Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

Chapter 32

lonizing Radiation, Nuclear Energy, and Elementary Particles - all with Video Answers

Educators

Chapter Questions

Problem 1

E ssm Neutrons $(R B E=2.0)$ and $\alpha$ particles have the same biologically equivalent dose. However, the absorbed dose of the neutrons is six times the absorbed dose of the $\alpha$ particles. What is the $\mathrm{RBE}$ for the $\alpha$ particles?

Narayan Hari

Narayan Hari

Numerade Educator

Problem 2

E What absorbed dose (in rads) of $\alpha$ particles $(\mathrm{RBE}=15)$ causes as much biological damage as a 60 -rad dose of protons $(R B E=10) ?$

Narayan Hari

Numerade Educator

Problem 3

E Blo Over a full course of treatment, two different tumors are to receive the same absorbed dose of therapeutic radiation. The smaller of the tumors (mass $=0.12 \mathrm{kg})$ absorbs a total of $1.7 \mathrm{J}$ of energy. (a) Determine the absorbed dose, in Gy. (b) What is the total energy absorbed by the larger of the tumors (mass $=0.15 \mathrm{kg}$ )?

Narayan Hari

Numerade Educator

Problem 4

E Over a year's time, a person receives a biologically equivalent dose of 24 mrem (millirems) from cosmic rays, which consist primarily of highenergy protons bombarding earth's atmosphere from space. The relative biological effectiveness of protons is $10 .$ (a) What is the person's absorbed dose in rads? (b) The person absorbs $1.9 \times 10^{-3} \mathrm{J}$ of energy from cosmic rays in a year. What is the person's mass?

Narayan Hari

Numerade Educator

Problem 5

E BIO GO SSM A beam of particles is directed at a $0.015-\mathrm{kg}$ tumor. There are $1.6 \times 10^{10}$ particles per second reaching the tumor, and the energy of each particle is $4.0 \mathrm{MeV}$. The $\mathrm{RBE}$ for the radiation is $14 .$ Find the biologically equivalent dose given to the tumor in $25 \mathrm{s}$.

Narayan Hari

Numerade Educator

Problem 6

A $75-\mathrm{kg}$ person is exposed to 45 mrem of $\alpha$ particles $(\mathrm{RBE}=12)$. How much energy (in joules) has this person absorbed?

Nicholas Majtenyi

Nicholas Majtenyi

Numerade Educator

Problem 7

E Blo Available in WileyPLUS.

Manish Jain

Numerade Educator

Problem 8

E Go The biologically equivalent dose for a typical chest X-ray is $2.5 \times$ $10^{-2}$ rem. The mass of the exposed tissue is $21 \mathrm{kg},$ and it absorbs $6.2 \times 10^{-3} \mathrm{J}$ of energy. What is the relative biological effectiveness $(\mathrm{RBE})$ for the radiation on this particular type of tissue?

Narayan Hari

Numerade Educator

Problem 9

M BIO A 2.0-kg tumor is being irradiated by a radioactive source. The tumor receives an absorbed dose of 12 Gy in a time of 850 s. Each disintegration of the radioactive source produces a particle that enters the tumor and delivers an energy of 0.40 MeV. What is the activity $\Delta N / \Delta t$ (see Section 31.6 ) of the radioactive source?

Narayan Hari

Numerade Educator

Problem 10

M N-HINT Available in WileyPLUS.

Manish Jain

Numerade Educator

Problem 11

M CHALK SSM A beam of nuclei is used for cancer therapy. Each nucleus has an energy of $130 \mathrm{MeV}$, and the relative biological effectiveness $(\mathrm{RBE})$ of this type of radiation is $16 .$ The beam is directed onto a $0.17-\mathrm{kg}$ tumor, which receives a biologically equivalent dose of 180 rem. How many nuclei are in the beam?

