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College Physics

Roger A. Freedman; Todd Ruskell; Philip R. Kesten

Chapter 27

Nuclear Physics - all with Video Answers

Educators

Chapter Questions

01:20

Problem 1

What is an isotope?

Declan Nell
Declan Nell
Numerade Educator
03:42

Problem 2

What is the difference between atomic number and mass number?

Niamat Khuda
Niamat Khuda
Numerade Educator
02:07

Problem 3

(a) Describe what is meant by the phrase "larger nuclei are neutron rich." (b) Why do most nuclei contain at least as many neutrons as protons?

Declan Nell
Declan Nell
Numerade Educator
01:04

Problem 4

Some historians would claim that without Einstein's special theory of relativity, nuclear physics would never have developed. Explain why.

Declan Nell
Declan Nell
Numerade Educator
01:40

Problem 5

A simple idea of nuclear physics can be stated as follows: "The whole nucleus weighs less than the sum of its parts." Explain why.

Declan Nell
Declan Nell
Numerade Educator
00:55

Problem 6

Describe two characteristics of the binding energy that are comparable to the work function (from the photoelectric effect) and two characteristics that are dissimilar to the concept of the work function.

Keshav Singh
Keshav Singh
Numerade Educator
02:35

Problem 7

Describe the basic characteristics of the nuclear force that exists between nucleons. What other competing force between nucleons is present in the nucleus?

Declan Nell
Declan Nell
Numerade Educator
00:26

Problem 8

What is the difference between fission and fusion?

David Collins
David Collins
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01:13

Problem 9

(a) Which elements in the periodic table are more likely to undergo nuclear fission? (b) Which are more likely to undergo nuclear fusion?

Declan Nell
Declan Nell
Numerade Educator
01:12

Problem 10

Astronomy (a) Describe the nuclear reactions that occur in our Sun. (b) Discuss how the equilibrium state of the Sun is not permanent and discuss the eventual future of our solar system.

Keshav Singh
Keshav Singh
Numerade Educator
02:25

Problem 11

Explain how conservation of energy and momentum would be violated if a neutrino were not emitted in beta decay.

Declan Nell
Declan Nell
Numerade Educator
02:25

Problem 12

The decay constant of a radioactive nucleus is just that, constant. It does not depend on the size of the nuclear sample, the temperature, or any external fields (such as gravity, electricity, or magnetism). Define the decay constant and comment on how nuclear radioactivity would change if the quantity were dependent on temperature.

Declan Nell
Declan Nell
Numerade Educator
03:00

Problem 13

At any given instant a sample of radioactive uranium contains many, many different isotopes of atoms that are not uranium. Explain why.

Declan Nell
Declan Nell
Numerade Educator
02:52

Problem 14

(a) Explain how radioactive ${ }^{14} \mathrm{C}$ is used to determine the age of ancient artifacts. (b) Which types of artifacts can have their age determined in this way and which types cannot?

Declan Nell
Declan Nell
Numerade Educator
02:13

Problem 15

If atomic masses are used, explain why the mass of a beta particle is not accounted for in the basic beta decay
$$
\mathrm{n} \rightarrow \mathrm{p}^{+\mathrm{e}-+\mathrm{v}^{-}} \mathrm{e}^{n \rightarrow \mathrm{p}+\mathrm{e}^{-}+\bar{v}_{\mathrm{e}}}
$$ Assume that the mass of the antineutrino $\left(\mathrm{v}^{-} \mathrm{e}\right)^{\left(\bar{v}_{e}\right)}$ is very small and can be neglected.

Declan Nell
Declan Nell
Numerade Educator
03:12

Problem 16

Describe, in broad terms, the health risks associated with the three major forms of radioactivity: alpha, beta, and gamma. Focus on the dangers due to inherent health risks and the ability of each to penetrate shielding material.

Declan Nell
Declan Nell
Numerade Educator
01:25

Problem 17

In an atomic nucleus, the nuclear force binds _______ together.
A. electrons
B. neutrons
C. protons
D. neutrons and protons
E. neutrons, protons, and electrons

Mayank Tripathi
Mayank Tripathi
Numerade Educator
01:52

Problem 18

The mass of a nucleus is __________ the sum of the masses of its nucleons.
A. always less than
B. sometimes less than
C. always more than
D. always equal to
E. sometimes equal to

Declan Nell
Declan Nell
Numerade Educator
01:30

Problem 19

Which of the following statements is true?
A. Fusion absorbs energy and fission releases energy.
B. Fusion releases energy and fission absorbs energy.
C. Both fusion and fission absorb energy.
D. Both fusion and fission release energy.
E. Both fusion and fission can release or absorb energy.

Mayank Tripathi
Mayank Tripathi
Numerade Educator
01:24

Problem 20

In fission processes, which of the following statements is true?
A. Only the total number of nuclei remains the same.
B. Only the total number of protons remains the same.
C. Only the total number of neutrons remains the same.
D. The total number of protons and the total number of nuclei both remain the same.
E. The total number of protons and the total number of neutrons both remain the same.

