what energy is delivered to the tumor per second?

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Problem ane

How many protons and how many neutrons are there in a
nucleus of the about mutual isotope of (a) silicon, $_{fourteen}^{28} \mathrm{Si} ;$ (b)
rubidium, $\frac{85}{37} \mathrm{Rb} ;$ (c) thallium, $_{81}^{205} \mathrm{Tl} ?$

Dading C.

Numerade Educator

Problem ii

Hydrogen atoms are placed in an external $one.65-\mathrm{T}$ magnetic field. (a) The protons can brand transitions between states where the nuclear spin component is parallel and antiparallel to the
field past absorbing or emitting a photon. Which state has lower free energy: the state with the nuclear spin component parallel or antiparallel to the field? What are the frequency and wavelength of the photon? In which region of the electromagnetic spectrum does it lie? (b) The electrons can brand transitions between states where the electron spin component is parallel and antiparallel to the field by absorbing or emitting a photon. Which state has lower energy: the land with the electron spin component parallel or antiparallel to the field? What are the frequency and wavelength of the photon? In which region of the electromagnetic spectrum does it prevarication?

Dading C.

Numerade Educator

Trouble three

Hydrogen atoms are placed in an external magnetic field. The protons tin can make transitions betwixt states in which the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. What magnetic-field magnitude is required for this transition to be induced past photons with frequency 22.seven $\mathrm{MHz} ?$

Pankaj S.

Numerade Educator

Problem four

Neutrons are placed in a magnetic field with magnitude
2.thirty $\mathrm{T}$ . (a) What is the energy departure between the states with
the nuclear spin angular momentum components parallel and
antiparallel to the field? Which state is lower in energy: the one
with its spin component parallel to the field or the 1 with its spin
component antiparallel to the field? How practise your results compare
with the free energy states for a proton in the same field (see Example
43.2)? (b) The neutrons tin make transitions from one of these
states to the other by emitting or absorbing a photon with energy
equal to the free energy difference of the 2 states. Find the frequency
and wavelength of such a photon.

Sheh Lit C.

University of Washington

Trouble 5

The virtually common isotope of boron is i$\frac{xi}{v} \mathrm{B}$ (a) Determine
the total binding energy of $\frac{11}{v} \mathrm{B}$ from Table 43.ii in Section $43.1 .$
(b) Calculate this binding energy from Eq. $(43.xi) .$ . Why is the fifth
term zero? Compare to the result you lot obtained in office (a). What is
the percent difference? Compare the accuracy of Eq. (43.eleven) for
11 $\mathrm{B}$ to its accurateness for $\frac{62}{28} \mathrm{Ni}($ see Example 43.iv$)$

Problem 6

The nearly mutual isotope of uranium, $^{238} \mathrm{U},$ has diminutive
mass 238.050783 u. Calculate (a) the mass defect; (b) the bounden
energy (in MeV); (c) the bounden energy per nucleon.

Dading C.

Numerade Educator

Problem 7

What is the maximum wavelength of a $\gamma$ ray that could
intermission a deuteron into a proton and a neutron? (This process is
chosen photodisintegration.)

Zachary W.

Numerade Educator

Problem 8

Calculate (a) the total binding energy and (b) the binding
energy per nucleon of $^{12} \mathrm{C}$ (c) What percent of the residue mass of this
nucleus is its total bounden free energy?

Dading C.

Numerade Educator

Problem ix

A photon with a wavelength of $3.l \times 10^{-13} \mathrm{m}$ strikes
a deuteron, splitting information technology into a proton and a neutron. (a) Calculate the
kinetic energy released in this interaction. (b) Assuming the 2
particles share the energy as, and taking their masses to exist
1.00 u, calculate their speeds after the photodisintegration.

Kai C.

Princeton University

Problem 10

Calculate the mass defect, the binding energy (in MeV),
and the binding free energy per nucleon of (a) the nitrogen nucleus, $\frac{fourteen}{vii} \mathrm{N}$ ,
and (b) the helium nucleus, $_{2}^{four}$ He. (c) How does the binding free energy
per nucleon compare for these ii nuclei?

Dading C.

Numerade Educator

Problem 11

Utilize Eq. $(43.11)$ to calculate the binding energy per nucleon for the nuclei $\frac{86}{36} \mathrm{Kr}$ and one$\frac{180}{73}$ Ta. Do your results confirm what is shown in Fig. $43.2-$ that for $A$ greater than 62 the bounden energy per nucleon deceases as $A$ increases?

Dading C.

Numerade Educator

Problem 12

(a) Is the decay n\rightarrowp $+\beta^{-}+\overline{\nu}_{\text { e }}$
energetically possible? If not, explain why non. If so, summate the full energy
released. (b) Is the decay p\rightarrow $\mathrm{\beta}^{+}+\boldsymbol{\nu}_{\mathrm{due east}}$ energetically
possible? If not, explain why non. If so, summate the total energy
released.

Nolan S.

Numerade Educator

Problem 13

What nuclide is produced in the following radioactive
decays? (a) $\alpha$ decay of $^{239} \mathrm{Pu} ;$ (b) $\beta^{-}$ decay of $_{11}^{24} \mathrm{Na} ;(\mathrm{c}) \beta^{+}$ decay of $_{8}^{15} \mathrm{O}$

Dading C.

