Holt Physics

Raymond A. Serway, Jerry S. Faughn

Chapter 25

Subatomic Physics - all with Video Answers

Educators

Chapter Questions

Problem 1

How many protons are there in the nucleus $^{197}_{79}$ Au? How many neutrons? How many electrons are there in the neutral atom?

Keshav Singh

Keshav Singh

Numerade Educator

Problem 2

What are isotopes?

Manish Kumar

Numerade Educator

Problem 3

What holds the nucleons in a nucleus together?

Keshav Singh

Numerade Educator

Problem 4

Is it possible to accurately predict an atom's mass from its atomic number? Explain.

Keshav Singh

Numerade Educator

Problem 5

What would happen if the binding energy of a nucleus was zero?

Manish Kumar

Numerade Educator

Problem 6

Why do heavier elements require more neutrons to maintain stability?

Keshav Singh

Numerade Educator

Problem 7

Calculate the total binding energy of $^{12}_6$ C. (See Sample Problem $25 \mathrm{A}$ and refer to Appendix G.)

Manish Kumar

Numerade Educator

Problem 8

Calculate the total binding energy of tritium ( $_{1}^{3} \mathrm{H}$ ) and helium- $3\left(^{3}_{2} \mathrm{He}\right)$. (Sec Sample Problem 25 A and refer to Appendix G. )

Manish Kumar

Numerade Educator

Problem 9

Calculate the average binding energy per nucleon of $^{24}_{12} \mathrm{Mg}$ and $_{37}^{85} \mathrm{Rb}$. (See Sample Problem 25 A and refer to Appendix G.)

Keshav Singh

Numerade Educator

Problem 10

Explain the main differences between alpha, beta, and gamma emissions.

Keshav Singh

Numerade Educator

Problem 11

What fraction of a radioactive sample has decayed after two half-lives have elapsed?

Manish Kumar

Numerade Educator

Problem 12

Figure $25-18$ shows the steps by which $^{235}_{92} \cup$ decays to $^{207}_{82} \mathrm{Pb}$. Draw this diagram, and enter the correct isotope symbol in each square.

Ren Jie Tuieng

Numerade Educator

Problem 13

What factors make a fusion reaction difficult to achieve?

Manish Kumar

Numerade Educator

Problem 14

If a film is kept in a box, alpha particles from a radioactive source outside the box cannot expose the film, but beta particles can. Explain.

Keshav Singh

Numerade Educator

Problem 15

An alpha particle has twice the charge of a beta particle. Why does the beta particle deflect more when both pass between electrically charged plates, assuming they both have the same speed?

Keshav Singh

Numerade Educator

Problem 16

If a nucleus has a half-life of one year, will it be completely decayed after two years? Explain.

Manish Kumar

Numerade Educator

Problem 17

Why is carbon dating unable to provide accurate estimates of very old materials?

Keshav Singh

Numerade Educator

Problem 18

Suppose it could be shown that cosmic ray intensity was much greater thousands of years ago. How would this affect the ages we assign to ancient samples of once-living matter?

Manish Kumar

Numerade Educator

Problem 19

A free neutron undergoes beta decay with a half-life of about 15 min. Can a free proton undergo a similar decay? (Hint: Compare the masses of the proton and the neutron.)

Keshav Singh

Numerade Educator

Problem 20

In a fission reactor, nuclear reactions produce energy to drive a generator. How is this energy produced?

Manish Kumar

Numerade Educator

Problem 21

Is it possible for a $^{12}_{6} \mathrm{C}(12.000000 \mathrm{u})$ nucleus to spontaneously decay into three alpha particles? Explain.

Keshav Singh

Numerade Educator

Problem 22

Why is the temperature required for deuterium-tritium fusion lower than that needed for deuterium-deuterium fusion? (Hint: Consider the Coulomb repulsion and nuclear attraction for each case.