Narayan Hari

Numerade Educator

Problem 12

E What is the atomic number $Z$, the atomic mass number $A$, and the element $X$ in the reaction ${ }_{s}^{10} B(\alpha, p)_{2}^{A} X ?$

Narayan Hari

Numerade Educator

Problem 13

E ssm write the equation for the reaction ${ }_{8}^{17} \mathrm{O}(\gamma, \alpha n){ }_{0}^{12} \mathrm{C}$. The notation $" \alpha n "$ means that an $\alpha$ particle and a neutron are produced by the reaction.

Narayan Hari

Numerade Educator

Problem 14

E GO For each of the nuclear reactions listed below, determine the unknown particle $\hat{z}$ X. Use the periodic table on the inside of the back cover as needed.
(a) $\frac{A}{2} X+{ }^{14} \mathrm{N} \longrightarrow{ }_{1}^{1} \mathrm{H}+{ }_{8}^{17} \mathrm{O}$
(b) ${ }^{15} \mathrm{N}+{ }_{2}^{4} \mathrm{X} \longrightarrow{ }_{6}^{12} \mathrm{C}+{ }_{2}^{4} \mathrm{He}$
(c) $\mathrm{H}+{ }_{13}^{27} \mathrm{Al} \longrightarrow{ }_{2}^{A} \mathrm{X}+{ }_{0}^{1} \mathrm{n}$
(d) ${ }_{3}^{7} \mathrm{Li}+{ }_{1}^{1} \mathrm{H} \longrightarrow{ }_{2}^{4} \mathrm{He}+{ }_{2}^{A} \mathrm{X}$

Narayan Hari

Numerade Educator

Problem 15

E A neutron causes ${ }^{232}$ Th to change according to the reaction
$$
{ }_{0}^{1} \mathrm{n}+{ }^{232} \mathrm{Th} \longrightarrow{ }_{2}^{A} \mathrm{X}+\gamma
$$
(a) Identify the unknown nucleus ${ }_{2} \mathrm{X}$, giving its atomic mass number $A$, its atomic number $Z,$ and the symbol $X$ for the element.
(b) The ${ }_{z} \mathrm{X}$ nucleus subsequently undergoes $\beta^{-}$ decay, and its daughter does too. Identify the final nucleus, giving its atomic mass number, atomic number, and name.

Narayan Hari

Numerade Educator

Problem 16

E Write the reactions below in the shorthand form discussed in the text.
(a) ${ }_{2}^{4} \mathrm{He}+{ }_{13}^{27} \mathrm{Al} \longrightarrow{ }_{5}^{30} \mathrm{P}+{ }_{0}^{1} \mathrm{n}$
(b) ${ }_{1}^{1} \mathrm{H}+{ }_{4}^{9} \mathrm{Be} \longrightarrow{ }_{3}^{6} \mathrm{Li}+{ }_{2}^{4} \mathrm{He}$
(c) ${ }_{0}^{1} \mathrm{n}+{ }_{25}^{55} \mathrm{Mn} \longrightarrow{ }_{25}^{56} \mathrm{Mn}+\gamma$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 17

E SSM Complete the following nuclear reactions, assuming that the unknown quantity signified by the question mark is a single entity:
(a) ${ }_{18}^{34} \mathrm{Ar}(n, \alpha) ?$
(b) $\frac{82}{34} \operatorname{Se}(?, n) \frac{82}{35} \mathrm{Br}$
(c) ${ }_{28}^{58} \mathrm{Ni}\left({ }_{18}^{40} \mathrm{Ar}, ?\right){ }_{27}^{57} \mathrm{Co}$
(d) $?(\gamma, \alpha)^{16} \mathrm{O}$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 18

M CHALK During a nuclear reaction, an unknown particle is absorbed by a copper ${ }_{29}^{63} \mathrm{Cu}$ nucleus, and the reaction products are ${ }_{29}^{62} \mathrm{Cu},$ a neutron, and a proton. What are the name, atomic number, and nucleon number of the nucleus formed temporarily when the copper ${ }_{29}^{63}$ Cu nucleus absorbs the unknown particle?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 19

M N-HINT Available in WileyPLUS.