Numerade Educator

Problem xiv

$^{238}\mathrm{U}$ decays spontaneously past $\alpha$ emission to $^{234} \mathrm{Th.}$
Summate (a) the total energy released by this process and (b) the
recoil velocity of the $^{234} \mathrm{Th}$ nucleus. The atomic masses are
238.050788 u for $^{238} \mathrm{U}$ and 234.043601 u for $^{234} \mathrm{Thursday}$.

Dading C.

Numerade Educator

Problem 15

The atomic mass of $^{fourteen} \mathrm{C}$ is 14.003242 u. Show that the
$\beta^{-}$ disuse of $^{14} \mathrm{C}$ is energetically possible, and calculate the energy
released in the decay.

Dading C.

Numerade Educator

Problem sixteen

What particle $(\alpha$ particle, electron, or positron) is
emitted in the following radioactive decays? (a) $_{fourteen}^{27} \mathrm{Si} \rightarrow_{13}^{27} \mathrm{Al}$ (b) $^{238} \mathrm{U} \rightarrow_{90}^{234} \mathrm{Th} ;$ (c) $_{33}^{74} \mathrm{As} \rightarrow_{34}^{74} \mathrm{Se}$

Dading C.

Numerade Educator

Problem 17

(a) Calculate the energy released past the electron-capture
decay of $^{57}_{27}$Co (encounter Example 43.7). (b) A negligible amount of this
free energy goes to the resulting $^{57}_{26}$Fe cantlet equally kinetic energy. Near
xc$\%$ of the time, the $^{57}_{26}$Fe nucleus emits two successive gamma-ray
photons after the electron-capture process, of energies 0.122 $\mathrm{MeV}$
and $0.014 \mathrm{MeV},$ respectively, in decaying to its footing state. What
is the energy of the neutrino emitted in this instance?

Dading C.

Numerade Educator

Trouble eighteen

Tritium ($^{iii}_{ane}$H) is an unstable isotope of hydrogen; its mass,
including ane electron, is iii.016049 u. (a) Show that tritium must
be unstable with respect to beta decay because the decay products
( $^{3}_{ii}$He plus an emitted electron ) have less total mass than the tritium. \right.
(b) Determine the full kinetic energy (in MeV) of the decay products, taking care to business relationship for the electron masses correctly.

Nolan S.

Numerade Educator

Problem 19

If a 6.13 -m sample of an isotope having a mass number of
124 decays at a rate of 0.350 Ci, what is its half-life?

Nolan S.

Numerade Educator

Problem xx

BIO Radioactive isotopes used in cancer therapy have a "shelf-life," like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the action of a sample of $^{60} \mathrm{Co}$ is 5000 $\mathrm{Ci} .$ When its action falls below $3500 \mathrm{Ci},$ it is considered too weak a source to use in treatment. You piece of work in the radiology department of a large infirmary. 1 of these $^{sixty} \mathrm{Co}$ sources in your inventory was manufactured on October $six,2004$ . It is at present April $six,2007$ . Is the source still usable? The half-life of $^{60} \mathrm{Co}$ is v.271 years.

Kai C.

Princeton University

Trouble 21

The common isotope of uranium, $^{238} \mathrm{U},$ has a half-life of
$4.47 \times 10^{ix}$ years, decomposable to $^{234} \mathrm{Thursday}$ by alpha emission. (a) What
is the decay constant? (b) What mass of uranium is required for an
activity of i.00 curie? (c) How many alpha particles are emitted
per 2d by 10.0 chiliad of uranium?

Kai C.

Princeton University

Problem 22

BIO Radiations Handling of Prostate Cancer. In
many cases, prostate cancer is treated by implanting 60 to 100
pocket-size seeds of radioactive textile into the tumor. The energy
released from the decays kills the tumor. Ane isotope that is used
(there are others) is palladium $\left(^{103} \mathrm{Pd}\correct),$ with a half-life of 17 days.
If a typical grain contains 0.250 g of $^{103} \mathrm{Pd},(\mathrm{a})$ what is its initial
activity rate in $\mathrm{Bq},$ and $(\mathrm{b})$ what is the charge per unit 68 days later?

Nolan S.

Numerade Educator

Trouble 23

A 12.0-g sample of carbon from living matter decays
at the rate of 180.0 decays/min due to the radioactive $^{14} \mathrm{C}$ in it.
What will be the decay rate of this sample in (a) 1000 years and
(b) $50,000$ years?

Dading C.

Numerade Educator

Problem 24

BIO Radioactive Tracers. Radioactive isotopes are
often introduced into the body through the bloodstream. Their
spread through the torso tin can then exist monitored by detecting the
appearance of radiation in dissimilar organs. $^{131} \mathrm{I},$ a $\beta^{-}$ emitter with
a half-life of viii.0 $\mathrm{d}$ , is ane such tracer. Suppose a scientist introduces
a sample with an activeness of 375 $\mathrm{Bq}$ and watches information technology spread to the
organs. (a) Bold that the sample all went to the thyroid gland,
what will be the decay rate in that gland 24 d (about three$\frac{1}{ii}$ weeks)
afterward? (b) If the decay rate in the thyroid 24 d later is actually measured to exist 17.0 Bq, what percentage of the tracer went to that
gland? (c) What isotope remains after the I-131 decays?

Dading C.

Numerade Educator

Trouble 25

The unstable isotope $^{40} \mathrm{Grand}$ is used for dating rock samples. Its half-life is $1.28 \times x^{ix} \mathrm{y}$ . (a) How many decays occur per 2nd in a sample containing $i.63 \times 10^{-half-dozen} \mathrm{one thousand}$ of $^{40} \mathrm{Thousand}$ (b) What is
the activity of the sample in curies?

