College Physics

Raymond A. Serway, Jerry S. Faughn, Chris Vuille

Chapter 29

Nuclear Physics - all with Video Answers

Educators

Chapter Questions

Problem 1

Compare the nuclear radii of the following nuclides: ${ }^{2} \mathrm{H}$, ${ }_{27}^{\mathrm{ti}} \mathrm{Co}_{-}{ }^{197} \mathrm{Au},{ }_{99}^{129} \mathrm{Pu}$.

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 2

(a) Determine the mass number of a nucleus having a radius approximately equal to two-thirds the radius of ${ }_{\mathrm{xF}}^{\mathrm{n} \mathrm{se}} \mathrm{Ra}$. (b) Identify the element. Are any other answers possible? Explain.

Declan Nell

Numerade Educator

Problem 3

Using $2.3 \times 10^{17} \mathrm{~kg} / \mathrm{m}^{3}$ as the density of nuclear matter, find the radius of a sphere of such matter that would have a mass equal to that of Earth. Earth has a mass equal to $5.98 \times 10^{24} \mathrm{~kg}$ and average radius of $6.37 \times 10^{6} \mathrm{~m}$.

Lisa Tarman

Numerade Educator

Problem 4

Consider the ${ }_{39}^{65} \mathrm{Cu}$ nucleus. Find approximate values for its (a) radius, (b) volume, an'd (c) density.

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 5

An alpha particle $\quad\left(Z=2\right.$, mass $\left.=6.64 \times 10^{-27} \mathrm{~kg}\right)$ approaches to within $1.00 \times 10^{-14} \mathrm{~m}$ of a carbon nucleus $(Z=6)$. What are (a) the maximum Coulomb force on the alpha particle, (b) the acceleration of the alpha parLicle at this time, and (c) the potential energy of the alpha particle at the same time?

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 6

Singly ionized carbon atoms are accelerated through $1000 \mathrm{~V}$ and passed into a mass spectrometer to determine the isotopes present. (See Chapter 19.) The magnetic field strength in the spectrometer is $0.200 \mathrm{~T}$. (a) Determine the orbital radii for the ${ }^{12} \mathrm{C}$ and the ${ }^{13} \mathrm{C}$ isotopes as they pass through the field. (b) Show that the ratio of the radii may be written in the form
$$
\frac{r_{1}}{r_{2}}=\sqrt{\frac{m_{1}}{m_{2}}}
$$
and verify that your radii in part (a) satisfy this formula.

Declan Nell

Numerade Educator

Problem 7

(a) Find the speed an alpha particle requires to come within $3.2 \times 10^{-14} \mathrm{~m}$ of a gold nucleus. (b) Find the energy of the alpha particle in MeV.

Lisa Tarman

Numerade Educator

Problem 8

At the end of its life, a star with a mass of two times the Sun's mass is expected to collapse, combining its protons and electrons to form a neutron star. Such a star could be thought of as a gigantic atomic nucleus. If a star of mass $2 \times 1.99 \times 10^{30} \mathrm{~kg}$ collapsed into neutrons $\left(m_{11}=1.67 \times\right.$
$10^{-27} \mathrm{~kg}$ ), what would its radius be? Assume $r=r_{0} A^{1 / 3}$

Declan Nell

Numerade Educator

Problem 9

Calculate the average binding energy per nucleon of (a) ${ }_{11}^{23} \mathrm{Na}$ (sodium), (b) ${ }_{27}^{60}$ Co (cobalt), and (c) ${ }_{4}{ }^{107} \mathrm{Ag}$ (silver).

Declan Nell

Numerade Educator

Problem 10

Calculate the binding energy per nucleon for (a) ${ }^{2} \mathrm{H}$,
(b) ${ }^{4} \mathrm{He},(\mathrm{c})^{\mathrm{se} \mathrm{Fe}, \text { and }(\mathrm{d})^{\mathrm{2} 38} \mathrm{U} \text { . }}$

Declan Nell

Numerade Educator

Problem 11

A pair of nuclei for which $Z_{1}=N_{2}$ and $Z_{2}=N_{1}$ are called mirror isoburs. (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 ${ }_{8}^{1} \mathrm{O}$ and ${ }_{7}^{15} \mathrm{~N}$.

Declan Nell

Numerade Educator

Problem 12

The peak of the stability curve occurs at ${ }^{56} \mathrm{Fe}$, which is why iron is prominent in the spectrum of the Sun and stars. Show that ${ }^{56} \mathrm{Fe}$ has a higher binding energy per nucleon than its neighbors ${ }^{55} \mathrm{Mn}$ and ${ }^{50}$ Co. Compare your results with Figure $29.4$.