Declan Nell
Declan Nell
Numerade Educator
01:28

Problem 21

In a spontaneous fission reaction the total mass of the products is _______ the mass of the original element.
A. greater than
B. less than
C. the same as
D. double
E. one-half

Declan Nell
Declan Nell
Numerade Educator
00:50

Problem 22

What is the source of the Sun's energy?
A. chemical reactions
B. fission reactions
C. fusion reactions
D. gravitational collapse
E. both fusion reactions and fission reactions

Mayank Tripathi
Mayank Tripathi
Numerade Educator
01:24

Problem 23

In a fusion reaction the total mass of the products is ________ the mass of the original elements.
A. greater than
B. less than
C. the same as
D. double
E. one-half

Declan Nell
Declan Nell
Numerade Educator
01:06

Problem 24

The decay constant $\lambda$ depends only on
A. the number of atoms at the initial time.
B. the initial decay rate.
C. the half-life.
D. the binding energy per nucleon.
E. whether the decay is alpha, beta, or gamma.

Declan Nell
Declan Nell
Numerade Educator
01:24

Problem 25

The number of radioactive atoms in a radioactive sample
A. decreases linearly with time.
B. increases linearly with time.
C. decreases exponentially with time.
D. increases exponentially with time.
E. remains constant.

Mayank Tripathi
Mayank Tripathi
Numerade Educator
01:15

Problem 26

The decay rate for a sample of any isotope
A. decreases linearly with time.
B. increases linearly with time.
C. decreases exponentially with time.
D. increases exponentially with time.
E. remains constant.

Declan Nell
Declan Nell
Numerade Educator
05:47

Problem 27

Estimate the relative size of the nuclear force compared to the electrostatic force between two adjacent protons in the nucleus.

Declan Nell
Declan Nell
Numerade Educator
05:55

Problem 28

Estimate the density of an atomic nucleus compared to the density of an atom.

Declan Nell
Declan Nell
Numerade Educator
00:28

Problem 29

Estimate the energy released in a typical nuclear reaction compared to that in a typical chemical reaction.

Keshav Singh
Keshav Singh
Numerade Educator
00:48

Problem 30

Estimate the ratio of the nuclear force between two nucleons when they are separated by a distance of $1.0 \mathrm{fm}$ compared to a separation distance of $2.0$ $\mathrm{fm} .$

Keshav Singh
Keshav Singh
Numerade Educator
03:05

Problem 31

Estimate the number of half-lives that must go by before $10 \%$ of an isotope remains. What about $1 \%$ ?

Declan Nell
Declan Nell
Numerade Educator
01:46

Problem 32

Estimate the mass of an object the size of a basketball that has the density of an atomic nucleus.

Declan Nell
Declan Nell
Numerade Educator
05:18

Problem 33

Estimate the number of nuclei that are present in a 50 -kg human body.

Declan Nell
Declan Nell
Numerade Educator
03:37

Problem 34

If the half-life of a radioactive isotope is 1 day, (a) estimate how long it takes before the sample is reduced to $62.5 \%$ of its original amount and (b) how long before it is reduced to $6.25 \%$ of its original amount.

Declan Nell
Declan Nell
Numerade Educator
06:53

Problem 35

(a) Using a spreadsheet or programmable calculator, calculate the binding energy per nucleon for the following isotopes of the five least massive elements. Masses given are atomic masses.
(c) Compare your results and comment on any patterns or trends that are obvious.

Steven Hammari
Steven Hammari
Numerade Educator
03:38

Problem 36

Provide the elemental abbreviation (e.g., ${ }^{16} \mathrm{O}$ for oxygen-16) and give the number of protons, the number of neutrons, and the mass number for each of the following isotopes:
A. hydrogen-3
B. beryllium-8
C. aluminum-26
D. gold-197
E. technetium-100
F. tungsten-184
G. osmium-190
H. plutonium-239

Declan Nell
Declan Nell
Numerade Educator
03:26

Problem 36

37. - Calculate the radius of each of the nuclei in problem 36.

Declan Nell
Declan Nell
Numerade Educator
03:21

Problem 36

Name the element and give the number of protons, the number of neutrons, and the mass number for each of the following nuclei:
A. ${ }^{2} \mathrm{H}$
B. ${ }^{4} \mathrm{He}$
C. ${ }^{6} \mathrm{Li}$
D. $^{12} \mathrm{C}$
E. $^{56} \mathrm{Fe}$
F. $^{90} \mathrm{Sr}$
G. 131 I
$\mathrm{H} \quad 235 \mathrm{I} \mathrm{J}$

Declan Nell
Declan Nell
Numerade Educator
02:17

Problem 39

If our Sun $(\operatorname{mass}=1.99 \times 1030 \mathrm{~kg}$, radius $=6.96 \times 108 \mathrm{~m}$ ),
(mass $=1.99 \times 10^{30} \mathrm{~kg}$, radius $=6.96 \times 10^{8} \mathrm{~m}$ ), were to collapse into a neutron star (an object composed of tightly packed neutrons with roughly the same density as a nucleus), what would the new radius of our "neutron-sun" be?

Declan Nell
Declan Nell
Numerade Educator
03:47

Problem 40

Given that a nucleus is approximately spherical and has a radius $\mathrm{r}=\mathrm{r} 0 \mathrm{~A} 1 / 3^{r}=r_{0} A^{1 / 3}$ (where $r_{0}$ is about $1.2 \mathrm{fm}$ ), determine its approximate mass density. Express your answer in SI units and convert to tons per cubic inch, units that might be used in a news report.

Declan Nell
Declan Nell
Numerade Educator
05:43

Problem 41

Calculate the atomic mass of each of the isotopes listed below. Give your answer in atomic mass units (u) and in grams (g). The values will include the mass of $Z$ electrons.
A. ${ }^{1} \mathrm{H}$
B. ${ }^{4} \mathrm{He}$
C. ${ }^{9} \mathrm{Be}$
D. ${ }^{12} \mathrm{C}$
E. $^{56} \mathrm{Fe}$
F. $^{90} \mathrm{Sr}$
G. 131 I
H. $^{238} \mathrm{U}$

Keshav Singh
Keshav Singh
Numerade Educator
02:35

Problem 42

What is the binding energy of carbon-12? Give your answer in MeV.