Dading C.

Numerade Educator

Trouble 26

As a health physicist, y'all are beingness consulted about a
spill in a radiochemistry lab. The isotope spilled was 500$\mu C$ of
$^{131} \mathrm{Ba}$, which has a half-life of 12 days. (a) What mass of $^{131} \mathrm{Ba}$ was spilled? (b) Your recommendation is to clear the lab until the
radiation level has fallen 1.00$\mu$ Ci. How long will the lab have to
exist airtight?

Dading C.

Numerade Educator

Problem 27

Measurements on a certain isotope tell y'all that the
decay rate decreases from 8318 decays/min to 3091 decays/min
in 4.00 days. What is the half-life of this isotope?

Nolan S.

Numerade Educator

Problem 28

The isotope $^{226} \mathrm{Ra}$ undergoes $\blastoff$ disuse with a one-half-life of
1620 years. What is the activeness of 1.00 $\mathrm{chiliad}$ of $^{226} \mathrm{Ra}$ ? Express your
answer in $\mathrm{Bq}$ and in $\mathrm{Ci}$ .

Dading C.

Numerade Educator

Problem 29

The radioactive nuclide $^{199} \mathrm{Pt}$ has a one-half-life of 30.8 minutes. A sample is prepared that has an initial activity of $7.56 \times 10^{eleven} \mathrm{Bq}$. (a) How many $^{199} \mathrm{Pt}$ nuclei are initially present in the sample? (b) How many are present later on 30.8 minutes? What is the activity at this time? (c) Repeat role (b) for a time 92.4 minutes after the sample is first prepared.

Dading C.

Numerade Educator

Problem 30

Radiocarbon Dating. A sample from timbers at an archeological site containing 500 1000 of carbon provides 3070 decays/min. What is the age of the sample?

Griffin 1000.

Numerade Educator

Problem 31

BIO (a) If a chest x ray delivers 0.25 $\mathrm{mSv}$ to five.0 $\mathrm{kg}$ of
tissue, how many full joules of energy does this tissue receive?
(b) Natural radiation and catholic rays deliver nearly 0.x $\mathrm{mSv}$ per
yr at sea level. Assuming an $\mathrm{RBE}$ of $1,$ how many rem and rads
is this dose, and how many joules of free energy does a 75 -kg person
receive in a year? (c) How many chest xays like the ane in role
(a) would it take to deliver the same total amount of free energy to a
75 -kg person as she receives from natural radiations in a year at ocean
level, as described in part (b)?

Dading C.

Numerade Educator

Problem 32

BIO A person exposed to fast neutrons receives a radiation dose of 200 rem on part of his manus, affecting 25 chiliad of tissue. The RBE of these neutrons is x. (a) How many rad did he receive? (b) How many joules of free energy did this person receive?
(c) Suppose the person received the same rad dosage, but from
beta rays with an RBE of ane.0 instead of neutrons. How many rem
would he take received?

Dading C.

Numerade Educator

Problem 33

BIO A nuclear chemist receives an accidental radiations dose of 5.0 Gy from slow neutrons (RBE = iv.0). What does she receive in rad, rem, and J/kg?

Dading C.

Numerade Educator

Trouble 34

BIO To Scan or Not to Browse? It has become popular
for some people to have yearly whole-torso scans (CT scans, formerly called CAT scans) using x rays, just to meet if they notice annihilation suspicious. A number of medical people have recently questioned the advisability of such scans, due in part to the radiations they impart. Typically, one such scan gives a dose of 12 $\mathrm{mSv}$ , practical to the whole body. Past contrast, a breast $x$ ray typically administers 0.xx mSv to simply five.0 kg of tissue. How many breast $ten$ rays would evangelize the same full corporeality of energy to the body of a 75 -kg person as one whole-torso scan?

Dading C.

Numerade Educator

Problem 35

BIO Food Irradiation. Nutrient is often irradiated with
either $x$ rays or electron beams to help prevent spoilage. A low
dose of $5-75$ kilorads (krad) helps to reduce and kill inactive parasites, a medium dose of $100-400$ krad kills microorganisms and
pathogens such as salmonella, and a high dose of $2300-5700$ krad
sterilizes nutrient so that information technology tin can be stored without refrigeration. (a) A
dose of 175 krad kills spoilage microorganisms in fish. If $x$ rays are
used, what would be the dose in Gy, Sv, and rem, and how much
free energy would a $220-\mathrm{g}$ portion of fish absorb? (See Table $43.3 . )$
(b) Echo part (a) if electrons of RBE ane.fifty are used instead of
x rays.

Dading C.

Numerade Educator

Problem 36

BIO In an industrial accident a 65-kg person receives a
lethal whole-body equivalent dose of 5.iv $\mathrm{Sv}$ from $\mathrm{ten}$ rays. (a) What
is the equivalent dose in rem? (b) What is the absorbed dose in rad? (c) What is the full energy absorbed by the person's body?
How does this amount of free energy compare to the amount of energy
required to raise the temperature of 65 kg of water 0.010 $\mathrm{C}^{\circ}$ ?

Dading C.

