Essential College Physics

Andrew F. Rex, Richard Wolfson

Chapter 25

Nuclear Physics - all with Video Answers

Educators

Chapter Questions

Problem 1

How can a nuclide be unstable and yet still occur in nature?

Shahab Ullah

Shahab Ullah

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Problem 2

Explain (without using a formula) why the nuclei ${ }^{60} \mathrm{Fe}$ and ${ }^{60} \mathrm{Co}$ should have the same radius.

Shahab Ullah

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Problem 3

Which do you expect to have a greater number of stable isotopes:
Sn or $\mathrm{Sb} ?$

Shahab Ullah

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Problem 4

Why does the atomic number $Z$ determine chemical properties, while the chemical properties are largely independent of the neutron number $N$ ?

Shahab Ullah

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Problem 5

The nuclide ${ }^{79} \mathrm{Br}$ is stable. Would you expect ${ }^{75} \mathrm{Br}$ to be stable or unstable? Why?

Shahab Ullah

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Problem 6

Explain why ${ }^{31} \mathrm{P}$ is stable, but ${ }^{32} \mathrm{P}$ and ${ }^{37} \mathrm{P}$ are not.

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Problem 7

Why is a stable nucleus with $Z>N$ unlikely? Are there any such stable nuclei?

Shahab Ullah

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Problem 8

The isotopes ${ }^{75} \mathrm{Br}$ and ${ }^{85} \mathrm{Br}$ are both beta emitters. Which is more likely to be the $\beta^{-}$ emitter and which the $\beta^{+}$ emitter?

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Problem 9

How can you tell whether a particular nuclide is a good candidate for alpha decay? How can you prove it using atomic masses?

Km Neeraj

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Problem 10

In $\beta^{+}$ decay, a proton in the nucleus changes into a neutron and a positron is emitted. How is this possible, given that the neutron's mass is larger than the proton's?

Km Neeraj

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Problem 11

What are some limitations of radiocarbon dating using ${ }^{14} \mathrm{C} ?$

Shahab Ullah

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Problem 12

Explain why ${ }^{222} \mathrm{Rn}$ occurs in the uranium decay series.

Km Neeraj

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Problem 13

The gray and sievert are both units of radiation dose, both equal to 1 joule of absorbed energy per kilogram. What's the difference between the two units?

Shahab Ullah

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Problem 14

In his experiments with neutron bombardment of uranium, Fermi noticed an increase in the measured activity if the incoming neutrons were first slowed by passing them through paraffin. Why did this happen?

Km Neeraj

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Problem 15

Is it possible for a nuclear reaction to occur even if the mass of the products exceeds that of the initial particles?

Km Neeraj

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Problem 16

In nuclear fission, which has more mass, reactants or products? Is the same true for fusion?

Shahab Ullah

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Problem 17

The number of neutrons in ${ }^{90} \mathrm{Zr}$ is $(\mathrm{a}) 50 ;(\mathrm{b}) 51 ;(\mathrm{c}) 52 ;$ (d) $53 .$

Shahab Ullah

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Problem 18

The approximate density of any nucleus is
(a) $4 \times 10^{15} \mathrm{~kg} / \mathrm{m}^{3}$
(b) $6 \times 10^{16} \mathrm{~kg} / \mathrm{m}^{3} ;$
(c) $2 \times 10^{17} \mathrm{~kg} / \mathrm{m}^{3}$;
(d) $6 \times 10^{18} \mathrm{~kg} / \mathrm{m}^{3}$

Narayan Hari

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Problem 19

The ratio of the diameter of the ${ }^{104} \mathrm{Pd}$ nucleus to that of ${ }^{26} \mathrm{Mg}$ is approximately
(a) 1.4 ;
(b) 1.6
(c) 1.8 ;
(d) 2.0 .

