Physics

John D. Cutnell, Kenneth W. Johnson

Chapter 31

Nuclear Physics and Radioactivity - all with Video Answers

Educators

Chapter Questions

Problem 1

For $\frac{208}{82} \mathrm{Pb}$ find $\quad$ (a) the net electrical charge of the nucleus, (b) the number of neutrons, (c) the number of nucleons, (d) the approximate radius of the nucleus, and (e) the nuclear density.

Mike Gaerlan

Mike Gaerlan

Numerade Educator

Problem 2

A nucleus contains 18 protons and 22 neutrons. What is the radius of
this nucleus?

Mike Gaerlan

Numerade Educator

Problem 3

In each of the following cases, what element does the symbol $\mathrm{X}$
represent and how many neutrons are in the nucleus? Use the periodic
table on the inside of the back cover as needed. (a) $\frac{195}{78} \mathrm{X} \quad$ (b) $\frac{32}{6} \mathrm{X}$ (c) $_{29}^{63} \mathrm{X}$ (d) $\frac{11}{5} X \quad(\text { e }) \stackrel{239}{94} X$

Mike Gaerlan

Numerade Educator

Problem 4

By what factor does the nucleon number of a nucleus have to increase
in order for the nuclear radius to double?

Mike Gaerlan

Numerade Educator

Problem 5

In electrically neutral atoms, how many (a) protons are in the uranium $\underset{92}{238} \mathrm{U}$ nucleus, (b) neutrons are in the mercury $\underset{80}{202} \mathrm{Hg}$ nucleus, and (c) electrons are in orbit about the niobium $\underset{41}{93} \mathrm{Nb}$ nucleus?

Mike Gaerlan

Numerade Educator

Problem 6

The largest stable nucleus has a nucleon number of 209, and the
smallest has a nucleon number of 1. If each nucleus is assumed to be a
sphere, what is the ratio (largest/smallest) of the surface areas of these
spheres?

Mike Gaerlan

Numerade Educator

Problem 7

The ratio $r_{X} / r_{\mathrm{T}}$ of the radius of an unknown nucleus $\frac{A}{2} \mathrm{X}$ to the radius of a tritium nucleus ${ }_{1}^{3} \mathrm{~T}$ is $\frac{r_{\mathrm{X}}}{r_{\mathrm{T}}}=1.10 .$ Both nuclei contain the same number of neutrons. Identify the unknown nucleus in the form $\frac{A}{2} \mathrm{X}$. Use the periodic table on the inside of the back cover as needed.

Mike Gaerlan

Numerade Educator

Problem 8

An unknown nucleus contains 70 neutrons and has twice the volume of the nickel $_{28}^{60} \mathrm{Ni}$ nucleus. Identify the unknown nucleus in the
form $_{Z}^{A} \mathrm{X}$ . Use the periodic table on the inside of the back cover as needed.

Mike Gaerlan

Numerade Educator

Problem 9

Refer to Conceptual Example 1 for a discussion of nuclear
densities. A neutron star is composed of neutrons and has a density that
is approximately the same as that of a nucleus. What is the radius of
a neutron star whose mass is 0.40 times the mass of the sun?

Mike Gaerlan

Numerade Educator

Problem 10

Suppose that you could pack neutrons (mass $=1.67 \times 10^{-27} \mathrm{kg} )$
inside a tennis ball (radius $=0.032 \mathrm{m} )$ in the same way as neutrons and
protons are packed together in the nucleus of an atom. (a) Approximately
how many neutrons would fit inside the tennis ball? $\quad$ (b) A small object is placed 2.0 $\mathrm{m}$ from the center of the neutron-packed tennis ball, and the
tennis ball exerts a gravitational force on it. When the object is released,
what is the magnitude of the acceleration that it experiences? Ignore the
gravitational force exerted on the object by the earth.