Declan Nell

Numerade Educator

Problem 13

Two nuclei having the same mass number are known as isobars. Calculate the difference in binding energy per nucleon for the isobars ${ }_{11}^{23} \mathrm{Na}$ and ${ }_{12}^{93} \mathrm{Mg}$. How do you account for this difference? (The mass of ${ }_{12}^{25} \mathrm{Mg}=$ $22.994127 \mathrm{u} .$ )

Declan Nell

Numerade Educator

Problem 14

Calculate the binding energy of the last neutron in the ${ }_{29}^{19}$ Ca nucleus. Hint: You should compare the mass of ${ }_{20}^{43} \mathrm{Ca}$ with the mass of ${ }_{20}^{4}$ Ca plus the mass of a neutron. The mass of ${ }_{20}^{4} \mathrm{Ca}=41.958622 \mathrm{u}$, whereas the mass of ${ }_{20}^{4} \mathrm{Ca}=$
$42.958770 \mathrm{u}$

Declan Nell

Numerade Educator

Problem 15

The half-life of an isotope of phosphorus is 14 days. If ? sample contains $3.0 \times 10^{16}$ such nuclei, determine its activity. Express your answer in curies.

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 16

A drug tagged with ${ }_{4 .}^{\text {99Tc }}$ (half-life $=6.05 \mathrm{~h}$ ) is prepared for a patient. If the original activity of the sample was $1.1 \times 10^{4} \mathrm{~Bq}$, what is its activity after it has been on the shelf for $2.0 \mathrm{~h}$ ?

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 17

The half-life of ${ }^{131} \mathrm{I}$ is $8.04$ days.
(a) Convert the halflife to seconds. (b) Calculate the decay constant for this isotope. (c) Convert $0.500 \mu \mathrm{Ci}$ to the SI unit the becquerel.
(d) Find the number of ${ }^{131}$ I nuclei necessary to produce a sample with an activity of $0.500 \mu \mathrm{Ci}$. (e) Suppose the activity of a certain ${ }^{131}$ I sample is $6.40 \mathrm{mCi}$ at a given time. Find the number of half-lives the sample goes through in $40.2 \mathrm{~d}$ and the activity at the end of that period.

Declan Nell

Numerade Educator

Problem 18

Tritium has a half-life of $12.33$ years. (a) What fraction of the nuclei in a tritium sample will remain after $5.00$ yr? (b) $10.0$ yr? (c) $123.3$ yr? (d) According to Equation $29.4 \mathrm{a}$, an infinite amount of time is required for the entire sample to decay. Is that realistic? Discuss.

Lisa Tarman

Numerade Educator

Problem 19

Many smoke detectors use small quantities of the isotope ${ }^{241} \mathrm{Am}$ in their operation. The half-life of ${ }^{241} \mathrm{Am}$ is 432 yr. How long will it take the activity of this material to decrease to $1.00 \times 10^{-3}$ of the original activity?

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 20

After a plant or animal dies, its ${ }^{14} \mathrm{C}$ content decreases with a half-life of 5780 yr. If an archaeologist finds an ancient firepit containing partially consumed firewood and the ${ }^{14} \mathrm{C}$ content of the wood is only $12.5 \%$ that of an equal carbon sample from a present-day tree, what is the age of the ancient site?

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 21

A freshly prepared sample of a certain radioactive isotope has an activity of $10.0 \mathrm{mCi}$. After $4.00 \mathrm{~h}$, the activity is $8.00 \mathrm{mCi}$.
(a) Find the decay constant and half-life of the isotope. (b) How many atoms of the isotope were contained in the freshly prepared sample? (c) What is the sample's activity $30 \mathrm{~h}$ after it is prepared?

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 22

A building has become accidentally contaminated with radioactivity. The longest-lived material in the building is strontium-90. (The atomic mass of ${ }_{38}^{00} \mathrm{Sr}$ is $89.9077 \mathrm{u}$.) If the building initially contained $5.0 \mathrm{~kg}$ of this substance and the safe level is less than $10.0$ counts/min, how long will the building be unsafe:

Declan Nell

Numerade Educator

Problem 23

Identify the missing nuclides ( $\mathrm{X}$ ) in the following decays:
(a) $\mathrm{X} \rightarrow{ }_{28}^{65} \mathrm{Ni}+\gamma$
(c) $\mathrm{X} \rightarrow{ }_{\mathrm{L} 5}^{5 \mathrm{~F}} \mathrm{~F}+\mathrm{e}^{+}+\nu$
(b) ${ }_{\mathrm{M} 4}^{21} \mathrm{Po} \rightarrow \mathrm{X}+\alpha$

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 24

Identify the missing particles $(\mathrm{X})$ in the following reactions:
(a) ${ }_{+5} \mathrm{C} \mathrm{C}+\mathrm{X} \rightarrow{ }_{4}^{\mathrm{in}} \mathrm{Ag}+\nu$
(b) ${ }_{7}^{14} \mathrm{~N}+{ }_{2}^{4} \mathrm{He} \rightarrow \mathrm{X}+{ }_{5}^{12} \mathrm{O}$

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 25

The mass of "ife is $55.9349 \mathrm{u}$, and the mass of ${ }^{16} \mathrm{Co}$ is $55.9399 \mathrm{u}$. Which isotope decays into the other and by what process?