Manish Jain

Numerade Educator

Problem 20

E Determine the atomic number $Z$, the atomic mass number $A$, and the element $X$ for the unknown species ${ }_{2}^{A} \mathrm{X}$ in the following reaction for the fission of uranium ${ }_{92}^{235} \mathrm{U}:$
$$
{ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \longrightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{2}^{A} \mathrm{X}+4{ }_{0}^{1} \mathrm{n}
$$
Consult the periodic table on the inside of the back cover of the text as needed.

Narayan Hari

Numerade Educator

Problem 21

E SSM When a ${ }_{92}^{23} \mathrm{U}$ ( $235.043924 \mathrm{u}$ ) nucleus fissions, about $200 \mathrm{MeV}$ of energy is released. What is the ratio of this energy to the rest energy of the uranium nucleus?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 21

E SSM When a ${ }_{92}^{235} \mathrm{U}$ (235.043 924 u) nucleus fissions, about 200 $\mathrm{MeV}$. of energy is released. What is the ratio of this energy to the rest energy of the uranium nucleus?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 22

E How many neutrons are produced when ${ }^{235}$ U fissions in the following way? $_{0}^{1} n+{ }_{92}^{235} U \rightarrow{ }^{132} \mathrm{Sn}+{ }_{42}^{10} \mathrm{Mo}+$ neutrons

Narayan Hari

Numerade Educator

Problem 23

E Neutrons released by a fission reaction must be slowed by collisions with the moderator nuclei before the neutrons can cause further fission's. Suppose a $1.5-$ MeV neutron leaves each collision with $65 \%$ of its incident energy. How many collisions are required to reduce the neutron's energy to at least $0.040 \mathrm{eV},$ which is the energy of a thermal neutron?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 24

E N-HINT The energy released by each fission within the core of a nuclear reactor is $2.0 \times 10^{2}$ MeV. The number of fission's occurring each second is $2.0 \times 10^{19}$. Determine the power (in watts) that the reactor generates.

Narayan Hari

Numerade Educator

Problem 25

E Uranium ${ }_{92}^{235} \mathrm{U}$ fissions into two fragments plus three neutrons:
${ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow(2$ fragments $)+3{ }_{0}^{1} \mathrm{n} .$ The mass of a neutron is $1.008665 \mathrm{u}$ and the mass of ${ }_{92}^{25} \mathrm{U}$ is $235.043924 \mathrm{u}$. If $225.0 \mathrm{MeV}$ of energy is released, what is the total mass of the two fragments?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 26

GO When $1.0 \mathrm{kg}$ of coal is burned, approximately $3.0 \times 10^{7} \mathrm{J}$ of energy is released. If the energy released during each ${ }_{92}^{235} \mathrm{U}$ fission is $2.0 \times$ $10^{2} \mathrm{MeV},$ how many kilograms of coal must be burned to produce the same energy as $1.0 \mathrm{kg}$ of ${ }_{92}^{235} \mathrm{U} ?$

Narayan Hari

Numerade Educator

Problem 27

M ssm Available in WileyPLUS.

Manish Jain

Numerade Educator

Problem 28

M GO The water that cools a reactor core enters the reactor at $216^{\circ} \mathrm{C}$ and leaves at $287^{\circ} \mathrm{C}$. (The water is pressurized, so it does not turn to steam.) The core is generating $5.6 \times 10^{9} \mathrm{W}$ of power. Assume that the specific heat capacity of water is $4420 \mathrm{J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)$ over the temperature range stated above, and find the mass of water that passes through the core each second.

Narayan Hari

Numerade Educator

Problem 29

H SSM A nuclear power plant is $25 \%$ efficient, meaning that only $25 \%$ of the power it generates goes into producing electricity. The remaining $75 \%$ is wasted as heat. The plant generates $8.0 \times 10^{8}$ watts of electric power. If each fission releases $2.0 \times 10^{2}$ MeV of energy, how many kilograms of ${ }_{92}^{235} \mathrm{U}$ are fissioned per year?

