrow_{43}^{99} \mathrm{Tc}+\stackrel{0}{0} \gamma
$$
Use the information provided in the question and the table to answer the following questions:
$$
\begin{array}{l}{\text { a. Given that all radioactive decay follows first-order kinetics, }} \\ {\text { determine the half-life of } _{43}^{99 \mathrm{m}} \mathrm{Tc}}\\{\text { b. Determine the decay constant, } k, \text { for }_{43}^{99 \mathrm{m}} \mathrm{Tc} \text { . }} \\ {\text { c. Complete the information in the table. }}\\{\text { d. How many atoms of } 99 \mathrm{m} \text { Tc are present at } t=0.0 \mathrm{h} ?} \\ {\text { e. How many atoms of } 9 \mathrm{gm} \text { Tc are present at } t=12.06 \mathrm{h} \text { ? }}\end{array}
$$

Hunza Gilgit

Numerade Educator