Declan Nell
Declan Nell
Numerade Educator
07:21

Problem 43

What is the binding energy per nucleon for the following isotopes? $\underline{\text { Example } 27-3}$
A. ${ }^{2} \mathrm{H}$
B. ${ }^{4} \mathrm{He}$
C. ${ }^{6} \mathrm{Li}$
D. ${ }^{12} \mathrm{C}$
E. $56 \mathrm{Fe}$
F. $^{90} \mathrm{Sr}$
G. $129 \mathrm{I}$
H. $^{235} \mathrm{U}$

Declan Nell
Declan Nell
Numerade Educator
03:14

Problem 44

What minimum energy is needed to remove a neutron from ${ }^{40} \mathrm{Ca}$ and so convert it to ${ }^{39} \mathrm{Ca}$ ? The atomic masses of the two isotopes are $39.96259098$ and $38.97071972 \mathrm{u}$, respectively.

Declan Nell
Declan Nell
Numerade Educator
02:40

Problem 45

What is the binding energy of the last neutron of carbon-13? The atomic mass of carbon-13 is $13.003355$ u.

Declan Nell
Declan Nell
Numerade Educator
02:33

Problem 46

Iodine-131 is a radioactive isotope that is used in the treatment of cancer of the thyroid. The natural tendency of the thyroid to take up iodine creates a pathway for which radiation $\left(\beta^{-}\right.$ and $\gamma$ ) that is emitted from this unstable nucleus can be directed onto the cancerous tumor with very little collateral damage to surrounding healthy tissue. Another advantage of the isotope is its relatively short half-life (8 days). Calculate the binding energy of iodine-131 and the binding energy per nucleon. The mass of iodine-131 is 130.906124 u.

Declan Nell
Declan Nell
Numerade Educator
03:16

Problem 47

Calculate the energy released in the following nuclear fission reaction:
$$
239 \mathrm{Pu}+\mathrm{n} \rightarrow 98 \mathrm{Tc}+138 \mathrm{Sb}+4 n^{239} \mathrm{Pu}+\mathrm{n} \rightarrow{ }^{98} \mathrm{Tc}+{ }^{138} \mathrm{Sb}+4 \mathrm{n}
$$
The atomic masses are $239 \mathrm{Pu}=239.052157 \mathrm{u}^{239} \mathrm{Pu}=239.052157 \mathrm{u}$
$98 \mathrm{Tc}=97.907215 \mathrm{u},{ }^{98} \mathrm{Tc}=97.907215 \mathrm{u}$, and $138 \mathrm{Sb}=137.940793 \mathrm{u}$ ${ }^{138} \mathrm{Sb}=137.940793 \mathrm{u}$.

Declan Nell
Declan Nell
Numerade Educator
03:58

Problem 48

Complete the following nuclear fission reaction of thorium-232 and calculate the energy released in the reaction: $232 \mathrm{Th}+\mathrm{n} \rightarrow 99 \mathrm{Kr}+124 \mathrm{Xe}+$ ${ }^{232} \mathrm{Th}+\mathrm{n} \rightarrow{ }^{99} \mathrm{Kr}+{ }^{124} \mathrm{Xe}+_{-} ?$ ? The atomic masses are
$020051 \mathrm{u}^{232} \mathrm{Th}=232.038051 \mathrm{u}$. ${ }^{99} \mathrm{Kr}=98.957606 \mathrm{u}$, and $124 \mathrm{Xe}=123.905894 \mathrm{u}^{124} \mathrm{Xe}=123.905894 \mathrm{u} .$

Declan Nell
Declan Nell
Numerade Educator
04:04

Problem 49

Complete the following fission reactions:
A. $235 \mathrm{U}+\mathrm{n} \rightarrow 128 \mathrm{Sb}+101 \mathrm{Nb}^{+}_{-} ?_{-}{ }^{235} \mathrm{U}+\mathrm{n} \rightarrow{ }^{128} \mathrm{Sb}+{ }^{101} \mathrm{Nb}+_{-} ?$
B. $235 \mathrm{U}+\mathrm{n} \rightarrow_{-} ?_{-}+116 \mathrm{Pd}+4 \mathrm{n}^{235} \mathrm{U}+\mathrm{n} \rightarrow_{-} ?_{-}+{ }^{116} \mathrm{Pd}+4 \mathrm{n}$
C. $238 \mathrm{U}+\mathrm{n} \rightarrow 99 \mathrm{Kr}+_{-} ?_{-}+11 \mathrm{n}^{238} \mathrm{U}+\mathrm{n} \rightarrow{ }^{99} \mathrm{Kr}+_{-} ?+11 \mathrm{n}$
D. $_{-} ?_{-}+n \rightarrow 101 \mathrm{Rb}+130 \mathrm{Cs}+8 \mathrm{n}_{-} ?-+\mathrm{n} \rightarrow{ }^{101} \mathrm{Rb}+{ }^{130} \mathrm{Cs}+8 \mathrm{n}$