Mike Gaerlan

Numerade Educator

Problem 11

Find the binding energy (in MeV) for lithium $\frac{7}{3} \mathrm{Li}$ (atomic mass $=7.016003 \mathrm{u}$ )

Mike Gaerlan

Numerade Educator

Problem 12

The binding energy of a nucleus is 225.0 MeV. What is the mass
defect of the nucleus in atomic mass units?

Mike Gaerlan

Numerade Educator

Problem 13

Determine the mass defect (in atomic mass units) for (a) helium $_{2}^{3} \mathrm{He}$ which has an atomic mass of $3.016030 \mathrm{u},$ and $\quad(\mathrm{b})$ the isotope of hydrogen known as tritium $_{1}^{3} \mathrm{T}$ , which has an atomic mass of 3.016050 $\mathrm{u}$ (c) On the basis of your answers to parts (a) and (b), state which nucleus
requires more energy to disassemble it into its separate and stationary
constituent nucleons. Give your reasoning.

Mike Gaerlan

Numerade Educator

Problem 14

A $245-\mathrm{kg}$ boulder is dropped into a mine shaft that is $3.0 \times 10^{3} \mathrm{m}$ deep. During the boulder's fall, the system consisting of the earth and the
boulder loses a certain amount of gravitational potential energy. It would
take an equal amount of energy to "free "the boulder from the shaft by
raising it back to top, so this can be considered the system's binding
energy. (a) Determine the binding energy (in joules) of the earth-boulder
system. (b) How much mass does the earth-boulder system lose when
the boulder falls to the bottom of the shaft?

Mike Gaerlan

Numerade Educator

Problem 15

For lead $\underset{82}{206} \mathrm{Pb}$ (atomic mass $=205.9744440$ u) obtain $(\text { a) the }$ mass defect in atomic mass units, (b) the binding energy (in MeV), and (c) the binding energy per nucleon (in MeV/nucleon).

Mike Gaerlan

Numerade Educator

Problem 16

(a) Energy is required to separate a nucleus into its constituent
nucleons, as Figure 31.3 indicates; this energy is the total binding energy
of the nucleus. In a similar way one can speak of the energy that binds a
single nucleon to the remainder of the nucleus. For example, separating nitrogen $\stackrel{14}{7} \mathrm{N}$ into nitrogen $\frac{13}{7} \mathrm{N}$ and a neutron takes energy equal to the
binding energy of the neutron, as shown below:
$\stackrel{14}{7} \mathrm{N}+$ Energy $\longrightarrow^{13}_{7} \mathrm{N}+_{0}^{1} \mathrm{n}$
Find the energy (in Mev) that binds the neutron to the $\frac{14}{7}$ N nucleus by considering the mass of $\frac{13}{7} \mathrm{N}$ (atomic mass $=13.005738 \mathrm{u}$ and the mass of $_{0}^{1} \mathrm{n}$ (atomic mass $=$ 1.008665 $\mathrm {u} )$ as compared to the mass of $\frac{14}{7} \mathrm{N}$ (atomic mass $=14.003 \quad 074$ u). (b) Similarly, one can speak of the energy that binds a single proton to the $\frac{14}{7}$ N nucleus:
$$ ^{14} \mathrm{N}+\text { Energy } \longrightarrow_{6}^{13} \mathrm{C}+\mathrm{IH}$$
Following the procedure outlined in part (a), determine the energy (in MeV) that binds the proton (atomic mass $=1.007825$ u) to the $\frac{14}{7} N$ nucleus. The atomic mass of carbon $\frac{13}{6} \mathrm{C}$ is 13.003355 $\mathrm{u}$ . (c) Which nucleon is more tightly bound, the neutron or the proton?

Mike Gaerlan

Numerade Educator

Problem 17

Two isotopes of a certain element have binding energies that
differ by 5.03 MeV. The isotope with the larger binding energy contains
one more neutron than the other isotope. Find the difference in atomic
mass between the two isotopes.