Narayan Hari

Numerade Educator

Problem 30

H Available in WileyPLUS.

Manish Jain

Numerade Educator

Problem 31

E Two deuterium atoms $\left({ }_{1}^{2} \mathrm{H}\right)$ react to produce tritium $\left({ }_{1}^{3} \mathrm{H}\right)$ and hydrogen $(1 \mathrm{H})$ according to the following fusion reaction:
$$
\frac{{ }_{1}^{2} \mathrm{H}}{2.014102 \mathrm{u}}+\frac{{ }_{1}^{2} \mathrm{H}}{2.014102 \mathrm{u}} \longrightarrow{ }_{3.016}^{3} \frac{\mathrm{H}}{050 \mathrm{u}}+\frac{1 \mathrm{H}}{1.007825 \mathrm{u}}
$$
What is the energy (in MeV) released by this deuterium-deuterium reaction?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 32

E Go In one type of fusion reaction a proton fuses with a neutron to form a deuterium nucleus:
$$
{ }_{1}^{1} \mathrm{H}+{ }_{0}^{1} \mathrm{n} \longrightarrow{ }_{1}^{2} \mathrm{H}+\gamma
$$
The masses are ${ }_{1} \mathrm{H}(1.0078 \mathrm{u}),{ }_{0}^{1} \mathrm{n}(1.0087 \mathrm{u}),$ and ${ }_{1}^{2} \mathrm{H}(2.0141 \mathrm{u}) .$ The $\gamma$ -ray
photon is massless. How much energy (in $\mathrm{MeV}$ ) is released by this reaction?

Narayan Hari

Numerade Educator

Problem 33

E MMH The fusion of two deuterium nuclei $\left({ }_{1}^{2} \mathrm{H},\right.$ mass $\left.=2.0141 \mathrm{u}\right)$ can yield a helium nucleus $\left({ }_{2}^{3} \mathrm{He},\right.$ mass $\left.=3.0160 \mathrm{u}\right)$ and a neutron $\left({ }_{0}^{1} \mathrm{n},\right.$ mass $=$ 1.0087 u). What is the energy (in MeV) released in this reaction?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 34

E (N-HINT Tritium $\left({ }_{1}^{3} \mathrm{H}\right)$ is a rare isotope of hydrogen that can be produced by the following fusion reaction:
(a) Determine the atomic mass number $A$, the atomic number $Z,$ and the names $X$ and $Y$ of the unknown particles.
(b) Using the masses given in the reaction, determine how much energy (in $\mathrm{MeV}$ ) is released by this reaction.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 35

M CHALK SSM One proposed fusion reaction combines lithium ${ }_{3}^{6} \mathrm{Li}$ $(6.015 \mathrm{u})$ with deuterium ${ }_{1}^{2} \mathrm{H}(2.014 \mathrm{u})$ to give helium ${ }_{2}^{4} \mathrm{He}(4.003 \mathrm{u}):$ ${ }_{1}^{2} \mathrm{H}+{ }_{3}^{6} \mathrm{Li} \rightarrow 2{ }_{2}^{4}$ He. How many kilograms of lithium would be needed to supply the energy needs of one household for a year, estimated to be $3.8 \times 10^{10} \mathrm{J} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 36

GO In Example 6 it was determined that 17.6 MeV of energy is released when the following fusion reaction occurs:
$$
\frac{{ }_{1}^{2} \mathrm{H}}{2.0141}+\frac{{ }_{1}^{3} \mathrm{H}}{3.0161} \longrightarrow \frac{{ }_{2}^{2} \mathrm{He}}{4.0026}+\frac{{ }_{0}^{1} \mathrm{n}}{1.0087} \mathrm{u}
$$
Ignore relativistic effects and determine the kinetic energies of the neutron and the $\alpha$ particle.