Declan Nell
Declan Nell
Numerade Educator
04:05

Problem 50

Complete the following fission reactions: A. $242 \mathrm{Am}^{+}-?_{-} \rightarrow 90 \mathrm{Sr}+149 \mathrm{La}+4 \mathrm{n}^{242} \mathrm{Am}+\ldots ?-\rightarrow{ }^{90} \mathrm{Sr}+{ }^{149} \mathrm{La}+4 \mathrm{n}$
B. $244 \mathrm{~Pa}+\mathrm{n} \rightarrow-?{ }^{2}+131 \mathrm{Sb}+12 \mathrm{n}^{244} \mathrm{~Pa}+\mathrm{n} \rightarrow-?{-}^{131} \mathrm{Sb}+12 \mathrm{n}$
C. $\quad$ ? $-n+92 \mathrm{Se}+153 \mathrm{Sm}+6 \mathrm{n}-?-+\mathrm{n}+{ }^{92} \mathrm{Se}+{ }^{153} \mathrm{Sm}+6 \mathrm{n}$
D. $262 \mathrm{Fm}+\mathrm{n} \rightarrow 112 \mathrm{Rh}^{+}_{-} ?_{-}+9 \mathrm{n}^{262} \mathrm{Fm}+\mathrm{n} \rightarrow{ }^{112} \mathrm{Rh}+{ }_{-} ?+9 \mathrm{n}$

Declan Nell
Declan Nell
Numerade Educator
04:09

Problem 51

Calculate the energy (in MeV) released in the following nuclear fission reaction:
$$
242 \mathrm{Am}^{+}_{-} ?_{-} \rightarrow 90 \mathrm{Sr}+149 \mathrm{La}+4 \mathrm{n}^{242} \mathrm{Am}+{ }_{-} ? \rightarrow{ }^{90} \mathrm{Sr}+{ }^{149} \mathrm{La}+4 \mathrm{n}
$$
Start by completing the reaction and use the following nuclear masses:
$242 \mathrm{Am}=242.059549 \mathrm{u},^{242} \mathrm{Am}=242.059549 \mathrm{u}, 90 \mathrm{Sr}=89.9077387 \mathrm{u}$ ${ }^{90} \mathrm{Sr}=89.9077387 \mathrm{u}$ and $149 \mathrm{La}=148.934733 \mathrm{u}^{149} \mathrm{La}=148.934733 \mathrm{u}$.

Declan Nell
Declan Nell
Numerade Educator
02:13

Problem 52

Assuming that in a fission reactor a neutron loses half its energy in each collision with an atom of the moderator, determine how many collisions are required to slow a 200-MeV neutron to an energy of $0.04 \mathrm{eV}$.

Declan Nell
Declan Nell
Numerade Educator
03:53

Problem 53

Knowing that the binding energy per nucleon for uranium-235 is about $7.6 \mathrm{MeV} /$ nucleon and the binding energy per nucleon for typical fission fragments is about $8.5 \mathrm{MeV} /$ nucleon, find an average energy release per uranium-235 fission reaction in MeV.

Declan Nell
Declan Nell
Numerade Educator
04:49

Problem 54

How many kilograms of uranium-235 must completely fission to produce $1000 \mathrm{MW}$ of power continuously for one year?

Declan Nell
Declan Nell
Numerade Educator
03:51

Problem 55

Repeat problem 54 in the more realistic case where the fission reactions are about $30 \%$ efficient in producing $1000 \mathrm{MW}$ of power over 1 year of continuous operation.

Declan Nell
Declan Nell
Numerade Educator
03:37

Problem 56

Calculate the number of fission reactions per second that take place in a 1000-MW reactor. Assume that $200 \mathrm{MeV}$ of energy is released in each reaction.

Declan Nell
Declan Nell
Numerade Educator
05:33

Problem 57

Complete the following fusion reactions:
A. $2 \mathrm{H}+3 \mathrm{H} \rightarrow 4 \mathrm{He}^{+} \longrightarrow ?{ }^{2} \mathrm{H}+{ }^{3} \mathrm{H} \rightarrow{ }^{4} \mathrm{He}+\underline{?}$
?. $4 \mathrm{H}+4 \mathrm{He} \rightarrow 7 \mathrm{Be}+\ldots ?{ }^{4} \mathrm{H}+{ }^{4} \mathrm{He} \rightarrow{ }^{7} \mathrm{Be}+\ldots ?$
C. $2 \mathrm{H}+2 \mathrm{H} \rightarrow 3 \mathrm{He}+\underline{?}-{ }^{2} \mathrm{H}+{ }^{2} \mathrm{H} \rightarrow{ }^{3} \mathrm{He}+\underline{?}$
D. $2 \mathrm{H}+1 \mathrm{H} \rightarrow \mathrm{Y}^{+}-?{ }^{2} \mathrm{H}+{ }^{1} \mathrm{H} \rightarrow \gamma+\ldots^{?}$
E. $2 \mathrm{H}+2 \mathrm{H} \rightarrow 3 \mathrm{H}+\underline{?}{ }^{2} \mathrm{H}+{ }^{2} \mathrm{H} \rightarrow{ }^{3} \mathrm{H}+\underline{ }^{?}=$

Declan Nell
Declan Nell
Numerade Educator
01:29

Problem 58

Give your answers in MeV.