Shahab Ullah

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Problem 20

The total binding energy of a stable nucleus with mass number 60 is about
(a) $100 \mathrm{MeV}$
(b) $300 \mathrm{MeV}$
(c) $400 \mathrm{MeV}$
(d) $500 \mathrm{MeV}$

Narayan Hari

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Problem 21

Of these four nuclides, the one with the largest total binding energy is
(a) $^{55} \mathrm{Mn}$
(b) $^{66} \mathrm{Zn} ;$
(c) $^{72} \mathrm{Ge}$;
(d) ${ }^{84} \mathrm{Kr}$

Km Neeraj

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Problem 22

Of these four nuclides, the one with the largest binding energy per nucleon is
(a) ${ }^{60} \mathrm{Ni}$
(b) ${ }^{96} \mathrm{Mo} ;$
(c) ${ }^{113} \mathrm{In}$
(d) ${ }^{146} \mathrm{Nd}$.

Km Neeraj

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Problem 23

The $\beta^{-}$ decay of ${ }^{20} \mathrm{O}$ produces $(\mathrm{a}){ }^{21} \mathrm{O} ;(\mathrm{b}){ }^{20} \mathrm{~F} ;(\mathrm{c}){ }^{20} \mathrm{~N} ;(\mathrm{d}){ }^{21} \mathrm{~F}$

Shahab Ullah

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Problem 24

What's the approximate energy release in alpha decay of ${ }^{226} \mathrm{Ac}$ ?
(a) $2.5 \mathrm{MeV}$
(b) $4.0 \mathrm{MeV}$
(c) $5.5 \mathrm{MeV}$
(d) $7.0 \mathrm{MeV}$.

Narayan Hari

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Problem 25

The isotope ${ }^{17} \mathrm{~F}$ has a $65-\mathrm{s}$ half-life. If you start with a $10-\mathrm{g}$ sample of ${ }^{17} \mathrm{~F},$ after $32.5 \mathrm{~s}$ the amount remaining is
(a) $7.5 \mathrm{~g}$;
(b) $7.1 \mathrm{~g}$
(c) $6.2 \mathrm{~g}$
(d) $5.0 \mathrm{~g}$.

Shahab Ullah

Numerade Educator

Problem 26

Iodine-131's half-life is 8.0 days. Ten percent of the original sample of this isotope remains after
(a) 22.7 days;
(b) 24.9 days;
(c) 26.6 days;
(d) 28.1 days.

Shahab Ullah

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Problem 27

Complete the following fission process: ${ }^{1} n+{ }^{235} \mathrm{U} \rightarrow{ }^{144} \mathrm{Ba}+$ _____ $+2^{1} n \cdot(\mathrm{a})^{88} \mathrm{Kr},(\mathrm{b}){ }^{89} \mathrm{Kr},(\mathrm{c}){ }^{90} \mathrm{Kr},(\mathrm{d}){ }^{91} \mathrm{Kr}$.

Shahab Ullah

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Problem 28

Complete the following fusion process: ${ }^{3} \mathrm{He}+{ }^{4} \mathrm{He} \rightarrow{ }^{6} \mathrm{Li}+$ _____.
(a) $^{1} n ;(\mathrm{b}){ }^{1} \mathrm{H} ;(\mathrm{c}){ }^{2} \mathrm{H} ;$ (d) ${ }^{2} \mathrm{He}$

Shahab Ullah

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Problem 29

Write the isotope symbol $A X$ for nuclei with (a) 24 protons and 25 neutrons; (b) 43 protons and 51 neutrons; (c) 82 protons and 108 neutrons.

Shahab Ullah

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Problem 30

What are the neutron numbers of these nuclides:
(a) ${ }^{13} \mathrm{C}$;
(b) $^{51} \mathrm{~V} ;$
(c) $^{79} \mathrm{Br}$,
(d) ${ }^{136} \mathrm{Ba}$ ?

Shahab Ullah

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Problem 31

Find the numbers of protons and neutrons in ${ }^{80} \mathrm{Br}$ and ${ }^{80} \mathrm{Kr}$.

Shahab Ullah

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Problem 32

Write out the full nuclide symbol ${ }_{Z}^{A} X$ for the following isotopes:
(a) oxygen-17;
(b) xenon-139;
(c) iridium-191;
(d) lead-208.

Shahab Ullah

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Problem 33

Find the nuclear radii for
(a) ${ }^{7} \mathrm{Li} ;$
(b) ${ }^{20} \mathrm{Ne} ;$
(c) ${ }^{133} \mathrm{Cs} ;$
(d) ${ }^{239} \mathrm{Pu}$.