Numerade Educator

Problem 37

BIO A 67 -kg person accidentally ingests 0.35 Ci of tritium. (a) Presume that the tritium spreads uniformly throughout the body and that each decay leads on the average to the absorption of 5.0 $\mathrm{keV}$ of energy from the electrons emitted in the decay. The one-half-life of tritium is $12.3 \mathrm{y},$ and the RBE of the electrons is $1.0 .$ Calculate the absorbed dose in rad and the equivalent dose in rem during one calendar week. (b) The $\beta^{-}$ decay of tritium releases more than than 5.0 keV of energy. Why is the boilerplate energy absorbed less than the full energy released in the decay?

Nolan Due south.

Numerade Educator

Problem 38

BIO In a diagnostic x-ray process, $5.00 \times 10^{10}$ photons are absorbed by tissue with a mass of 0.600 $\mathrm{kg.}$ The $\mathrm{x}$ -ray wavelength is 0.0200 $\mathrm{nm.}$ (a) What is the total free energy absorbed past the tissue? (b) What is the equivalent dose in rem?

Dading C.

Numerade Educator

Trouble 39

Consider the nuclear reaction
$$_{1}^{2} \mathrm{H}+\stackrel{xiv}{vii} \mathrm{Northward} \rightarrow \mathrm{Ten}+_{5}^{10} \mathrm{B}$$
where $X$ is a nuclide. (a) What are $Z$ and $A$ for the nuclide $10 ?$ (b) Calculate the reaction energy $Q$ (in MeV). (c) If the $_{one}^{2}$ H nucleus is incident on a stationary $xiv^{\circ} \mathrm{N}$ nucleus, what minimum kinetic energy must it accept for the reaction to occur?

Dading C.

Numerade Educator

Problem xl

Free energy from Nuclear Fusion. Calculate the energy
released in the fusion reaction
$$
\frac{three}{2} \mathrm{He}+_{1}^{2} \mathrm{H} \rightarrow_{2}^{4} \mathrm{He}+_{ane}^{1} \mathrm{H}
$$

Dading C.

Numerade Educator

Trouble 41

Consider the nuclear reaction
$$^{2} \mathrm{H}+\stackrel{9}{4} \mathrm{Be} \rightarrow \mathrm{10}+\stackrel{4}{two} \mathrm{He}$$
where $\mathrm{X}$ is a nuclide. (a) What are the values of $Z$ and $A$ for the nuclide $\mathrm{Ten} ?$ (b) How much energy is liberated? (c) Estimate the threshold free energy for this reaction.

Dading C.

Numerade Educator

Problem 42

The United States uses $1.0 \times 10^{20} \mathrm{J}$ of electrical energy per year. If all this free energy came from the fission of $^{235} \mathrm{U},$ which releases 200 MeV per fission event, (a) how many kilograms of 235 $\mathrm{U}$ would be used per year and (b) how many kilograms of uranium would have to exist mined per yr to provide that much $^{235} \mathrm{U} ?$ (Recall that only 0.lxx$\%$ of naturally occurring uranium is $^{235} \mathrm{U} .$ )

Zachary W.

Numerade Educator

Problem 43

At the beginning of Department 43.7 the equation of a fission process is given in which $^{235} \mathrm{U}$ is struck by a neutron and undergoes fission to produce $^{144} \mathrm{Ba}, ^{89} \mathrm{Kr},$ and iii neutrons. The measured masses of these isotopes are 235.043930 $\mathrm{u}$ $\left(^{235} \mathrm{U}\correct)$ 143.922953 $\mathrm{u}\left(^{144} \mathrm{Ba}\right),$ 88.917630 $\mathrm{u}$ $\left(^{89} \mathrm{Kr}\correct),$ and 1.0086649 $\mathrm{u}$ (neutron). (a) Calculate the energy (in MeV) released by each fission reaction. (b) Calculate the energy released per gram of $^{235} \mathrm{U}$ , in MeV/one thousand.

Nolan South.

Numerade Educator

Problem 44

Consider the nuclear reaction
$$
_{14}^{28} \mathrm{Si}+\gamma \rightarrow_{12}^{24} \mathrm{Mg}+\mathrm{X}
$$
where $X$ is a nuclide. (a) What are $Z$ and $A$ for the nuclide $X$ ?
(b) Ignoring the effects of recoil, what minimum energy must the
photon have for this reaction to occur? The mass of a $_{14}^{28}$ Si cantlet is
27.976927 $ \mathrm{u},$ and the mass of a $^{24}_{12} \mathrm{Mg}$ atom is 23.985042 $\mathrm{u}$

Nolan S.

Numerade Educator

Problem 45

The 2d reaction in the proton-proton chain (see
Fig. 43.16$)$ produces a $_{2}^{3}$ He nucleus. A $_{ii}^{3}$He nucleus produced in
this way can combine with a $_{2}^{four}$ He nucleus:
$$
\frac{three}{2} \mathrm{He}+_{2}^{iv} \mathrm{He} \rightarrow_{four}^{7} \mathrm{Exist}+\gamma
$$
Calculate the free energy liberated in this procedure. (This is shared
between the energy of the photon and the recoil kinetic free energy of
the beryllium nucleus.) The mass of a $^{7}_{4}$Be cantlet is vii.016929 u.

Dading C.

Numerade Educator

Problem 46

Consider the nuclear reaction
$$
_{two}^{4} \mathrm{He}+_{three}^{7} \mathrm{Li} \rightarrow \mathrm{X}+_{0}^{ane} \mathrm{n}
$$
where $X$ is a nuclide. (a) What are $Z$ and $A$ for the nuclide $Ten ?$ (b) Is
free energy captivated or liberated? How much?

Dading C.