Mike Gaerlan

Numerade Educator

Problem 18

A copper penny has a mass of 3.0 g. Determine the energy
(in MeV) that would be required to break all the copper nuclei into their
constituent protons and neutrons. Ignore the energy that binds the
electrons to the nucleus and the energy that binds one atom to another
in the structure of the metal. For simplicity, assume that all the copper nuclei are $\frac{63}{29} \mathrm{Cu}$ (atomic mass $=62.939598 \mathrm{u} )$

Mike Gaerlan

Numerade Educator

Problem 19

Write the $\beta^{+}$ decay process for each of the following nuclei,
being careful to include $Z$ and $A$ and the proper chemical symbol for each daughter nucleus: (a) $\stackrel{18}{9} \mathrm{F} \quad$ (b) $\frac{15}{8} \mathrm{O}$

Mike Gaerlan

Numerade Educator

Problem 20

Write the $\beta^{-}$ decay process for carbon $_{6}^{14} \mathrm{C},$ including the chemical symbols as well as the values of $Z$ and $A$ for the parent and daughter nuclei and the $\beta^{-}$ particle.

Mike Gaerlan

Numerade Educator

Problem 21

Osmium $\stackrel{191}{76} \mathrm{Os}$ (atomic mass $=190.960920 \mathrm{u}$ is converted into iridium $\frac{191}{77}$ Ir (atomic mass $=190.960584$ u) via $\beta^{-}$ decay. What is the energy (in MeV) released in this process?

Mike Gaerlan

Numerade Educator

Problem 22

Find the energy that is released when a nucleus of lead $^{211} 82 \mathrm{Pb}$ (atomic mass $=210.988735$ u) undergoes $\beta^{-}$ decay to become bismuth $_{83}^{211} \mathrm{Bi}$ (atomic mass $=210.987255 \mathrm{u} )$

Mike Gaerlan

Numerade Educator

Problem 23

Find the energy (in MeV) released when $\alpha$ decay converts radium $\frac{226}{88} \mathrm{Ra}$ (atomic mass $=226.02540$ u) into radon $\frac{222}{86} \mathrm{Rn}$ (atomic
mass $=222.01757 \mathrm{u} )$ The atomic mass of an $\alpha$ particle is 4.002603 $\mathrm{u}$

Mike Gaerlan

Numerade Educator

Problem 24

Lead $_{82}^{207} \mathrm{Pb}$ is a stable daughter nucleus that can result from
either an $\alpha$ decay or a $\beta^{-}$ decay. Write the decay processes, including
the chemical symbols and values for Z and A of the parent nuclei, for (a) the $\alpha$ decay and $\quad$ (b) the $\beta^{-}$ decay.

Mike Gaerlan

Numerade Educator

Problem 25

In the form $\frac{A}{Z} \mathrm{X},$ identify the daughter nucleus that results when (a) plutonium
$\stackrel{242}{94} \mathrm{Pu}$ undergoes $\alpha$ decay (b) sodium $\frac{24}{11}$ Na undergoes $\beta^{-}$ decay, and (c) nitrogen $\frac{13}{7}$ N undergoes $\beta^{+}$ decay.

Mike Gaerlan

Numerade Educator

Problem 26

Multiple-Concept Example 7 reviews the concepts needed to
solve this problem. When uranium $\stackrel{235}{92} \mathrm{U}$ decays, it emits (among other
things) a $\gamma$ ray that has a wavelength of $1.14 \times 10^{-11}$ m. Determine the
energy (in MeV) of this $\gamma$ ray.

Mike Gaerlan

Numerade Educator

Problem 27

Polonium $\stackrel{210}{84} \mathrm{Po}$ (atomic mass $=209.982848$ u) undergoes $\alpha$ decay. Assuming that all the released energy is in the form of kinetic
energy of the $\alpha$ particle (atomic mass $=4.002603$ u) and ignoring the recoil of the daughter nucleus (lead $\stackrel{206}{82} \mathrm{Pb}$ $205.9744440 \mathrm{u} ),$ find the speed of the $\alpha$ particle. Ignore relativistic effects.