Shahab Ullah

Numerade Educator

Problem 34

(a) What's the ratio of the diameters of the nuclei ${ }^{77}$ Se and ${ }^{14} \mathrm{~N} ?$
(b) What's the ratio of the densities of these nuclei?

Shahab Ullah

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Problem 35

What's the nuclide whose nuclear diameter is closest to twice that of the ${ }^{27} \mathrm{Al}$ nucleus?

Shahab Ullah

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Problem 36

Find a stable nucleus with half the volume of the ${ }^{46} \mathrm{Ti}$ nucleus.

Km Neeraj

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Problem 37

Consider a large nucleus with diameter $10 \mathrm{fm}$. (a) Suppose an electron is confined within this nucleus. Use the Heisenberg uncertainty principle (Chapter 23 ) to estimate the electron's minimum kinetic energy. (b) Electrons emitted in beta decay normally have kinetic energies on the order of $1 \mathrm{MeV}$. Use this fact to argue that an electron cannot be confined to a nucleus.

Narayan Hari

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Problem 38

Compute the binding energy of (a) ${ }^{14} \mathrm{~N}$ and ( $\mathrm{b}$ ) ${ }^{28} \mathrm{Si}$.

Narayan Hari

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Problem 39

For the two nuclides in the preceding problem, compute the binding energy per nucleon. Compare with the data shown in Figure $25.5 .$

Narayan Hari

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Problem 40

(a) Which nuclide do you expect to have the larger binding energy per nucleon: ${ }^{136} \mathrm{Ba}$ or ${ }^{144} \mathrm{Sm} ?$ (b) Calculate the binding energy per nucleon for both.

Km Neeraj

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Problem 41

Suppose that the centers of the two protons in a ${ }^{4}$ He nucleus are separated by approximately $2.0 \mathrm{fm} .$ Find the electrostatic energy associated with the repulsive force between the protons. Compare with the binding energy of the ${ }^{4}$ He nucleus.

Narayan Hari

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Problem 42

How much energy is required to remove one proton from a ${ }^{16} \mathrm{O}$ nucleus?

Narayan Hari

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Problem 43

(a) Find the energy to remove (a) one proton and (b) one neutron from a ${ }^{32} \mathrm{~S}$ nucleus. (c) Explain the difference between your answers to parts (a) and (b).

Km Neeraj

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Problem 44

Mirror nuclides are pairs with the numbers $Z$ and $N$ reversed, such as ${ }^{21}$ Ne and ${ }^{21}$ Na. (a) Find the binding energies of ${ }^{21}$ Ne and ${ }^{21} \mathrm{Na}$. (b) What does the size of the difference between their binding energies suggest about the charge independence of the strong force?

Km Neeraj

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Problem 45

(a) Use the astronomical data from Appendix $\mathrm{E}$ to find the binding energy of the Earth-Sun system. (b) How much energy would be required to remove the Earth completely from the solar system? (c) How would the mass of the Earth-Sun system change if Earth were removed from the solar system?

Narayan Hari

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Problem 46

Write the full reactions for the alpha decay of (a) ${ }^{205} \mathrm{At}$ (b) $^{216} \mathrm{Rn} ;(\mathrm{c})^{211} \mathrm{Ac}$

Shahab Ullah

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Problem 47

Write the full reactions for the $\beta^{-}$ decay of $(\mathrm{a})^{67} \mathrm{Cu} ;(\mathrm{b})^{85} \mathrm{Kr}$
(c) $^{112} \mathrm{Pd}$.

Shahab Ullah

Numerade Educator

Problem 48

Write the full reactions for the $\beta^{-}$ decay of (a) ${ }^{67} \mathrm{Cu} ;$ (b) ${ }^{85} \mathrm{Kr}$
(c) ${ }^{112} \mathrm{Pd}$ ____ (b) $^{66} \mathrm{Ge} \rightarrow$_____ $+\beta^{+} ;(\mathrm{c})^{213} \mathrm{Ac} \rightarrow$ _____ $+{ }^{4} \mathrm{He}^{*}(\mathrm{~d})$ _____ $\rightarrow^{210} \mathrm{Bi}+\gamma$.