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 37

M Deuterium $\left({ }_{1}^{2} \mathrm{H}\right)$ is an attractive fuel for fusion reactions because it is abundant in the oceans, where about $0.015 \%$ of the hydrogen atoms in the water $\left(\mathrm{H}_{2} \mathrm{O}\right)$ are deuterium atoms. (a) How many deuterium atoms are there in one kilogram of water? (b) If each deuterium nucleus produces about 7.2 MeV in a fusion reaction, how many kilograms of water would be needed to supply the energy needs of the United States for one year, estimated to be $1.1 \times 10^{20} \mathrm{J} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 38

H Available in WileyPLUS.

Manish Jain

Numerade Educator

Problem 39

E The main decay mode for the negative pion is $\pi^{-} \rightarrow \mu^{-}+\bar{\nu}_{\mu^{*}}$. Find the energy (in MeV) released in this decay. Consult Table 32.3 for rest energies and assume that the rest energy for $\bar{\nu}_{\mu}$ is $\approx 0 \mathrm{MeV}$.

Narayan Hari

Numerade Educator

Problem 40

E V-HINT A neutral pion $\pi^{0}$ (rest energy $=135.0$ MeV ) produced in a high-energy particle experiment moves at a speed of $0.780 \mathrm{c} .$ After a very short time, it decays into two $\gamma$ -ray photons. One of the $\gamma$ -ray photons has an energy of 192 MeV. What is the energy (in MeV) of the second $\gamma$ -ray photon? Take relativistic effects into account.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 41

E Available in WileyPLUS.

Manish Jain

Numerade Educator

Problem 42

E Go In addition to its rest energy, a moving proton $\left(p^{\prime}\right)$ has kinetic energy. This proton collides with a stationary proton $(p),$ and the reaction forms a stationary neutron ( $n$ ), a stationary proton ( $p$ ), and a stationary pion $\left(\pi^{+}\right),$ according to the following reaction: $p^{\prime}+p \rightarrow n+p+\pi^{+} .$ The rest energy of each proton is 938.3 MeV, and the rest energy of the neutron is 939.6 MeV. The rest energy of the pion is 139.6 MeV. What is the kinetic energy (in MeV) of the moving proton?

Narayan Hari

Numerade Educator

Problem 43

E ssm Suppose a neutrino is created and has an energy of 35 MeV. (a) Assuming the neutrino, like the photon, has no mass and travels at the speed of light, find the momentum of the neutrino. (b) Determine the de Broglie wavelength of the neutrino.

Narayan Hari

Numerade Educator

Problem 44

$\mathrm{M}$ Go Review Conceptual Example 7 as background for this problem. An electron and its antiparticle annihilate each other, producing two $\gamma$ -ray photons. The kinetic energies of the particles are negligible. Determine the magnitude of the momentum of each photon.

Narayan Hari

Numerade Educator

Problem 45

$\mathrm{M}$ Review Conceptual Example 5 as background for this problem. An energetic proton is fired at a stationary proton. For the reaction to produce new particles, the two protons must approach each other to within a distance of about $8.0 \times 10^{-15} \mathrm{m} .$ The moving proton must have a sufficient speed to overcome the repulsive Coulomb force. What must be the minimum initial kinetic energy (in MeV) of the proton?

Narayan Hari

Numerade Educator

Problem 46

E GO Someone stands near a radioactive source and receives doses of the following types of radiation: $\gamma$ rays $(20 \mathrm{mrad}, \mathrm{RBE}=1),$ electrons $(30 \mathrm{mrad}, \mathrm{RBE}=1),$ protons $(5 \mathrm{mrad}, \mathrm{RBE}=10),$ and slow neutrons $(5 \mathrm{mrad}$ $\mathrm{RBE}=2$ ). Rank the types of radiation, highest first, as to which produces the largest biologically equivalent dose.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 47

E SSM Available in WileyPLUS.