Mike Gaerlan

Numerade Educator

Problem 28

Radon $\stackrel{220}{86} \mathrm{Rn}$ produces a daughter nucleus that is radioactive.
The daughter, in turn, produces its own radioactive daughter, and so on.
This process continues until lead $\stackrel{208}{82} \mathrm{Pb}$ is reached. What are the total
number $N_{\alpha}$ of $\alpha$ particles and the total number $N_{\beta}$ of $\beta^{-}$ particles that are generated in this series of radioactive decays?

Mike Gaerlan

Numerade Educator

Problem 29

Review Conceptual Example 5 as background for this problem.
The $\alpha$ decay of uranium $\stackrel{238}{92} \mathrm{U}$ produces thorium $\stackrel{234}{90} \mathrm{Th}$ (atomic mass $=$ 234.0436 u). In Example $4,$ the energy released in this decay is determined to be 4.3 MeV. Determine how much of this energy is carried away by the recoiling $\stackrel{234}{90} \mathrm{Th}$ daughter nucleus and how much by the $\alpha$ particle (atomic mass $=4.002603$ u). Assume that the energy of each particle is kinetic energy, and ignore the small amount of energy carried away by the $\gamma$ ray that is also emitted. In addition, ignore
relativistic effects.

Mike Gaerlan

Numerade Educator

Problem 30

An isotope of beryllium (atomic mass $=7.017$ u) emits a $\gamma$ ray and recoils with a speed of $2.19 \times 10^{4} \mathrm{m} / \mathrm{s}$ . Assuming that the beryllium
nucleus is stationary to begin with, find the wavelength of the $\gamma$ ray.

Dading Chen

Numerade Educator

Problem 31

Find the energy (in MeV) released when $\beta^{+}$ decay converts sodium $\frac{22}{11} \mathrm{Na}$ (atomic mass $=21.994434 \mathrm{u}$ ) into neon $\frac{22}{10} \mathrm{Ne}$ (atomic mass $=21.991383$ u). Notice that the atomic mass for $\frac{22}{11}$ Na includes the
mass of 11 electrons, whereas the atomic mass for $\frac{22}{10}$ Ne includes the
mass of only 10 electrons.

Mike Gaerlan

Numerade Educator

Problem 32

In 9.0 days the number of radioactive nuclei decreases to one-eighth
the number present initially. What is the half-life (in days) of the material?

Mike Gaerlan

Numerade Educator

Problem 33

The half-lives in two different samples, A and B, of radioactive nuclei are related according to $T_{1 / 2, \mathrm{B}}=\frac{1}{2} T_{1 / 2, \mathrm{A}}$ In a certain period the
number of radioactive nuclei in sample A decreases to one-fourth
the number present initially. In this same period the number of radioactive
nuclei in sample B decreases to a fraction $f$ of the number present initially.
Find $f$.

Mike Gaerlan

Numerade Educator

Problem 34

The $\frac{32 \mathrm{P}}{15} \mathrm{P}$ isotope of phosphorus has a half-life of 14.28 days. What is its decay constant in units of $\mathrm{s}^{-1} ?$

Mike Gaerlan

Numerade Educator

Problem 35

Strontium $_{38}^{90} \mathrm{Sr}$ has a half-life of 29.1 $\mathrm{yr.}$ it is chemically similar
to calcium, enters the body through the food chain, and collects in the bones. Consequently, $\frac{90}{38} \mathrm{Sr}$ is a particularly serious health hazard. How long (in years) will it take for 99.9900$\%$ of the $\frac{90}{38}$ Sr released in a nuclear reactor accident to disappear?

Mike Gaerlan

Numerade Educator

Problem 36

Two radioactive waste products from nuclear reactors are strontium $_{38}^{90} \operatorname{Sr}\left(T_{1 / 2}=29.1 \mathrm{yr}\right)$ and cesium $\frac{134}{55} \mathrm{Cs}\left(T_{1 / 2}=2.06 \mathrm{yr}\right) .$ These two species are present initially in a ratio of $N_{0, S_{\mathrm{r}}} / N_{0, \mathrm{Cs}}=7.80 \times 10^{-3}$ What is the ratio $N_{\mathrm{Sr}} / N_{\mathrm{Cs}}$ fifteen years later?