Numerade Educator

Problem 47

In a $100.0-\mathrm{cm}^{3}$ sample of water, 0.015$\%$ of the molecules are $\mathrm{D}_{two} \mathrm{O} .$ Compute the energy in joules that is liberated if all the deuterium nuclei in the sample undergo the fusion reaction of
Example $43.13 .$

Dading C.

Numerade Educator

Problem 48

Comparison of Energy Released per Gram of Fuel.
(a) When gasoline is burned, it releases $1.three \times 10^{8} \mathrm{J}$ of free energy per
gallon $(3.788 \mathrm{50}) .$ Given that the density of gasoline is 737 $\mathrm{kg} / \mathrm{g}^{iii}$ , express the quantity of energy released in $\mathrm{J} / \mathrm{g}$ of fuel. (b) During fission, when a neutron is absorbed past a $^{235} \mathrm{U}$ nucleus, about 200 $\mathrm{MeV}$ of energy is released for each nucleus that undergoes fission. Express this quantity in $\mathrm{J} / \mathrm{g}$ of fuel. (c) In the proton-proton chain that takes place in stars like our sun, the overall fusion reaction can be summarized equally six protons fusing to course i $^{4}$He nucleus with two leftover protons and the liberation of 26.seven $\mathrm{MeV}$
of energy. The fuel is the six protons. Express the energy produced hither in units of $\mathrm{J} / \mathrm{g}$ of fuel. Find the huge difference between the 2 forms of nuclear energy, on the one manus, and the chemical energy from gasoline, on the other. (d) Our dominicus produces energy at a measured rate of $3.86 \times 10^{26} \mathrm{W}$ . If its mass of $1.99 \times 10^{xxx} \mathrm{kg}$ were all gasoline, how long could it terminal earlier consuming all its fuel? (Historical note: Earlier the discovery of nuclear fusion and the vast amounts of energy it releases, scientists were confused. They knew that the globe was at least many millions of years old, but could non explicate how the sun could survive that long if its free energy came from chemic burning.)

Dading C.

Numerade Educator

Problem 49

Apply conservation of mass-energy to evidence that the energy released in alpha decay is positive whenever the mass of the original neutral atom is greater than the sum of the masses of the terminal neutral atom and the neutral $^{iv}$ He atom. (Hint: Let the parent nucleus take atomic number $Z$ and nucleon number $A .$ Offset write the reaction in terms of the nuclei and particles involved, so add $Z$ electron masses to both sides of the reaction and destine them as needed to arrive at neutral atoms.)

Dading C.

Numerade Educator

Problem 50

Apply conservation of mass-energy to show that the energy released in $\beta^{-}$ decay is positive whenever the neutral atomic mass of the original atom is at to the lowest degree two electron masses greater than that of the final atom. (Come across the hint in Problem 43.49.)

Dading C.

Numerade Educator

Trouble 51

Use conservation of mass-free energy to prove that the
free energy released in $\beta^{+}$ decay is positive whenever the neutral
atomic mass of the original cantlet is at least two electron masses
greater than that of the final atom. (Meet the hint in Problem $43.49 .$)

Problem 52

(a) Calculate the minimum free energy required to remove i proton from the nucleus $^{12}_{half dozen} \mathrm{C}$ . This is called the proton-removal energy. (Hint: Detect the difference betwixt the mass of a $^{12}_{6} \mathrm{C}$ nucleus and the mass of a proton plus the mass of the nucleus formed when a proton is removed from $^{12}_{6} \mathrm{C} .$ (b) How does the proton-removal energy for $^{12}_{6} \mathrm{C}$ compare to the binding energy per nucleon for $^{12}_{6} \mathrm{C},$ calculated using Eq. $(43.10) ?$

Nolan Southward.

Numerade Educator

Problem 53

(a) Calculate the minimum energy required to remove one neutron from the nucleus $_{8}^{17} \mathrm{O}$. This is called the neutron-removal free energy. (Run across Problem $43.52 . )$ (b) How does the neutron-removal energy for $_{8}^{17} \mathrm{O}$ compare to the bounden free energy per nucleon for $_{8}^{17} \mathrm{O}$ calculated using Eq. $(43.10) ?$

Trouble 54

The neutral atomic mass of $^{14}_{six} \mathrm{C}$ is 14.003242 u. Calculate the proton removal energy and the neutron removal free energy for $^{15}_{vii} \mathrm{N} .$ (Encounter Problems 43.52 and $43.53 . )$ What is the percentage difference betwixt these two energies, and which is larger?

Problem 55

BIO Radioactive Fallout. One of the bug of in-air
testing of nuclear weapons (or, even worse, the utilise of such
weapons!) is the danger of radioactive fallout. One of the near
problematic nuclides in such fallout is strontium-90 $\left(^{ninety} \mathrm{Sr}\right),$ which
breaks down by $\beta^{-}$ decay with a one-half-life of 28 years. It is chemically similar to calcium and therefore can exist incorporated into
bones and teeth, where, due to its rather long half-life, it remains for
years as an internal source of radiation. (a) What is the daughter
nucleus of the $^{90}$ Sr decay? (b) What percentage of the original level
of $^{ninety}$ Sr is left after 56 years? (c) How long would yous have to wait
for the original level to be reduced to 6.25$\%$ of its original value?

Dading C.