Km Neeraj

Numerade Educator

Problem 49

Complete the following reactions:
(a) ${ }^{158} \mathrm{Tm}+\beta^{-} \rightarrow$ ____
(b) ${ }^{178} \mathrm{Hf} \rightarrow{ }^{178} \mathrm{Lu}+$ _____
(c) ${ }^{216} \mathrm{Fr} \rightarrow{ }^{212} \mathrm{At}+$ _____
(d) ${ }^{8} \mathrm{Be} \rightarrow$ _____ $+{ }^{4} \mathrm{He}$

Km Neeraj

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Problem 50

Find the energy released in the alpha decay of ${ }^{227} \mathrm{Ac}$

Km Neeraj

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Problem 51

Find the energy released in the $\beta^{-}$ decay of ${ }^{210} \mathrm{~Pb}$.

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Problem 52

Determine whether the following nuclides will undergo alpha decay: (a) $^{214}$ Po; (b) ${ }^{199} \mathrm{Hg}(\mathrm{mass}=198.968262 \mathrm{u})$

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Problem 53

In The EPA estimates that the limit for safe exposure to indoor radon- 222 is $4 \mathrm{pCi}$ per liter of air. (a) What is this activity in $\mathrm{Bq} ?$ (b) At this rate, how many nuclei decay in 1 day?

Shahab Ullah

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Problem 54

Trace the steps in the uranium series that lead to ${ }^{222} \mathrm{Rn}$, listing all the decays starting with ${ }^{238} \mathrm{U}$ and ending with ${ }^{222} \mathrm{Rn}$.

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Problem 55

An alpha particle and $\beta^{-}$ particle, each with kinetic energy $40 \mathrm{keV},$ are sent through a 1.5 - $\mathrm{T}$ magnetic field. The particles move perpendicular to the field, as in Figure $25.6 .$ Find the curvature radius for each particle's trajectory. Hint: The kinetic energy is small enough to neglect relativity.

Km Neeraj

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Problem 56

You begin with 50,000 radioactive nuclei, and after $2.5 \mathrm{~h}$ only 12,500 of them remain. What's the half-life of this nuclide?

Shahab Ullah

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Problem 57

Oxygen-15, used in PET scans, has a 2.0-min half-life. A hospital cyclotron produces $2.60 \mathrm{mg}$ of ${ }^{15} \mathrm{O} .$
(a) It's delivered to the diagnostic facility 6.0 min later. How much ${ }^{15} \mathrm{O}$ remains at this time? (b) After another $4.0 \mathrm{~min}$, the ${ }^{15} \mathrm{O}$ is injected into a patient. How much is there at that point?

Narayan Hari

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Problem 58

A radioactive sample containing $125 \times 10^{15}$ nuclei has activity $2.57 \times 10^{12} \mathrm{~Bq} .$ What's this nuclide's half-life?

Shahab Ullah

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Problem 59

The activity of a ${ }^{60}$ Co sample measures at $3.90 \times 10^{11} \mathrm{~Bq}$ What's the mass of the cobalt-60?

Shahab Ullah

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Problem 60

Potassium is an essential element that normally comprises about $0.30 \%$ of a person's body mass. $0.012 \%$ of potassium is the radioactive ${ }^{40} \mathrm{~K},$ with halflife $1.28 \times 10^{9}$ years. What's the potassium activity in a $60-\mathrm{kg}$ person?

Narayan Hari

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Problem 61

A sealed container has $25 \mu \mathrm{g}$ of radon- 222
(a) What's the sample's activity? (b) Find the activity and the amount of radon remaining after 30 days.

Km Neeraj

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Problem 62

In 1991 , hikers discovered the frozen remains of a human (the "Iceman') in a Swiss glacier. Measurements of ${ }^{14} \mathrm{C}$ beta emission from the Iceman revealed an activity of $0.121 \mathrm{~Bq} / \mathrm{g}$ of carbon. How old was the Iceman?