Manish Kumar

Numerade Educator

Problem 23

Determine the product of the following reaction: $$^7_3 \mathrm{Li}+^{4}_{2} \mathrm{Hc} \rightarrow ?+_{0}^{1} n$$ (Sce Sample Problem 25B.)

Manish Kumar

Numerade Educator

Problem 24

A nuclear reaction of significant historical note occurred in $1932,$ when a beryllium target was bombarded with alpha particles. Analysis of the experiment indicated that the following reaction occurred: $$^{4}_2 \mathrm{He}+_{4}^{9} \mathrm{Be} \rightarrow_{6}^{12} \mathrm{C}+\mathrm{X}$$What is $X$ in this reaction? (See Sample Problem 25B.)

Manish Kumar

Numerade Educator

Problem 25

Complete the following nuclear reactions:
a. $?+^{1} $$^{1}_{7}$$ \mathrm{N} \rightarrow_{1}^{1} \mathrm{H}+^{17}_8 \mathrm{O}$
b. $_{3}^{7} \mathrm{Li}+\mathrm{i} \mathrm{H} \rightarrow_{2}^{4} \mathrm{He}+?$
(See Sample Problem 25B.)

Lisa Tarman

Numerade Educator

Problem 26

A radioactive sample contains $1.67 \times 10^{11}$ atoms of $_{47}^{108} \mathrm{Ag}$ (half-life $=2.42 \mathrm{min}$ ) at some instant. Calculate the decay constant and the activity of the sample in mCi. (Sce Sample Problem 25C.)

Keshav Singh

Numerade Educator

Problem 27

How long will it take a sample of polonium- 210 with a half-life of 140 days to decay to one-sixteenth its original strength? (See Sample Problem $25 \mathrm{C}$.)

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 28

The amount of carbon- $14\left(^{14}_{6} \mathrm{C}\right)$ in a wooden artifact is measured to be 6.25 percent the amount in a fresh sample of wood from the same region. The half-life of carbon-14 is 5730 years. Assuming the same amount of carbon-14 was initially present in the artifact, determine the age of the artifact. (See Sample Problem 25C.)

Keshav Singh

Numerade Educator

Problem 29

A sample of organic material is found to contain $18 \mathrm{g}$ of carbon. Based on samples of pottery found at the site, investigators believe the material is about 23000 years old. Estimate what percentage of the material's carbon-14 has decayed. (See Sample Problem 25C.)

Bin Chen

Numerade Educator

Problem 30

Describe the properties of quarks.

Keshav Singh

Numerade Educator

Problem 31

What is the electrical charge of the particles with the following quark compositions?
a. $u d d$
b.$ utud$
c. $ud$

Keshav Singh

Numerade Educator

Problem 32

What is the electrical charge of the baryons with the following quark compositions?
a. $\bar{u} \bar{u} d$
b. $\bar{u} d d$

Keshav Singh

Numerade Educator

Problem 33

What are each of the baryons in item 32 called?

Keshav Singh

Numerade Educator

Problem 34

How many quarks or antiquarks are there in the following particles?
a. a baryon
b. an antibaryon
c. a meson
d. an antimeson

Keshav Singh

Numerade Educator

Problem 35

Compare a neutrino with a photon.

Keshav Singh

Numerade Educator

Problem 36

Consider the statement, "All mesons are hadrons, but not all hadrons are mesons." Is this statement true? Discuss.

Keshav Singh

Numerade Educator

Problem 37

The $W$ and $Z$ bosons were first produced in 1983. Why was this an important discovery?

Sanjeev Kumar

Numerade Educator

Problem 38

Consider the hydrogen atom to be a sphere with a radius equal to the Bohr radius, $0.53 \times 10^{-10} \mathrm{m},$ and calculate the approximate value of the ratio of atomic density to nuclear density.