Declan Nell

Numerade Educator

Problem 26

Find the energy released in the alpha decay of ${ }^{239} \mathrm{U}$. The following mass value will be useful: ${ }_{90}^{28} \mathrm{Th}$ has a mass of $284.043583 \mathrm{u} .$

Declan Nell

Numerade Educator

Problem 27

Determine which of the following suggested decays can occur spontaneously:
(a) ${ }_{20}^{40} \mathrm{Ca} \rightarrow \mathrm{e}^{*}+{ }_{19}^{+0} \mathrm{~K}$
(b) ${ }_{\text {in }}^{14} \mathrm{Nd} \rightarrow{ }_{2}^{4} \mathrm{He}+{ }^{16}{ }_{5} \mathrm{Ce}$

Declan Nell

Numerade Educator

Problem 28

${ }_{28} \mathrm{Ni}$ (mass $=65.929 \mathrm{l} \mathrm{u}$ ) undergoes beta decay to ${ }_{\mathrm{s} 9} \mathrm{Cu}$ (mass $=65.9289 \mathrm{u}$ ). (a) Write the complete decay formula for this process. (b) Find the maximum kinetic energy of the emerging electrons.

Declan Nell

Numerade Educator

Problem 29

An ${ }^{3} \mathrm{H}$ nucleus beta decays into ${ }^{3} \mathrm{He}$ by creating an electron and an antineutrino according to the reaction
$$
{ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2} \mathrm{He}+\mathrm{e}^{-}+\bar{\nu}
$$
Use Appendix $B$ to decermine the total energy released in this reaction.

Declan Nell

Numerade Educator

Problem 30

A piece of charcoal used for cooking is found at the remains of an ancient campsite. A $1.00-\mathrm{kg}$ sample of carbon from the wood has an activity of $2.00 \times 10^{3}$ decays per minute. Find the age of the charcoal. Hint: Living material has an activity of $15.0$ decays/minute per gram of carbon present.

Declan Nell

Numerade Educator

Problem 31

A wooden artifact is found in an ancient tomb. Its carbon$14\left(\frac{14}{6} \mathrm{C}\right)$ activity is measured to be $60.0 \%$ of that in a fresh sample of wood from the same region. Assuming the same amount of ${ }^{14} \mathrm{C}$ was initially present in the wood from which the artifact was made, determine the age of the artifact.

Eduard Sanchez

Numerade Educator

Problem 32

A beam of $6.61-\mathrm{MeV}$ protons is incident on a target of ${ }_{17}^{27} \mathrm{Al}$. Those protons that collide with the target produce the reaction
$$
\mathrm{p}+{ }_{\mathrm{i} 3}^{27} \mathrm{Al} \rightarrow{ }_{14}^{27} \mathrm{Si}+\mathrm{n}
$$
$\left({ }_{14}^{27} \mathrm{Si}\right.$ has a mass of $26.986721$ u.) Neglecting any recoil of the product mucleus, determine the kinetic energy of the emerging neutrons.

Declan Nell

Numerade Educator

Problem 33

Identify the unknown particles $\mathrm{X}$ and $\mathrm{X}^{\prime}$ in the following nuclear reactions:

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 34

One method of producing neutrons for experimental use is to bombard ${ }_{3}^{7} \mathrm{~L}$ with protons. The neutrons are emitted according to the reaction
$$
{ }_{1} \mathrm{H}+{ }_{3}^{2} \mathrm{Li} \rightarrow{ }_{1}^{2} \mathrm{Be}+{ }_{0}^{1} \mathrm{n}
$$
(a) Calculate the mass in atomic mass units of the particles on the left side of the equation. (b) Calculate the mass (in atomic mass units) of the particles on the right side of the equation. (c) Subtract the answer for part
(b) from that for part (a) and convert the result to mega electron volts, obtaining the $Q$ value for this reaction.
(d) Assuming lithium is initially at rest, the proton is moving at velocity $v$, and the resulting beryllium and neutron are both moving at velocity Vafter the collision, write an expression describing conservation of momentum for this reaction in terms of the masses $m_{p} m_{n e} m_{p}$, and the velocities. (e) Write an expression relating the kinetic energies of particles before and after together with Q. (f) What minimum kinetic energy must the incident proton have if this reaction is to occur?