Zulfiqar Ali
Zulfiqar Ali
Numerade Educator
09:58

Problem 59

Astronomy Consider the proton-proton cycle that occurs in most stars (including our own Sun): Step $1: 1 \mathrm{H}+1 \mathrm{H} \rightarrow 2 \mathrm{H}+\mathrm{e}++\mathrm{ve}^{1} \mathrm{H}+{ }^{1} \mathrm{H} \rightarrow{ }^{2} \mathrm{H}+\mathrm{e}^{+}+v_{\mathrm{e}}$
Step $2: 2 \mathrm{H}+1 \mathrm{H} \rightarrow 3 \mathrm{He}+\mathrm{Y}^{2} \mathrm{H}+{ }^{1} \mathrm{H} \rightarrow{ }^{3} \mathrm{He}+\gamma$
Step $3: 3 \mathrm{He}+3 \mathrm{He} \rightarrow 4 \mathrm{He}+21 \mathrm{H}+{ }^{3} \mathrm{He}+{ }^{3} \mathrm{He} \rightarrow{ }^{4} \mathrm{He}+2{ }^{1} \mathrm{H}+\gamma$
Calculate the net energy released from the three steps. Do not ignore the mass of the positron in step $1 .$ (You may ignore the mass of the neutrino.)

Keshav Singh
Keshav Singh
Numerade Educator
02:59

Problem 60

The fissionability parameter is defined as the atomic number squared divided by the mass number for any given nucleus $\left(Z^{2} / A\right) .$ It can be shown that when this parameter is less than 44 , a nucleus will be stable against small deformation; essentially, the nucleus will be stable against spontaneous fission. Calculate the value of this parameter for (a) ${ }^{235} \mathrm{U},(\mathrm{b})^{238} \mathrm{U},(\mathrm{c})^{239} \mathrm{Pu}$, (d) ${ }^{240} \mathrm{Pu},(\mathrm{e})^{246} \mathrm{Cf}$, and (f) ${ }^{254} \mathrm{Cf}$.

Declan Nell
Declan Nell
Numerade Educator
02:46

Problem 60

Each fusion reaction of deuterium $\left({ }^{2} \mathrm{H}\right)$ and tritium $\left({ }^{3} \mathrm{H}\right)$ releases about $20 \mathrm{MeV}$. What mass of tritium is needed to create $10^{14} \mathrm{~J}$ of energy, the same as that released by exploding 25,000 tons of TNT? Assume that an endless supply of deuterium is available.

Declan Nell
Declan Nell
Numerade Educator
04:20

Problem 61

How many fusion reactions per second must be sustained to operate a deuterium-tritium fusion power plant that outputs $1000 \mathrm{MW}$, operating at $33 \%$ efficiency? Example $27-4$

Declan Nell
Declan Nell
Numerade Educator
04:14

Problem 62

Complete the following conversions:
A. $100 \mu \mathrm{Ci}=$ __________ $\mathrm{Ba}^{100} \mu \mathrm{Ci}=$ ___________ Bq
B. 1500 decays $/ \mathrm{min}=$ 1500 decays $/ \min =$ __________ Bq
C. $16,500 \mathrm{~Bq}=$ ________ $\mathrm{Ci} 16,500 \mathrm{~Bq}=$ _____ $\mathrm{Ci}$
D. $7.55 \times 1010 \mathrm{~Bq}=$ ____________ decays/min

Mayank Tripathi
Mayank Tripathi
Numerade Educator
02:18

Problem 63

The curie unit is defined as $1 \mathrm{Ci}=3.7 \times 1010 \mathrm{~Bq}, 1 \mathrm{Ci}=3.7 \times 10^{10} \mathrm{~Bq}$, which is about the rate at which radiation is emitted by $1.00 \mathrm{~g}$ of radium. (a) Calculate the half-life of radium from the definition. (b) What does your calculation tell you about the radiation emission rate of radium?

Declan Nell
Declan Nell
Numerade Educator
01:31

Problem 64

A certain radioactive isotope has a decay constant of $0.00334 \mathrm{~s}^{-1}$. Find the half-life in seconds and days.

Mayank Tripathi
Mayank Tripathi
Numerade Educator
02:15

Problem 65

A radioactive sample is monitored with a radiation detector which registers 5640 counts per minute. Twelve hours later, the detector reads 1410 counts per minute. Calculate the decay constant and the half-life of the sample.

Mayank Tripathi
Mayank Tripathi
Numerade Educator
02:25

Problem 65

A radioactive sample is monitored with a radiation detector which registers 5640 counts per minute. Twelve hours later, the detector reads 1410 counts per minute. Calculate the decay constant and the half-life of the sample.

Mayank Tripathi
Mayank Tripathi
Numerade Educator
02:00

Problem 66

What fraction of a sample of 32 p will be left after 4 months? Its half-life is $14.3$ days.

Mayank Tripathi
Mayank Tripathi
Numerade Educator
02:16

Problem 67

What fraction of a radioactive sample will be left after 6 half-lives? What about $7.5$ half-lives?

Mayank Tripathi
Mayank Tripathi
Numerade Educator
01:43

Problem 68

Medical A patient is injected with $7.88 \mu$ Ci of radioactive iodine-131 that has a half-life of $8.02$ days. Assuming that $90 \%$ of the iodine ultimately finds its way to the thyroid, what decay rate do you expect to find in the thyroid after 30 days?

Declan Nell
Declan Nell
Numerade Educator
05:15

Problem 69

The ratio of carbon- 14 to carbon-12 in living wood is $1.3 \times 10^{-12}$ $1.3 \times 10^{-12}$. How many decays per second are there in 550 g of wood?

Declan Nell
Declan Nell
Numerade Educator
03:49

Problem 70

You take a course in archaeology that includes field work. An ancient wooden totem pole is excavated from your archaeological dig. The beta decay rate is measured at 150 decays/min. If the totem pole contains 225 g of carbon and the ratio of carbon-14 to carbon-12 in living trees is $1.3 \times 10-12$, $1.3 \times 10^{-12}$, what is the age of the pole?