Keshav Singh

Numerade Educator

Problem 39

Certain stars are thought to collapse at the end of their lives, combining their protons and electrons to form a neutron star. Such a star could be thought of as a giant atomic nucleus, If a star with a mass equal to that of the sun $\left(1.99 \times 10^{30} \mathrm{kg}\right)$ were to collapse into neutrons, what would be the radius of the star?

Lisa Tarman

Numerade Educator

Problem 40

Tritium, $_{1}^{3} \mathrm{H}$, decays to $^{3}_{2} \mathrm{He}$ by beta emission. Deter mine the energy released in the process.

Farhanul Hasan

Numerade Educator

Problem 41

Find the energy released in the alpha decay of $_{92}^{238} \mathrm{U}$ Use the masses in the following table:

Shahab Ullah

Numerade Educator

Problem 42

Disregard binding energies and estimate the masses of the $u$ and $d$ quarks from the masses of the proton and neutron.

Shahab Ullah

Numerade Educator

Problem 43

A pair of nuclei for which $Z_{1}=N_{2}$ and $Z_{2}=N_{1}$ are called mirror isobars (the atomic and neutron numbers are interchangeable). Binding energy measurements on such pairs can be used to obtain evidence of the charge independence of nuclear forces, Charge independence means that the proton-proton, proton neutron, and neutron-neutron forces are approximately equal. Calculate the difference in binding energy for the two mirror nuclei, $_{8}^{15} \mathrm{O}(15.003065 \mathrm{u})$ and $^{15}_{7} N$ $(15.000108 \mathrm{u})$.

Declan Nell

Numerade Educator

Problem 44

Find the threshold kinetic energy that the incident neutron must have to produce the following reaction: $_{0}^{1} n+_{2}^{4} \mathrm{He} \rightarrow_{1}^{2} \mathrm{H}+_{1}^{3} \mathrm{H}$

Lisa Tarman

Numerade Educator

Problem 45

A photon with an energy of $2.09 \mathrm{GeV}$ creates a proton-antiptoton pair in which the proton has a kinetic energy of 95 MeV. What is the kinetic energy of the antiproton?

Ren Jie Tuieng

Numerade Educator

Problem 46

Natural gold has only one stable isotope, $^{197}_{79}$ gold is bombarded with slow neutrons, $\beta^{-}$ particles are emitted.
a. Write the appropriate reaction equation.
b. Calculate the maximum energy of the emitted beta particles

Lisa Tarman

Numerade Educator

Problem 47

Two ways $^{235} \mathrm{U}$ can undergo fission when bombarded with a neutron are described below, In each case, neutrons are also released. Find the number of neutrons released in each of the following:
a. $^{140} \mathrm{Xe}$ and $^{94} \mathrm{Sr}$ released as fission fragments
b. $^{132} \mathrm{Sn}$ and $^{101}$ Mo released as fission fragments

Keshav Singh

Numerade Educator

Problem 48

When a $_{3}^{6} \mathrm{Li}$ nucleus is struck by a proton, an alpha particle and a product nucleus are released. What is the product nucleus?

Keshav Singh

Numerade Educator

Problem 49

Suppose $^{10}_5$ B is struck by an alpha particle, releasing a proton and a product nucleus in the reaction. What is the product nucleus?

Keshav Singh

Numerade Educator

Problem 50

When $^{18} \mathrm{O}$ is struck by a proton, $^{18} \mathrm{F}$ and another particle are produced. What is the other particle?

Keshav Singh

Numerade Educator

Problem 51

Complete the following nuclear reactions:
a. $^{27}_{13} \mathrm{Al}+_{2}^{4} \mathrm{Hc} \rightarrow ?+^{30}_{15} \mathrm{P}$
b. $_{0}^{1} n+? \rightarrow_{2}^{4} \mathrm{He}+_{3}^{7} \mathrm{L}$

Matthew Lueckheide

Matthew Lueckheide

Numerade Educator

Problem 52

A fission reaction that occurs when uranium- 235 absorbs a neutron leads to the formation of barium141 and krypton- 92.
a. Write the equation that describes this fission reaction
b. How many neutrons are released at the end of this reaction?