Narayan Hari

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Problem 63

The hydrogen isotope tritium $\left({ }^{3} \mathrm{H}\right)$ is used as a neutron source in nuclear weapons, so it's produced continually for military stockpiles. Tritium's half-life is 12.3 years. If we stopped producing tritium today with $2500 \mathrm{~kg}$ stockpiled, how much would remain after 100 years?

Narayan Hari

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Problem 64

Smoke detectors use the isotope ${ }^{241} \mathrm{Am},$ with half-life 433 years. (a) If you keep a smoke detector for 5 years, by what factor is ${ }^{241}$ Am activity reduced relative to when it was new? (b) How many years pass before the activity falls to $99 \%$ of its initial value?

Km Neeraj

Numerade Educator

Problem 65

The uranium isotopes ${ }^{235} \mathrm{U}$ and ${ }^{238} \mathrm{U}$ were present in roughly equal amounts when the solar system was formed. Today only $0.72 \%$ is the lighter isotope, with the remainder $\mathrm{U}-238 .$ Use these data and half-lives from Table 25.2 to estimate the age of the solar system.

Ronald Prasad

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Problem 66

Complete the following transmutation processes:
(a) ${ }^{2} \mathrm{H}+$ _____ ${ }^{16} \mathrm{O} \rightarrow{ }^{14} \mathrm{~N}+$
(b) ${ }^{1} \mathrm{H}+{ }^{7} \mathrm{Li} \rightarrow{ }^{1} n+$ _____
(c) ${ }^{4} \mathrm{He}+{ }^{13} \mathrm{C} \rightarrow$ ____ $+{ }^{1} n$

Narayan Hari

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Problem 67

Compute the energy released or required for each of the smutations in the preceding problem.

Km Neeraj

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Problem 68

Complete the following transmutation processes:
(a) ${ }^{1} n+$ $\rightarrow{ }^{4} \mathrm{He}+{ }^{17} \mathrm{O}$ _____$\rightarrow{ }^{4} \mathrm{He}+{ }^{17} \mathrm{O}$
(b) ${ }^{4} \mathrm{He}+{ }^{88} \mathrm{Sr} \rightarrow{ }^{3} \mathrm{H}+$ _____
(c) $^{2} \mathrm{H}+{ }^{28} \mathrm{Si} \rightarrow+{ }^{27} \mathrm{Al}+$ _____.

Narayan Hari

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Problem 69

Compute the energy released or required for the tran tions in the preceding problem.

Km Neeraj

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Problem 70

A common neutron source uses alpha particles striking beryllium, causing the reaction ${ }^{4} \mathrm{He}+{ }^{9} \mathrm{Be} \rightarrow{ }^{12} \mathrm{C}+{ }^{1} n .$ If the incoming alphas have kinetic energy $5.0 \mathrm{MeV},$ find the total kinetic energy of the reaction products (carbon and neutron).

Km Neeraj

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Problem 71

Complete the following fission reactions:
(a) ${ }^{1} n+{ }^{235} \mathrm{U} \rightarrow$ ${ }^{144} \mathrm{Ba}+$_____ $+3^{1} n ;(b)^{1} n+{ }^{235} \mathrm{U} \rightarrow{ }^{91} \mathrm{Br}+$ _____ $+2^{1} n$ (c) $^{1} n+{ }^{239} \mathrm{Pu} \rightarrow{ }^{142} \mathrm{Xe}+$ _____ $+2^{1} n$.

Narayan Hari

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Problem 72

Compute the energy released in the reaction in part (a) of the preceding problem.

Narayan Hari

Numerade Educator

Problem 73

Complete the following fission reactions:
(a) ${ }^{1} n+$ _____ $\rightarrow$ ${ }^{144} \mathrm{Ba}+{ }^{92} \mathrm{Sr}+4^{1} n ;$
(b) ${ }^{1} n+{ }^{235} \mathrm{U} \rightarrow{ }^{97} \mathrm{Y}+{ }^{137} \mathrm{I}+$ _____.
(c) ${ }^{1} n+{ }^{239} \mathrm{Pu} \rightarrow{ }^{117} \mathrm{Ag}+$ ____ $+3^{1} n$.

Narayan Hari

Numerade Educator

Problem 74

Compute the energy released in the reaction in part (a) of the preceding problem. Note: The mass of ${ }^{92} \mathrm{Sr}$ is $91.911030 \mathrm{u}$.