Declan Nell
Declan Nell
Numerade Educator
02:05

Problem 72

Determine the decay rate for 500 g of carbon from a tree limb twelve centuries after it is cut off.

Declan Nell
Declan Nell
Numerade Educator
02:21

Problem 72

How many nuclei of radon-222 are present in a sample for which you measure 485 decays/min?

Declan Nell
Declan Nell
Numerade Educator
03:40

Problem 73

The ages of rocks that contain fossils can be determined using the isotope ${ }^{87} \mathrm{Rb}$. This isotope of rubidium undergoes beta decay with a half-life of $4.75 \times 1010 \mathrm{y}^{4.75 \times 10^{10} \mathrm{y}}$. Ancient samples contain a ratio of ${ }^{87} \mathrm{Sr}$ to ${ }^{87} \mathrm{Rb}$
of $0.0225 .$ Given that ${ }^{87} \mathrm{Sr}$ is a stable product of the beta decay of ${ }^{87} \mathrm{Rb}$, and there was originally no ${ }^{87} \mathrm{Sr}$ present in the rocks, calculate the age of the rock sample. Assume that the decay rate is constant over the relatively short lifetime of the rock compared to the half-life of ${ }^{87} \mathrm{Rb}$.

Ivan Kochetkov
Ivan Kochetkov
Numerade Educator
03:22

Problem 74

Complete the following alpha decays:

Declan Nell
Declan Nell
Numerade Educator
01:16

Problem 75

Complete the following beta decays:
A. $14 \mathrm{C} \rightarrow \mathrm{e}^{-+} \mathrm{v}^{-} \mathrm{e}^{+}_{-} ?_{-}{ }^{14} \mathrm{C} \rightarrow \mathrm{e}^{-}+\bar{v}_{\mathrm{e}}+_{-} ?$
B. $239 \mathrm{~Np} \rightarrow \mathrm{e}^{-+} \mathrm{v}^{-} \mathrm{e}^{+}_{-} ?_{-}^{239} \mathrm{~Np} \rightarrow \mathrm{e}^{-}+\bar{v}_{\mathrm{e}}+_{-} ?$

Declan Nell
Declan Nell
Numerade Educator
01:35

Problem 76

Complete the following gamma decays:
A. $131 \mathrm{I}^{*} \rightarrow \mathrm{Y}^{+}_{-} ?_{-}^{131} \mathrm{I}^{*} \rightarrow \gamma+{ }_{-} ?_{-}$
B. $145 \mathrm{Pm}^{*} \rightarrow 145 \mathrm{Pm}+_{-} ?_{-}{ }^{145} \mathrm{Pm}^{*} \rightarrow{ }^{145} \mathrm{Pm}+_{-} ?$
C. $_{-} ?_{-} \rightarrow \mathrm{Y}+24 \mathrm{Na}^{-} ? \rightarrow \gamma+{ }^{24} \mathrm{Na}$

Mayank Tripathi
Mayank Tripathi
Numerade Educator
05:04

Problem 77

Nickel-64 has an excited state $1.34 \mathrm{MeV}$ above the ground state. The atomic mass of the ground state of this isotope of nickel is $63.927967$ u. (a) What is the mass of the atom when the nucleus is in this excited state? (b) What is the wavelength of the gamma ray that is emitted when the nucleus decays to the ground state?

Declan Nell
Declan Nell
Numerade Educator
03:14

Problem 78

78. ? (a) What is the approximate radius of the ${ }^{238} \mathrm{U}$ nucleus? (b) What electric force do two protons on opposite ends of the ${ }^{238} \mathrm{U}$ nucleus exert on each other? (c) If the electric force in part (b) were the only force acting on the protons, what would be their acceleration just as they left the nucleus? (d) Why do the protons in part (b) not accelerate apart?

Declan Nell
Declan Nell
Numerade Educator
04:33

Problem 79

The semi-empirical binding energy formula is given as follows:
$$
\begin{array}{l}
\begin{array}{l}
\mathrm{EB}=(15.8 \mathrm{MeV}) \mathrm{A}-(17.8 \mathrm{MeV}) \mathrm{A} 2 / 3 \\
-1) \mathrm{A} 1 / 3-(23.7 \mathrm{MeV})(\mathrm{N}-\mathrm{Z}) 2 \mathrm{~A} \\
E_{B}=(15.8 \mathrm{MeV}) A-(17.8 \mathrm{MeV}) A^{2 / 3} \\
-(0.71 \mathrm{MeV}) \frac{Z(Z-1)}{A^{1 / 3}}-(23.7 \mathrm{MeV}) \frac{(N-Z)^{2}}{A}
\end{array}
\end{array}
$$
where $A$ is the mass number, $N$ is the number of neutrons, and $Z$ is the number of protons. Using the formula, calculate the binding energy per nucleon for fermium-252. Compare your answer with the standard common expression for the binding energy: EB=(Nmn+Zmp-mwhole)c2 $E_{B}=\left(N m_{\mathrm{n}}+Z m_{\mathrm{p}}-m_{\text {whole }}\right) c^{2}$.

Declan Nell
Declan Nell
Numerade Educator
02:33

Problem 81

The stable isotope of sodium is ${ }^{23} \mathrm{Na}$. What kind of radioactivity would be expected from (a) ${ }^{22} \mathrm{Na}$ and (b) ${ }^{24} \mathrm{Na}$ ?