Mike Gaerlan

Numerade Educator

Problem 37

Suppose that the activity of a radioactive substance is initially
398 disintegrations/min and two days later it is 285 disintegrations/min.
What is the activity four days later still, or six days after the start? Give
your answer in disintegrations/min

Mike Gaerlan

Numerade Educator

Problem 38

Iodine $\stackrel{131}{53} \mathrm{I}$ is used in diagnostic and therapeutic techniques in
the treatment of thyroid disorders. This isotope has a half-life of 8.04 days. What percentage of an initial sample of $\stackrel{131}{53} \mathrm{I}$ remains after 30.0 days?

Mike Gaerlan

Numerade Educator

Problem 39

The number of radioactive nuclei present at the start of an experiment is $4.60 \times 10^{15}$ . The number present twenty days later is $8.14 \times 10^{14} .$ What is the half-life (in days) of the nuclei?

Mike Gaerlan

Numerade Educator

Problem 40

One day, a cell phone company sends a text message to each of its
5800 subscribers, announcing that they have been automatically enrolled
as contestants in a promotional lottery modeled on nuclear decay. On the first day, 10$\%$ of the 5800 contestants are notified by text message that
they have been randomly eliminated from the lettery. The other 90$\%$ of
the contestants automatically advance to the next round. On each of the
following days, 10$\%$ of the remaining contestants are randomly eliminated,
until fewer than 10 contestants remain. Determine (a) the activity (number of contestants eliminated per day on the second day of the lottery, $(\mathbf{b})$ the
decay constant (in $\mathrm{d}^{-1} )$ of the lottery, and $(\mathbf{c})$ the half-life (in d) of the
lottery.

Mike Gaerlan

Numerade Educator

Problem 41

A device used in radiation therapy for cancer contains 0.50 $\mathrm{g}$
of cobalt $\frac{60}{27} \mathrm{Co}(59.933819 \mathrm{u}) .$ The half-life of $_{27}^{60} \mathrm{Co}$ is 5.27 $\mathrm{yr.}$ Determine the activity of the radioactive material.

Mike Gaerlan

Numerade Educator

Problem 42

A one-gram sample of radium $\stackrel{224}{88} \mathrm{Ra}$ (atomic mass $=224.020186 \mathrm{u}$ $T_{1 / 2}=3.66$ days contains $2.69 \times 10^{21}$ nuclei and undergoes $\alpha$ decay to produce radon $\stackrel{220}{86} \mathrm{Rn}$ (atomic mass $=220.011368 \mathrm{u}$ ). The atomic mass of an $\alpha$ particle is 4.002603 u. The latent heat of fusion for water is
$33.5 \times 10^{4} \mathrm{J} / \mathrm{kg}$ . With the energy released in 3.66 days, how many
kilograms of ice could be melted at $0^{\circ} \mathrm{C} ?$

Mike Gaerlan

Numerade Educator

Problem 43

The isotope $\stackrel{198}{79} \mathrm{Au}$ (atomic mass 197.968 u) of gold
has a half-life of 2.69 days and is used in cancer therapy. What
mass (in grams) of this isotope is required to produce an activity of 315 Ci?

Mike Gaerlan

Numerade Educator

Problem 44

Outside the nucleus, the neutron itself is radioactive and
decays into a proton, an electron, and an antineutrino. The half-life of
a neutron (mass $=1.675 \times 10^{-27} \mathrm{kg} )$ outside the nucleus is 10.4 $\mathrm{min}$ . On average, over what distance (in meters) would a beam of $5.00-\mathrm{eV}$
neutrons travel before the number of neutrons decreased to 75.0$\%$ of its
initial value?