Km Neeraj

Numerade Educator

Problem 75

A fission reactor produces $1000 \mathrm{MW}$ of electric power. Assume it operates at $30 \%$ efficiency, with an average of $200 \mathrm{MeV}$ produced in each fission event. At what rate is the ${ }^{235} \mathrm{U}$ fuel consumed?

Narayan Hari

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Problem 76

The isotope ${ }^{90} \mathrm{Sr}$ is a common fission product and is dangerous because it's easily absorbed by the body, especially bones, because it's similar chemically to calcium. Strontium-90's half-life is 28.8 years. What fraction of an absorbed dose of this isotope remains after 1 year? After 10 years?

Km Neeraj

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Problem 77

The energy released in a nuclear explosion is stated as the equivalent mass of the chemical explosive TNT, usually in thousands of tons (kilotons; kt) or megatons (Mt). Exploding 1 g of TNT releases about 1000 calories $=4.184 \mathrm{~kJ}$ of energy. Early fission weapons yielded around 15 kilotons. How much uranium235 had to fission to produce this explosive yield, assuming $200 \mathrm{MeV}$ per fission event? Compare with the total mass of uranium in early bombs, about $50 \mathrm{~kg}$.

Narayan Hari

Numerade Educator

Problem 78

Complete the following fusion reactions:
(a) ${ }^{4} \mathrm{He}+{ }^{4} \mathrm{He} \rightarrow$ ${ }^{6} \mathrm{Li}+$ _____
(b) ${ }^{4} \mathrm{He}+{ }^{3} \mathrm{He} \rightarrow{ }^{2} \mathrm{H}+$ _____
(c) ${ }^{2} \mathrm{H}+$ ${ }^{3} \mathrm{H} \rightarrow{ }^{1} n+$ _____

Narayan Hari

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Problem 79

Find the energy released in each reaction in the preceding problem.

Km Neeraj

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Problem 80

Find the energy released in each of these fusion reactions:
(a) ${ }^{4} \mathrm{He}+{ }^{3} \mathrm{He} \rightarrow{ }^{7} \mathrm{Be}$
(b) ${ }^{2} \mathrm{H}+{ }^{2} \mathrm{H} \rightarrow{ }^{3} \mathrm{H}+{ }^{1} \mathrm{H}$
(c) ${ }^{12} \mathrm{C}+$ ${ }^{1} \mathrm{H} \rightarrow{ }^{13} \mathrm{~N}$

Km Neeraj

Numerade Educator

Problem 81

Find the energy released in each of these fusion reactions:
(a) ${ }^{3} \mathrm{He}+{ }^{3} \mathrm{He} \rightarrow{ }^{4} \mathrm{He}+2{ }^{1} \mathrm{H}$
(b) ${ }^{1} \mathrm{H}+{ }^{7} \mathrm{Li} \rightarrow 2^{4} \mathrm{He}$
(c) ${ }^{3} \mathrm{He}+$
${ }^{2} \mathrm{H} \rightarrow{ }^{4} \mathrm{He}+{ }^{1} \mathrm{H}$

Km Neeraj

Numerade Educator

Problem 82

Approximately three-fourths of Earth's surface is covered by water, with an average ocean depth of about $3 \mathrm{~km}$. (a) Deuterium makes up $0.015 \%$ of the hydrogen in water. How many deuterium nuclei are in all the oceans? (b) Suppose this deuterium were used in the fusion reaction ${ }^{2} \mathrm{H}+{ }^{2} \mathrm{H} \rightarrow{ }^{1} \mathrm{H}+{ }^{3} \mathrm{H},$ which
yields $4.0 \mathrm{MeV}$ of energy. What's the total energy available from fusion of all that deuterium? Compare with the world's yearly energy use, about $4 \times 10^{20} \mathrm{~J}$. How many years' supply of deuterium would we have?

Km Neeraj

Numerade Educator

Problem 83

Suppose your car uses 400 gallons of gasoline per year, with each gallon producing $1.3 \times 10^{8} \mathrm{~J}$ of energy. If you had a fusion-powered car using the reaction ${ }^{2} \mathrm{H}+{ }^{3} \mathrm{H} \rightarrow{ }^{1} n+{ }^{4} \mathrm{He}$
what mass of fusion fuel would be required instead of that 400 gal of gasoline?