Numerade Educator

Problem 56

Thorium $^{230}_{90}$ Th decays to radium $^{226}_{88}$ Ra by $\alpha$ emission. The masses of the neutral atoms are 230.033127 u for $^{230} \mathrm{Thursday}$ and 226.025403 u for $^{226}_{88} \mathrm{Ra}$. If the parent thorium nucleus is at remainder, what is the kinetic energy of the emitted $\alpha$ particle? (Exist sure to business relationship for the recoil of the daughter nucleus.)

Nolan S.

Numerade Educator

Problem 57

The atomic mass of $_{12}^{25} \mathrm{Mg}$ is 24.985837 $\mathrm{u},$ and the atomic mass of $^{25}_{13}$ Al is 24.990429 u. (a) Which of these nuclei will disuse into the other? (b) What type of decay will occur? Explain how yous determined this. (c) How much energy (in MeV) is released in the decay?

Dading C.

Numerade Educator

Trouble 58

The polonium isotope $_{84}^{210} \mathrm{Po}$ has atomic mass
209.982857 u. Other atomic masses are $_{82}^{206} \mathrm{Pb}$, 205.974449 $\mathrm{u}$; $_{83}^{209} \mathrm{Bi}$, 208.980383 $\mathrm{u}$; $^{210}_{83} \mathrm{Bi}$, 209.984105 $\mathrm{u}$; $^{209}_{84} \mathrm{PO}$, 208.982416 $\mathrm{u}$; and $_{85}^{210} \mathrm{At}$, 209.987131 $\mathrm{u}$. (a) Bear witness that the blastoff disuse of $^{210}_{84} \mathrm{Po}$ is energetically possible, and discover the free energy of the emitted $\alpha$ particle. (b) Is $^{210}_{84} \mathrm{Po}$ energetically stable with respect to emission of a proton? Why or why not? (c) Is $^{210}_{84} \mathrm{Po}$ energetically stable with respect to emission of a neutron? Why or why non? (d) Is $^{210}_{84} \mathrm{Po}$ energetically stable with respect to $\beta^{-}$ disuse? Why or why not? (eastward) Is $^{210}_{84} \mathrm{Po}$ energetically stable with respect to $\beta^{+}$ decay? Why or why not?

Problem 59

BIO Irradiating Ourselves! The radiocarbon in our
bodies is i of the naturally occurring sources of radiation. Permit's
see how big a dose we receive. $^{xiv} \mathrm{C}$ decays via $\beta^{-}$ emission, and 18$\%$ of our torso's mass is carbon. (a) Write out the decay scheme
of carbon-fourteen and prove the finish production. (A neutrino is as well produced.) (b) Neglecting the effects of the neutrino, how much kinetic energy (in MeV) is released per decay? The atomic mass of $^{14} \mathrm{C}$ is 14.003242 $\mathrm{u}$ . (c) How many grams of carbon are there in a 75 -kg person? How many decays per 2nd does this carbon produce? (Hint: Use data from Example $43.ix . )$ (d) Assuming that all
the free energy released in these decays is absorbed by the trunk, how many MeV/southward and J/south does the $^{14} \mathrm{C}$ release in this person's trunk?
(east) Consult Table 43.3 and use the largest appropriate RBE for the particles involved. What radiation dose does the person give himself in a year, in Gy, rad, Sv, and rem?

Dading C.

Numerade Educator

Problem 60

BIO Pion Radiation Therapy. A neutral pion $\left(\pi^{0}\right)$
has a mass of 264 times the electron mass and decays with a lifetime of $8.4 \times 10^{-17} \mathrm{s}$ to 2 photons. Such pions are used in the radiation treatment of some cancers. (a) Notice the energy and wavelength of these photons. In which part of the electromagnetic spectrum exercise they lie? What is the RBE for these photons? (b) If you want
to deliver a dose of 200 rem (which is typical) in a single handling to 25 one thousand of tumor tissue, how many $\pi^{0}$ mesons are needed?

Nolan Southward.

Numerade Educator

Problem 61

Gold, $_{79}^{198} \mathrm{Au}$, undergoes $\beta^{-}$ decay to an excited state of $^{198}_{eighty} \mathrm{Hg}$. If the excited land decays by emission of a photon with energy 0.412 MeV, what is the maximum kinetic energy of the
electron emitted in the decay? This maximum occurs when the antineutrino has negligible energy. (The recoil energy of the $^{198}_{eighty} \mathrm{Hg}$ nucleus tin be ignored. The masses of the neutral atoms in their basis states are 197.968225 u for $^{198}_{lxxx} \mathrm {Au}$ and 197.966752 u for $\frac{198}{80} \mathrm{Hg}_{\cdot} $)

Dading C.

Numerade Educator

Problem 62

Calculate the mass defect for the $\beta^{+}$ decay of $_{6}^{11} \mathrm{C} .$ Is this decay energetically possible? Why or why non? The atomic mass of $^{eleven}_{6} \mathrm{C}$ is 11.011434 $\mathrm{u}$ .

Dading C.

Numerade Educator

Trouble 63

Calculate the mass defect for the $\beta^{+}$ decay of $^{13}_{seven} \mathrm{Due north} .$ Is this decay energetically possible? Why or why not? The atomic mass of $^{13}_{7} \mathrm{Due north}$ is 13.005739 $\mathrm{u}$.

Dading C.

Numerade Educator

Problem 64

The results of activity measurements on a radioactive
sample are given in the table. (a) Find the half-life. (b) How many radioactive nuclei were present in the sample at $t=0 ?$ (c) How many were present later seven.0 $\mathrm{h}$ ?