Declan Nell
Declan Nell
Numerade Educator
02:58

Problem 82

82. $^{\circ}$ In 2010 physicists first created element number 117 (tennessine, Ts) by colliding ${ }^{48} \mathrm{Ca}$ and ${ }^{249} \mathrm{Bk}$ nuclei. The result was two isotopes of the new element, one of which had a half-life of $14 \mathrm{~ms}$ and contained 176 neutrons.
(a) What is the radius of the nucleus of the new element 117 ? (b) What percent of the newly created isotope was left $1.0 \mathrm{~s}$ after its creation?

Declan Nell
Declan Nell
Numerade Educator
05:02

Problem 83

Natural uranium is made up of two isotopes: ${ }^{235} \mathrm{U}$ and ${ }^{238} \mathrm{U}$. The halflife of ${ }^{235} \mathrm{U}$ is $7.04 \times 108 \mathrm{y}, 7.04 \times 10^{8} \mathrm{y}$, and the half-life of ${ }^{238} \mathrm{U}$ is $4.47 \times 109 \mathrm{y}$ $4.47 \times 10^{9} \mathrm{y}$. Assuming that all uranium isotopes were created simultaneously and in equal amounts at the same time that Earth was formed, estimate the age of Earth. The current percent abundance of ${ }^{235} \mathrm{U}$ is $0.72 \%$ and for ${ }^{238} \mathrm{U}$ it is $99.28 \% . \underline{\text { Example } 27-7}$

Declan Nell
Declan Nell
Numerade Educator
04:02

Problem 84

The atom technetium (Tc) has no stable isotopes, yet its spectral lines have been detected in red giant stars (stars at the end of their lifetimes). Tc can be produced artificially on Earth. Its longest-lived isotope, ${ }^{98} \mathrm{Tc}$, has a half-life of $4.2$ million years. (a) If any ${ }^{98}$ Tc was present when Earth formed $4.5 \times 109 \mathrm{y} 4.5 \times 10^{9} \mathrm{y}$ ago, what percentage of it is still present? (Careful! You cannot do this calculation with your calculator. You must use logarithms to express the answer in scientific notation.) (b) What percent of the original ${ }^{98} \mathrm{Tc}$ would be present in a red giant that is 10 billion years old? (Careful again! You'll need to use logarithms.) (c) Explain why the detection of technetium in old stars is strong evidence that stars manufacture the atoms in the universe.

Declan Nell
Declan Nell
Numerade Educator
02:11

Problem 85

An old wooden bowl unearthed in an archeological dig is found to have one-fourth of the amount of carbon-14 present in a similar sample of fresh wood. Determine the age of the bowl.

Declan Nell
Declan Nell
Numerade Educator
02:10

Problem 86

In an attempt to determine the age of the cave paintings in ChauvetPont-d'Arc Cave in France, scientists used carbon-14 dating to measure the age of bones of bears found in the cave. The bears are depicted in the paintings, so presumably the bones are approximately the same age as the paintings. The results showed that the level of ${ }^{14} \mathrm{C}$ was reduced to $2.35 \%$ of its present-day level. How old were the bones (and presumably the paintings)?

Declan Nell
Declan Nell
Numerade Educator
05:25

Problem 87

In one common type of household smoke detector, the radioactive isotope americium-241 decays by alpha emission. The alpha particles produce a small electrical current because they are charged. If smoke enters the detector, it blocks the alpha particles, which reduces the current and causes the alarm to go off. The half-life of ${ }^{241} \mathrm{Am}$ is $433 \mathrm{y}$, and its atomic weight is $241 \mathrm{~g} / \mathrm{mol}$. Typical decay rates in smoke detectors are 690 Bq. (a) Write the alpha decay reaction of ${ }^{241} \mathrm{Am}$ and identify the daughter nucleus. (b) By how much does the alpha particle current decrease in $1.0$ y due to the decay of the americium? How much in 50 y? (c) How many grams of ${ }^{241} \mathrm{Am}$ are there in a typical smoke detector?

Keshav Singh
Keshav Singh
Numerade Educator
02:50

Problem 88

In March 2011 a giant tsunami struck the Fukushima nuclear reactor in Japan, resulting in very large radiation leaks, including cesium-137. The isotope has a 30-y half-life and is a beta-minus emitter. (a) What daughter nucleus is left after cesium-137 decays? (b) How long after the release will it take for the decay rate of the cesium-137 to be reduced by $99 \%$ ?

Declan Nell
Declan Nell
Numerade Educator
06:25

Problem 89

Three isotopes of aluminum are given in the following table:
$$
\begin{array}{ccc}
\text { Isotope } & \text { Atomic mass (u) } & \boldsymbol{E}_{\mathbf{B}} / \text { nucleon } & \text { Decay process } \\
\hline{ }^{26} \mathrm{Al} & 25.986892 & & \\
{ }^{27} \mathrm{Al} & 26.981538 & & \text { stable } \\
{ }^{28} \mathrm{Al} & 27.981910 & & \\
\hline
\end{array}
$$
Calculate the binding energy per nucleon for each isotope and make a prediction of the decay processes for the unstable isotopes aluminum-26 andaluminum-28.

Keshav Singh
Keshav Singh
Numerade Educator
03:15

Problem 90

Biology In February 2010 it was announced that water containing the carcinogen tritium $\left({ }^{3} \mathrm{H}\right)$ was leaking from aging pipes at 27 U.S. nuclear reactors. In one well in Vermont, contaminated water registered 70,500 $\mathrm{pCi} / \mathrm{L} ;$ the federal safety limit was $20,000 \mathrm{pCi} / \mathrm{L}$. Tritium is a $\beta^{-}$ emitter with a half-life of $12.3 \mathrm{y} .$ (a) How many protons and neutrons does the tritium nucleus contain? (b) Write out the decay equation for tritium and identify the daughter nucleus. (c) If the leak at the Vermont site is stopped, how long will it take for the water in the contaminated well to reach the federal safety level?