Arpit Gupta

Numerade Educator

Problem 53

When a star has exhausted its hydrogen fuel, it may fuse other nuclear fuels, such as helium. At temperatures above $1.0 \times 10^{8} \mathrm{K}$, helium fusion can occur.
a. Two alpha particles fuse to produce a nucleus, A, and a gamma ray. What is nucleus $A$ ?
b. Nucleus A absorbs an alpha particle to produce a nucleus, $B$, and a gamma ray. What is nucleus B?

Keshav Singh

Numerade Educator

Problem 54

A piece of charcoal known to be approximately 25000 years old contains $7.96 \times 10^{10} \mathrm{C}-14$ atoms.
a. Determine the number of decays per minute expected from this sample.
b. If the radioactive background in the counter without a sample is 20.0 counts/min and we assume 100.0 percent efficiency in counting. explain why 25000 years is close to the limit of dating with this technique.

Keshav Singh

Numerade Educator

Problem 55

The half-life of radium- 228 is 5.76 years. At some instant a sample contains $2.0 \times 10^{9}$ nuclei. Calculate the decay constant and theactivity of the sample in Ci.

Declan Nell

Numerade Educator

Problem 56

A sample of a radioactive isotope is measured to have an activity of $240.0 \mathrm{mCi}$. If the sample has a half-life of 14 days, how many nuclei of the isotope are there at this time?

Keshav Singh

Numerade Educator

Problem 57

At some instant of time the activity of a sample of radioactive material is $5.0 \mu \mathrm{Ci}$. If the sample contains $1.0 \times 10^{9}$ radioactive nuclei, what is the halflife of the material?

Keshav Singh

Numerade Educator

Problem 58

Smoke detectors use the isotope $^{241} \mathrm{Am}$ in their operation. The half-life of $A m$ is 432 years. If the smoke detector is improperly discarded in a landfill,estimate how long will it take for its activity to reduce to a relatively safe level of 0.1 percent of its original activity? (Hint: The estimation process you should use notes that the activity reduces to $50 \%$ in one half-life, to $25 \%$ in two half-lives, and so on.

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 59

It has been estimated that Earth has $9.1 \times 10^{11} \mathrm{kg}$ of natural uranium that can be economically mined. Of this total, 0.70 percent is $^{235} \mathrm{U}$. If all the world's energy needs $\left(7.0 \times 10^{12} \mathrm{J} / \mathrm{s}\right)$ were supplied by $^{235} \mathrm{U}$ fission, how long would this supply last? Assume that $208 \mathrm{MeV}$ of energy is released per fission event and that the mass of $^{235} \mathrm{U}$ is about $3.9 \times 10^{-25} \mathrm{kg}$.

Vipender Yadav

Numerade Educator

Problem 60

If the average energy released in a fission event is $208 \mathrm{MeV},$ find the total number of fission events required to provide enough energy to keep a $100.0 \mathrm{W}$ light bulb burning for $1.0 \mathrm{h}$.

Keshav Singh

Numerade Educator

Problem 61

How many atoms of $^{235} \mathrm{U}$ must undergo fission to operate a $1.0 \times 10^{3} \mathrm{MW}$ power plant for one day if the conversion efficiency is 30.0 percent? Assume $208 \mathrm{MeV}$ released per fission event.

Keshav Singh

Numerade Educator

Problem 62

An all-electric home uses about $20 \times 10^{3} \mathrm{kW} \cdot \mathrm{h}$ of clectrical encrgy per month, How many $^{235} \mathrm{U}$ atoms would be required to provide this house with its energy needs for one year? Assume 100.0 percent conversion efficiency and $208 \mathrm{MeV}$ released per fission.

Keshav Singh

Numerade Educator