Dading C.

Numerade Educator

Trouble 65

BIO A person ingests an corporeality of a radioactive source
with a very long lifetime and activity 0.63$\mu \mathrm{Ci} .$ The radioactive fabric lodges in the lungs, where all of the four.0 -MeV $\alpha$ particles
emitted are absorbed within a 0.50 -kg mass of tissue. Calculate the
absorbed dose and the equivalent dose for one year.

Dading C.

Numerade Educator

Trouble 66

Measuring Very Long Half-Lives. Some radio-
isotopes such every bit samarium $\left(^{149} \mathrm{Sm}\right)$ and gadolinium $\left(^{152} \mathrm{Gd}\right)$ have half-lives that are much longer than the age of the universe, and then we can't measure their half-lives by watching their decay charge per unit subtract. Luckily, at that place is some other way of calculating the half-life, using Eq. $(43.16) .$ Suppose a 12.0 -m sample of $^{149} \mathrm{Sm}$ is observed to disuse at a charge per unit of 2.65 Bq. Calculate the half-life of the sample in years. (Hint: How many nuclei are in that location in the 12.0 -g sample?)

Dading C.

Numerade Educator

Problem 67

We Are Stardust. In 1952 spectral lines of the element technetium- 99$\left(^{99} \mathrm{Tc}\right)$ were discovered in a carmine giant star. Reddish giants are very sometime stars, often around ten billion years old, and virtually the terminate of their lives. Technetium has $no$ stable isotopes, and the half-life of $^{99} \mathrm{Tc}$ is $200,000$ years. (a) For how many half-lives has the $^{99} \mathrm{Tc}$ been in the ruddy-giant star if its age is 10 billion years? (b) What fraction of the original $^{99} \mathrm{Tc}$ would exist left at the terminate of that time? This discovery was extremely of import because it provided convincing evidence for the theory (now essentially known to be true) that near of the atoms heavier than hydrogen and helium were fabricated inside of stars by thermonuclear fusion and other nuclear processes. If the $^{99} \mathrm{Tc}$ had been part of the star since it was born, the amount remaining subsequently 10 billion years would accept been and then minute that it would not have been detectable. This noesis is what led the late astronomer Carl Sagan to proclaim that "we are stardust."

Nolan S.

Numerade Educator

Problem 68

BIO A seventy.0-kg person experiences a whole-body exposure to $\alpha$ radiation with energy 4.77 MeV. A total of $6.25 \times 10^{12} \alpha$ particles are absorbed. (a) What is the absorbed dose in rad? (b) What is the equivalent dose in rem? (c) If the source is 0.0320 $\mathrm{g}$ of $^{226} \mathrm{Ra}$ (one-half-life 1600 $\mathrm{y}$) somewhere in the trunk, what is the activity of this source? (d) If all the alpha particles produced are absorbed, what time is required for this dose to be delivered?

Dading C.

Numerade Educator

Problem 69

Measurements indicate that 27.83$\%$ of all rubidium atoms currently on the earth are the radioactive $^{87} \mathrm{Rb}$ isotope. The remainder are the stable $^{87} \mathrm{Rb}$ isotope. The one-half-life of $^{87} \mathrm{Rb}$ is $4.75 \times 10^{x} \mathrm{y}$ . Bold that no rubidium atoms have been formed since, what percentage of rubidium atoms were $^{87} \mathrm{Rb}$ when our solar system was formed $4.6 \times 10^{9} \mathrm{y}$ ago?

Dading C.

Numerade Educator

Problem 70

A $^{186}_{76} \mathrm{Os}$ nucleus at residue decays by the emission of a 2.76 -MeV $\alpha$ particle. Calculate the atomic mass of the girl nuclide produced past this decay, assuming that it is produced in its footing state. The diminutive mass of $^{186}_{76} \mathrm{Bone}$ is 185.953838 $\mathrm{u}$

Dading C.

Numerade Educator

Problem 71

$\mathrm{A}^{60} \mathrm{Co}$ source with activeness $two.6 \times x^{-4} \mathrm{Ci}$ is embedded in a tumor that has mass 0.200 $\mathrm{kg} .$ The source emits
$\gamma$ photons with average energy 1.25 $\mathrm{MeV} .$ Half the photons are
absorbed in the tumor, and half escape. (a) What energy is delivered to the tumor per 2d? (b) What absorbed dose (in rad) is
delivered per 2d? (c) What equivalent dose (in rem) is delivered per 2nd if the RBE for these $\gamma$ rays is 0.seventy$?$ (d) What exposure fourth dimension is required for an equivalent dose of 200 rem?

Dading C.

Numerade Educator

Problem 72

The nucleus $^{15}_{8} \mathrm{O}$ has a half-life of 122.2 $\mathrm{southward}$; $^{19}_{8} \mathrm{O}$ has a half-life of 26.nine s. If at some time a sample contains equal amounts of $^{fifteen}_{8} \mathrm{O}$ and $^{19}_{8} \mathrm{O}$, what is the ratio of $^{15}_{8} \mathrm{O}$ to $^{19}_{eight} \mathrm{O}$ (a) after 4.0 minutes and (b) later 15.0 minutes?

Dading C.

Numerade Educator

Trouble 73

A bone fragment found in a cavern believed to take been inhabited by early humans contains 0.29 times as much $^{14} \mathrm{C}$ as an equal corporeality of carbon in the atmosphere when the organism containing the os died. (See Case 43.9 in Section $43.4 .$ . Notice the approximate age of the fragment.