Keshav Singh
Keshav Singh
Numerade Educator
03:43

Problem 91

91. - Medical Iodine-125 is used to treat, among other things, brain tumors and prostate cancer. It decays by gamma decay with a half-life of $59.4$ days. Patients who fly soon after receiving ${ }^{125}$ I implants are given medical statements from the hospital verifying such treatment because their radiation could set off radiation detectors at airports. If the initial decay rate was 525 $\mu \mathrm{Ci}$, (a) what will the rate be at the end of the first year, and (b) how many months after the treatment will the decay rate be reduced by $90 \%$ ?

Declan Nell
Declan Nell
Numerade Educator
04:01

Problem 92

t Medical Ruthenium-106 is used to treat melanoma in the eye. This
isotope decays by $\beta^{-}$ emission with a half-life of $373.59$ days. One source of the isotope is reprocessed nuclear reactor fuel. (a) How many protons and neutrons does the ${ }^{106}$ Ru nucleus contain? (b) Could we expect to find significant amounts of 106 Ru in ore mined from the ground? Why or why not?
(c) Write the decay equation for ${ }^{106} \mathrm{Ru}$ and identify the daughter nucleus. (d) How many years after ${ }^{106} \mathrm{Ru}$ is implanted in the eye does it take for its decay rate to be reduced by $75 \%$ ? Example $27-5$

Keshav Singh
Keshav Singh
Numerade Educator
04:03

Problem 93

You are asked to prepare a sample of ruthenium-106 for a radiation treatment. Its half-life is $373.59$ days, it is a beta emitter, its atomic weight is $106 / \mathrm{g} / \mathrm{mol}$, and its density at room temperature is $12.45 \mathrm{~g} / \mathrm{cm}^{2}$. (a) How many grams will you need to prepare a sample having an activity rate of $125 \mu \mathrm{Ci}$ ? (b) If the sample in part (a) is a spherical droplet, what will be its radius?

Keshav Singh
Keshav Singh
Numerade Educator
02:16

Problem 94

Electron capture by a proton is not allowed in nature. Explain why. Specifically, describe why the following nuclear reaction does not occur (and for good reason!):
$$
\mathrm{e}^{-+} \mathrm{p} \rightarrow \mathrm{n}+\mathrm{ve}^{\mathrm{e}^{-}+\mathrm{p} \dashv \mathrm{n}+v_{\mathrm{e}}}
$$

Declan Nell
Declan Nell
Numerade Educator
04:27

Problem 95

95. $^{\circ \circ}$ Taking into account the recoil (kinetic energy) of the daughter nucleus, calculate the kinetic energy of the alpha particle in the following decay of a $235 \mathrm{U}$ nucleus at rest: $\underline{\text { Example } 27-6}$
$$
235 \mathrm{U} \rightarrow \alpha+231 \mathrm{Th}^{235} \mathrm{U} \rightarrow \alpha+{ }^{231} \mathrm{Th}
$$

Declan Nell
Declan Nell
Numerade Educator
08:25

Problem 96

Several radioactive decay series are observed in nature. Four of the most well known are as shown here. The neptunium decay series actually is extinct. The first three all end in different, stable isotopes of lead.
A. Thorium decay series: $\mathrm{A}=4 \mathrm{n} A=4 n$ Starting isotope: ${ }^{232}$ Th Ending isotope: ${ }^{208} \mathrm{~Pb}$
B. Radium or uranium decay series: $\mathrm{A}=4 \mathrm{n}+2 \mathrm{~A}=4 n+2$ Starting isotope: ${ }^{238} \mathrm{U}$ Ending isotope: ${ }^{206} \mathrm{~Pb}$
C. Actinium decay series: $\mathrm{A}=4 \mathrm{n}+3 \mathrm{~A}=4 n+3$ Starting isotope: ${ }^{235} \mathrm{U}$ Ending isotope: ${ }^{207} \mathrm{~Pb}$
D. Neptunium decay series: $\mathrm{A}=4 \mathrm{n}+1^{A}=4 n+1$ Starting isotope: ${ }^{237}$ Np Ending isotope: ${ }^{209} \mathrm{Bi}$
Trace out the pathway (keeping count of the total number of alpha and beta emissions) that terminates with a stable nucleus for each of the radioactive decay series above.

Keshav Singh
Keshav Singh
Numerade Educator
03:07

Problem 97

A friend suggests that the world's energy problems could be solved if only physicists were to pursue the fusion of heavy nuclei rather than the fusion of light nuclei. To prove his point he suggests that the following fusion reaction should be considered: $157 \mathrm{Nd}+80 \mathrm{Ge} \rightarrow 235 \mathrm{U}+2 \mathrm{n}$.
$$
{ }^{157} \mathrm{Nd}+{ }^{80} \mathrm{Ge} \rightarrow{ }^{235} \mathrm{U}+2 \mathrm{n}
$$
Using the insights that you have acquired in this chapter, show that his argument is flawed. The atomic mass of neodymium-157 is $156.939032$ u, and the mass of germanium-80 is $79.925373 \mathrm{u}$.

Declan Nell
Declan Nell
Numerade Educator