Mike Gaerlan

Numerade Educator

Problem 45

Two radioactive nuclei A and B are present in equal numbers
to begin with. Three days later, there are three times as many A nuclei
as there are B nuclei. The half-life of species B is 1.50 days. Find the
half-life of species A

Mike Gaerlan

Numerade Educator

Problem 46

A sample has a 14 $\mathrm{C}$ activity of 0.0061 $\mathrm{Bq}$ per gram of carbon.
(a) Find the age of the sample, assuming that the activity per gram of
carbon in a living organism has been constant at a value of 0.23 $\mathrm{Bq}$ .
(b) Evidence suggests that the value of 0.23 $\mathrm{Bq}$ might have been as much
as 40$\%$ larger. Repeat part (a), taking into account this 40$\%$ increase.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 47

Review Multiple-Concept Example 11 for help in approaching
this problem. An archaeological specimen containing 9.2 g of carbon has
an activity of 1.6 Bq. How old (in years) is the specimen?

Mike Gaerlan

Numerade Educator

Problem 48

The half-life for the $\alpha$ decay of uranium $\stackrel{238}{92} \mathrm{U}$ is $4.47 \times 10^{9} \mathrm{yr}$ Determine the age (in years) of a rock specimen that contains 60.0$\%$ of its original number of $\stackrel{238}{92} \mathrm{U}$ atoms.

Mike Gaerlan

Numerade Educator

Problem 49

Review Conceptual Example 12 before starting to solve this problem.
The number of unstable nuclei remaining after a time $t=5.00$ yr is $N$ and the number present initially is $N_{0}$ . Find the ratio $N / N_{0}$ for $(\mathrm{a}) \stackrel{14}{6} \mathrm{C}$ (half-life $=5730$ yr), (b) $\frac{15}{8} \mathrm{O}$ (half-life $=122.2 \mathrm{s} ;$ use $t=1.00 \mathrm{h}$ since otherwise the answer is out of the range of your calculator), and
(c) $\frac{3}{1} \mathrm{H}$ (half-life $=12.33$ yr). Verify that your answers are consistent
with the reasoning in Conceptual Example 12.

Mike Gaerlan

Numerade Educator

Problem 50

Multiple-Concept Example 11 reviews most of the concepts that
are needed to solve this problem. Material found with a mummy in the
arid highlands of southern Peru has a $^{14}_{6} \mathrm{C}$ activity per gram of carbon that
is 78.5$\%$ of the activity present initially. How long ago (in years) did this individual die?

Mike Gaerlan

Numerade Educator

Problem 51

When any radioactive dating method is used, experimental
error in the measurement of the sample’s activity leads to error in the
estimated age. In an application of the radiocarbon dating technique to
certain fossils, an activity of 0.100 Bq per gram of carbon is measured
to within an accuracy of $\pm 10.0 \%$ Find the age of the fossils and the
maximum error (in years) in the value obtained. Assume that there is no
error in the 5730-year half-life of $^{14}_{6} \mathrm{C}$ nor in the value of 0.23 Bq per gram of carbon in a living organism.

Mike Gaerlan

Numerade Educator

Problem 52

(a) A sample is being dated by the radiocarbon technique. If the sample
vere uncontaminated, its activity would be 0.011 Bq per gram of carbon.
Find the true age (in years) of the sample. (b) Suppose the sample is
ontaminated, so that only 98.0$\%$ of its carbon is ancient carbon. The remaining 2.0$\%$ is fresh carbon, in the sense that the $_{6}^{14} \mathrm{C}$ it contains has
not had any time to decay. Assuming that the lab technician is unaware
of the contamination, what apparent age (in years) would be determined
for the sample?

Mike Gaerlan

Numerade Educator

Problem 53

Use the plot of binding energy per nucleon in Figure 31.5 to determine the mass defect for the oxygen $^{16}_{8} \mathrm{O}$ nucleus. Express your answer in kilograms.

Mike Gaerlan

Numerade Educator

Problem 54

In a nucleus, each proton experiences a repulsive electrostatic
force from each of the other protons. In a nucleus of gold $\stackrel{197}{79} \mathrm{Au}$ what is
the magnitude of the least possible electrostatic force of repulsion that
one proton can exert on another?