Km Neeraj

Numerade Educator

Problem 84

Show that the net energy released in the proton-proton cycle is about $26.7 \mathrm{MeV}$. Remember to include the annihilation of the positrons.

Narayan Hari

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Problem 85

Boron can absorb a slow neutron in the process ${ }^{1} n+{ }^{10} \mathrm{~B} \rightarrow{ }^{11} \mathrm{~B}+\gamma .$ Find the energy and wavelength of the emitted gamma ray.

Km Neeraj

Numerade Educator

Problem 86

(a) Find the radius of the ${ }^{4}$ He nucleus.
(b) Suppose that the helium atom, with a filled 1 s electron shell, has the same groundstate radius as the Bohr hydrogen atom (Chapter 24 ). Find the density of the ${ }^{4}$ He nucleus and the density of the ${ }^{4}$ He atom. Comnare the two densities

Km Neeraj

Numerade Educator

Problem 87

The isotope ${ }^{99} \mathrm{Tc}^{*}$ is commonly used in several different types of medical imaging procedures. It emits a $140-\mathrm{keV}$ gamma ray (comparable to the energies of diagnostic $x$ rays ) and has half-life 6.01 h.
(a) What's the change in the nuclear mass after emission of the gamma ray?
(b) What's the activity of $0.50 \mu \mathrm{g}$ of $99 \mathrm{Tc}^{*}$ in jected into a patient?
(c) How much of $99 \mathrm{Tc}$ remains after one week? After 30 days?

Km Neeraj

Numerade Educator

Problem 88

(a) Write a general formula for the energy released in $\beta^{+}$ decay of the nuclide ${ }^{A} X .$ (b) Apply your formula to find the energy released in $\beta^{+}$ decay of ${ }^{59} \mathrm{Ni}$.

Km Neeraj

Numerade Educator

Problem 89

A transatlantic airplane flight exposes you to a cosmic radiation dose of approximately $25 \mu \mathrm{Sv}$. What's your lifetime risk of developing cancer from one such flight? Repeat for a PET scan, where your radiation dose is $5 \mathrm{mSv}$.

Km Neeraj

Numerade Educator

Problem 90

(a) Show that the nucleus ${ }^{8}$ Be will undergo alpha decay.
(b) Write out the full reaction for this process. (c) Assuming that the parent nucleus was at rest before the decay, what are the speeds of the two daughter nuclei?

Km Neeraj

Numerade Educator

Problem 91

It's possible but difficult to realize the alchemists' dream of synthesizing gold. One reaction involves bombarding ${ }^{198} \mathrm{Hg}$ with neutrons, producing ${ }^{197} \mathrm{Au}$ and one other particle. Write the equation for the full reaction.

Narayan Hari

Numerade Educator

Problem 92

Suppose nuclei must be within a distance of $3 \mathrm{fm}$ for the strong force to become effective. What temperature is required in order to initiate fusion of ${ }^{2} \mathrm{H}$ and ${ }^{3} \mathrm{H}$ ? Assume a thermal energy of $\frac{3}{2} k T$ per nucleon.

Narayan Hari

Numerade Educator

Problem 93

Following the 1986 Chernobyl nuclear accident, a Swedish official claims that ${ }^{131}$ I contamination in milk would be reduced to safe levels in 5 days. You're asked to verify this claim. The initial activity level was $2900 \mathrm{~Bq} / \mathrm{L}$ of milk, and Sweden's limit is $2000 \mathrm{~Bq} / \mathrm{L}$. Is the 5-day figure accurate?

Narayan Hari

Numerade Educator

Problem 94

Recall that the solar constant- -the flux of solar energy reaching Earth's vicinity - is about $1400 \mathrm{~W} / \mathrm{m}^{2}$. If the Sun's energy originates in the proton-proton cycle, at what rate $(\mathrm{kg} / \mathrm{s})$ does the Sun lose mass? Compare the yearly mass loss with the Sun's total mass.

Km Neeraj

Numerade Educator