Kai C.

Princeton University

Problem 74

An Oceanographic Tracer. Nuclear weapons tests in
the 1950 s and 1960 southward released significant amounts of radioactive
tritium $(^{3}_{1} \mathrm{H},$ one-half-life 12.3 years $)$ into the temper. The tritium atoms were rapidly bound into h2o molecules and rained out of
the air, about of them ending upwards in the ocean. For any of this
tritium-tagged water that sinks beneath the surface, the amount of time
during which it has been isolated from the surface can be calculated by measuring the ratio of the disuse product, $^{3}_{2} \mathrm{He},$ to the remaining tritium in the h2o. For example, if the ratio of $_{2}^{iii} \mathrm{He}$ to $_{1}^{3} \mathrm{H}$ in a sample of water is $1 : i,$ the water has been beneath the surface for one half-life, or approximately 12 years. This method
has provided oceanographers with a user-friendly way to trace the
movements of subsurface currents in parts of the bounding main. Suppose that in a detail sample of water, the ratio of $_{two}^{three}$ He to $_{one}^{3} \mathrm{H}$ is 4.3 to ane.0. How many years ago did this water sink beneath the surface?

Nolan S.

Numerade Educator

Problem 75

Consider the fusion reaction $_{one}^{two} \mathrm{H}+_{1}^{two} \mathrm{H} \rightarrow_{ii}^{3} \mathrm{He}+_{0 \mathrm{n}}$ (a) Estimate the barrier free energy by calculating the repulsive electrostatic potential energy of the two $_{one}^{2} \mathrm{H}$ nuclei when they bear on. (b) Compute the energy liberated in this reaction in MeV and in joules. (c) Compute the energy liberated per mole of deuterium,
remembering that the gas is diatomic, and compare with the heat of combustion of hydrogen, about $two.nine \times 10^{5} \mathrm{J} / \mathrm{mol}$

Dading C.

Numerade Educator

Problem 76

In the 1986 disaster at the Chernobyl reactor in the Soviet Matrimony (at present Ukraine), most $\frac{i}{8}$ of the $^{137} \mathrm{Cs}$ present in the reactor was released. The isotope $^{137} \mathrm{Cs}$ has a half-life for $\beta$ decay of 30.07 $\mathrm{y}$ and decays with the emission of a total of one.17 $\mathrm{MeV}$ of free energy per decay. Of this, 0.51 $\mathrm{MeV}$ goes to the emitted electron and the remaining 0.66 $\mathrm{MeV}$ to a $\gamma$ ray. The radioactive $^{137} \mathrm{Cs}$ is captivated by plants, which are eaten past livestock and humans. How many $^{137} \mathrm{Cs}$ atoms would demand to be present in each kilogram of trunk tissue if an equivalent dose for i week is iii.5 $\mathrm{Sv}$ ? Assume that all of the energy from the decay is deposited in that i.0 $\mathrm{kg}$ of
tissue and that the RBE of the electrons is 1.v.

Dading C.

Numerade Educator

Problem 77

(a) Prove that when a particle with mass $m$ and kinetic energy $Thou$ collides with a stationary particle with mass $K,$ the full kinetic energy $K_{\mathrm{cm}}$ in the center-of-mass coordinate system (the energy available to crusade reactions) is
$$K_{\mathrm{cm}}=\frac{M}{Chiliad+m} Chiliad$$
Presume that the kinetic energies of the particles and nuclei are much lower than their rest energies.
(b) If $K_{\text { thursday }}$ is the minimum, or threshold, kinetic free energy to cause an endoergic reaction to occur in the situation of function (a), show that
$$K_{\mathrm{thursday}}=-\frac{Chiliad+thou}{M} Q$$

Dading C.

Numerade Educator

Problem 78

Calculate the energy released in the fission reaction $_{92}^{235} \mathrm{U}+_{0}^{i} \mathrm{n} \rightarrow ^{140}_{54} \mathrm{Xe}+ ^{94}_{38} \mathrm{Sr}+2_{0}^{1} \mathrm{n}$ You lot can ignore the initial kinetic free energy of the absorbed neutron. The atomic masses are $_{92}^{235} \mathrm{U},$ 235.04392 $\mathrm{u};$ $^{140}_{54} \mathrm{Xe},$ 139.921636 $\mathrm{u};$ and $^{94}_{38} \mathrm{Sr},$ 93.915360 $\mathrm{u}.$

Dading C.

Numerade Educator

Problem 79

The results of activity measurements on a mixed sample of radioactive elements are given in the tabular array. (a) How many different nuclides are nowadays in the mixture? (b) What are their half-lives? (c) How many nuclei of each type are initially present in the sample? (d) How many of each blazon are present at $t=5.0 \mathrm{h} ?$

Problem 80

Industrial Radioactivity. Radioisotopes are used in a variety of manufacturing and testing techniques. Wearable measurements can be made using the following method. An auto engine is produced using piston rings with a total mass of $100 \mathrm{g},$ which includes 9.4$\mu \mathrm{Ci}$ of $^{59} \mathrm{Fe}$ whose half-life is 45 days. The engine is test-run for 1000 hours, after which the oil is drained and its activity is measured. If the activity of the engine oil is 84 decays/s, how much mass worn from the piston rings per hour of functioning?

Nolan Due south.

Numerade Educator

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Source: https://www.numerade.com/books/chapter/nuclear-physics-2/

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