Mike Gaerlan

Numerade Educator

Problem 55

When a sample from a meteorite is analyzed, it is determined
that 93.8$\%$ of the original mass of a certain radioactive isotope is still
present. Based on this finding, the age of the meteorite is calculated to be
$4.51 \times 10^{9}$ yr. What is the half-life (in yr) of the isotope used to date the
meteorite?

Mike Gaerlan

Numerade Educator

Problem 56

The $\beta^{-}$ decay of phosphorus $\frac{32}{15} \mathrm{P}$ (atomic mass $=31.973907 \mathrm{u} )$ produces a daughter nucleus that is sulfur $\frac{32}{6} \mathrm{S}$ (atomic mass $=31.972070 \mathrm{u}$ ,
$\mathrm{a} \beta^{-}$ particle, and an antineutrino. The kinetic energy of the $\beta^{-}$ particle is 0.90 MeV. Find the maximum possible energy (in MeV) that the
antineutrino could carry away.

Mike Gaerlan

Numerade Educator

Problem 57

Complete the following decay processes by stating what the symbol $\mathrm{X}$ represents $\left(\mathrm{X}=\alpha, \beta^{-}, \beta^{+}, \text { or } \gamma\right) :$
(a) $\quad \frac{211}{82} \mathrm{Pb} \rightarrow_{83}^{211} \mathrm{Bi}+\mathrm{X}$
(b) $\stackrel{11}{6} \mathrm{C} \rightarrow_{5}^{11} \mathrm{B}+\mathrm{X}$
(c) $\quad \stackrel{231}{90} \mathrm{Th}^{*} \rightarrow_{90}^{231} \mathrm{Th}+\mathrm{X}$
(d) $\quad \frac{210}{84} \mathrm{Po} \rightarrow^{206} \mathrm{Pb}+\mathrm{X}$

Mike Gaerlan

Numerade Educator

Problem 58

To see why one curie of activity was chosen to be $3.7 \times 10^{10} \mathrm{Bq}$determine the activity (in disintegrations per second) of one gram of radium $\frac{226}{88} \operatorname{Ra}\left(T_{1 / 2}=1.6 \times 10^{3} \mathrm{yr}\right) .$

Mike Gaerlan

Numerade Educator

Problem 59

The photomultiplier tube in a commercial scintillation counter
contains 15 of the special electrodes, or dynodes. Each dynode produces
3 electrons for every electron that strikes it. One photoelectron strikes the
first dynode. What is the maximum number of electrons that strike the
15th dynode?

Mike Gaerlan

Numerade Educator

Problem 60

A sample of ore containing radioactive strontium $\frac{90}{38} \mathrm{Sr}$ has an activity of $6.0 \times 10^{5} \mathrm{Bq}$ . The atomic mass of strontium is $89.908 \mathrm{u},$ and
its half-life is 29.1 yr. How many grams of strontium are in the sample?

Mike Gaerlan

Numerade Educator

Problem 61

Determine the symbol $\frac{1}{2} \mathrm{X}$ for the parent nucleus whose $\alpha$ decay produces the same daughter as the $\beta^{-}$ decay of thallium $\frac{208}{81}$ TI.

Mike Gaerlan

Numerade Educator

Problem 62

In a radioactive decay series similar to that shown in Figure $31.15,$ thorium $_{90}^{228} \mathrm{Th}$ (atomic mass $=228.028715$ u) undergoes four successive $\alpha$ decays, producing a daughter nucleus. (a) Determine the symbol $\frac{A}{2} \mathrm{X}$ for the nucleus produced by four successive $\alpha$ decays of $\stackrel{228}{90} \mathrm{Th}$ (b) What is the total amount of energy (in MeV) released in this series of decays? The mass of the daughter nucleus can be obtained by using the result of part (a) and consulting Appendix F at the back of the book. The mass of a single particle is 4.002 603 u.

Mike Gaerlan

Numerade Educator