Manish Jain

Numerade Educator

Problem 48

E Identify the unknown species $\frac{A}{2} X$ in the following nuclear reaction:
$\frac{22}{11} \mathrm{Na}(d, \alpha)_{2} \mathrm{X} .$ Here, $d$ stands for the deuterium isotope $_{1}^{2} \mathrm{H}$ of hydrogen.

Narayan Hari

Numerade Educator

Problem 49

E Go mMH What energy (in MeV) is released by the following fission reaction?
$$
\frac{{ }_{0}^{1} \mathrm{n}}{1.009}+\frac{{ }_{92}^{235} \mathrm{U}}{235.044 \mathrm{u}} \longrightarrow \frac{{ }_{54}^{140} \mathrm{Xe}}{139.922 \mathrm{u}}+\frac{{ }_{38}^{94} \mathrm{Sr}}{93.915 \mathrm{u}}+\frac{2_{0}^{1} \mathrm{n}}{2(1.009 \mathrm{u})}
$$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 50

M N-HINT Multiple-Concept Example 1 discusses some of the physics principles that are used to solve this problem. What absorbed dose (in rads) of $\gamma$ rays is required to change a block of ice at $0.0^{\circ} \mathrm{C}$ into steam at $100.0^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 50

M N-HINT Multiple-Concept Example 1 discusses some of the physics principles that are used to solve this problem. What absorbed dose (in rads) of $\gamma$ rays is required to change a block of ice at $0.0^{\circ} \mathrm{C}$ into steam at $100.0^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 51

M SSM Imagine that your car is powered by a fusion engine in which the following reaction occurs: $3_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+{ }_{1} \mathrm{H}+{ }_{0}^{1} \mathrm{n} .$ The masses are ${ }_{1}^{2} \mathrm{H}$ $(2.0141 \mathrm{u}),{ }_{2}^{4} \mathrm{He}(4.0026 \mathrm{u}),{ }_{1}^{1} \mathrm{H}(1.0078 \mathrm{u}),$ and ${ }_{0}^{1} \mathrm{n}(1.0087 \mathrm{u}) .$ The engine uses $6.1 \times 10^{-6} \mathrm{kg}$ of deuterium $_{1}^{2} \mathrm{H}$ fuel. If one gallon of gasoline produces $2.1 \times 10^{9} \mathrm{J}$ of energy, how many gallons of gasoline would have to be burned to equal the energy released by all the deuterium fuel?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 52

M GO The energy consumed in one year in the United States is about $1.1 \times 10^{20} \mathrm{J} .$ With each ${ }_{92}^{235} \mathrm{U}$ fission, about $2.0 \times 10^{2} \mathrm{MeV}$ of energy is released. How many kilograms of ${ }_{92}^{235} \mathrm{U}$ would be needed to generate this energy if all the nuclei fissioned?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 53

$\mathrm{M}$ (a) If each fission reaction of a ${ }_{92}^{235} \mathrm{U}$ nucleus releases about $2.0 \times \mathrm{x}$ $10^{2} \mathrm{MeV}$ of energy, determine the energy (in joules) released by the complete fissioning of 1.0 gram of ${ }_{92}^{235} \mathrm{U}$. (b) How many grams of ${ }_{92}^{235} \mathrm{U}$ would be consumed in one year to supply the energy needs of a household that uses $30.0 \mathrm{kWh}$ of energy per day, on the average?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 54

(H One kilogram of dry air at STP conditions is exposed to $1.0 \mathrm{R}$ of X-rays. One roentgen is defined by Equation $32.1 .$ An equivalent definition can be based on the fact that an exposure of one roentgen deposits $8.3 \times 10^{-3} \mathrm{J}$ of energy per kilogram of dry air. Using the two definitions and assuming that all ions produced are singly charged, determine the average energy (in $\mathrm{eV}$ ) needed to produce one ion in air.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 55

When considering the biological effects of ionizing radiation, the concept of biologically equivalent dose is especially important. Its importance lies in the fact that the biologically equivalent dose incorporates both the amount of energy per unit mass that is absorbed and the effectiveness of a particular type of radiation in producing a certain biological effect. Problem 55 examines this concept and also reviews the notions of power (Section 6.7 ) and intensity (Section 16.7$)$ of a wave. Problem 56 illustrates the decay of a particle into two photons, and provides a review of the principles of conservation of energy and conservation of momentum.
M CHALK SSM A patient is being given a chest X-ray. The X-ray beam is turned on for $0.20 \mathrm{s},$ and its intensity is $0.40 \mathrm{W} / \mathrm{m}^{2} .$ The area of the chest being exposed is $0.072 \mathrm{m}^{2},$ and the radiation is absorbed by $3.6 \mathrm{kg}$ of tissue. The relative biological effectiveness (RBE) of the X-ray for this tissue is $1.1 .$ Concepts: (i) How is the power of the beam related to the beam intensity?
(ii) How is the energy absorbed by the tissue related to the power of the beam? (iii) What is the absorbed dose? (iv) How is the biologically equivalent dose related to the absorbed dose? Calculation: Calculate the biologically equivalent dose received by the patient.

Abid Hussain

Numerade Educator

Problem 56

M CHALK The $\pi^{0}$ meson is a particle that has a rest energy of $135.0 \mathrm{MeV}$ (see Table 32.3 ). It lives for a very short time and then decays into two $\gamma$ -ray photons: $\pi^{0} \rightarrow \gamma+\gamma .$ Suppose that one of the $\gamma$ -ray photons travels along the $+x$ axis. Concepts: (i) How is the energy $E$ of each $\gamma$ -ray photon related to the rest energy $E_{0}$ of the $\pi_{0}$ particle? (ii) How can the frequency and wavelength of a photon be determined from its energy? (iii) How is the total linear momentum of the photons related to the momentum of the $\pi^{0}$ particle, and what is the momentum of each particle? Calculations: If the $\pi^{0}$ is at rest when it decays, find (a) the energy (in $\mathrm{MeV}$ ), (b) the frequency and wavelength, and (c) the momentum of each $\gamma$ -ray photon.

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 57

$\mathrm{M}$ A Rough Measure of Exposure. You and your team are designing a crude device to estimate radiation exposure. The device consists of a set of parallel plates with a large voltage across them. The circular plates have a radius of $3.50 \mathrm{cm}$ and are separated by distance of $1.00 \mathrm{cm} .$ The region between the plates is filled with dry air at standard temperature and pressure (STP: $T=0^{\circ}, P=1$ ). A cubic meter of dry air at STP has a mass of $1.29 \mathrm{kg}$ When radiation ionizes an air molecule, the stripped electron is accelerated by the electric field between the plates and is registered as a current. When the device is located near a particularly strong source, it registers a current of $1.30 \times 10^{-9}$ A. What is the exposure between the plates after $5.00 \mathrm{s}$ (in roentgens)?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 58

58. M A Hypothetical Fusion Reactor. You and your team are tasked with evaluating the following deuterium-deuterium fusion reaction for use in a future fusion power reactor:
$$
\frac{{ }_{1}^{2} \mathrm{H}}{2.014102 \mathrm{u}}+\frac{{ }_{1}^{2} \mathrm{H}}{2.014102 \mathrm{u}} \longrightarrow \frac{{ }_{1}^{3} \mathrm{H}}{3.016050 \mathrm{u}}+\frac{1 \mathrm{H}}{1.007825 \mathrm{u}}
$$
(a) What is the energy released in this reaction (in joules)? (b) How many reactions per second would be required to run a 5000 MW reactor? (c) What mass of deuterium (in kg) would be needed to run the reactor for a year with a power output of $5000 \mathrm{MW}$ ?

Ren Jie Tuieng

Numerade Educator