Eduard Sanchez

Numerade Educator

Problem 35

(a) Suppose ${ }_{3}^{11} \mathrm{~B}$ is struck by an alpha particle, releasing a proton and a product mucleus in the reaction. What is the product nucleus? (b) An alpha particle and a product nucleus are produced when ${ }_{6}^{13} \mathrm{C}$ is struck by a proton. What is the product nucleus?

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 36

Consider two reactions:
$$
\begin{aligned}
&\text { (1) } \mathrm{n}+{ }_{i}^{2} \mathrm{H} \rightarrow{ }_{1}^{3} \mathrm{H} \\
&\text { (2) }{ }_{1} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}
\end{aligned}
$$
(a) Compute the $Q$ values for these reactions. 1 dentify whether each reaction is exothermic or endothermic.
(b) Which reaction results in more released energy? Why?
(c) Assuming the difference is primarily due to the work done by the electric force, calculate the distance between the two protons in helium-3.

Declan Nell

Numerade Educator

Problem 37

Natural gold has only one isotope, ${ }^{197} \mathrm{Au}$. If gold is bombarded with slow neutrons, $e^{-}$ particles are emitted.
(a) Write the appropriate reaction equation. (b) Calculate the maximum energy of the emitted beta particles. The mass of ${ }_{n=1}^{\ln \mathrm{H}} \mathrm{Hg}$ is $197.96675 \mathrm{u}$.

Declan Nell

Numerade Educator

Problem 38

The following reactions are observed:
$$
\begin{array}{lll}
{ }_{4}^{1} \mathrm{Be}+\mathrm{n} & \rightarrow{ }_{4}^{10} \mathrm{Be}+\gamma & Q=6.812 \mathrm{MeV} \\
{ }_{4} \mathrm{Be}+\gamma & \rightarrow{ }_{4}^{8} \mathrm{Be}+\mathrm{n} & Q=-1.665 \mathrm{MeV}
\end{array}
$$
Calculate the masses of ${ }^{8} \mathrm{Be}$ and ${ }^{10} \mathrm{Be}$ in atomic mass units to four decimal places.

Declan Nell

Numerade Educator

Problem 39

When ${ }^{18} \mathrm{O}$ is struck by a proton, ${ }^{18} \mathrm{~F}$ and another particle are produced. (a) What is the other particle? (b) The reaction has a Q value of $-2.453 \mathrm{MeV}$, and the atomic mass of $\mathrm{}^{14} \mathrm{O}$ is $17.999160 \mathrm{u}$. What is the atomic mass of ${ }^{18} \mathrm{~F}$ ?

Declan Nell

Numerade Educator

Problem 40

In terms of biological damage, how many rad of heavy ions are equivalent to $100 \mathrm{rad}$ of $\mathrm{x}$ -rays?

Lisa Tarman

Numerade Educator

Problem 41

A person whose mass is $75.0 \mathrm{~kg}$ is exposed to a wholebody dose of $25.0 \mathrm{rad}$. How many joules of energy are deposited in the person's body?

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 42

A 200 -rad dose of radiation is administered to a patient in an effort to combat a cancerous growth. Assuming all the energy deposited is absorbed by the growth, (a) calculate the amount of energy delivered per unit mass. (b) Assuming the growth has a mass of $0.25 \mathrm{~kg}$ and a specific heat equal to that of water, calculate its temperature rise.

Lisa Tarman

Numerade Educator

Problem 43

A "clever" technician decides to heat some water for his coffee with an x-ray machine. If the machine produces $10 \mathrm{rad} / \mathrm{s}$, how long will it take to raise the temperature of a cup of water by $50^{\circ} \mathrm{C}$. Ignore heat losses during this time.

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 44

An x-ray technician works 5 days per week, 50 weeks per year. Assume the technician takes an average of eight x-rays per day and receives a dose of $5.0 \mathrm{rem} / \mathrm{yr}$ as a result.
(a) Estimate the dose in rem per $\mathrm{x}$ -ray taken. (b) How does this result compare with the amount of low-level background radiation the technician is exposed to?

Lisa Tarman

Numerade Educator

Problem 45

A patient swallows a radiopharmaceutical tagged with phosphorus-32 $\left(\frac{1}{15} \mathrm{P}\right), \mathrm{a} \beta^{-}$ emitter with a half-life of $14.3$ days. The average kinetic energy of the emitted electrons is $700 \mathrm{keV}$. If the initial activity of the sample is 1.31 MBq, determine (a) the number of electrons emitted in a 10-day period, (b) the total energy deposited in the body during the 10 days, and (c) the absorbed dose if the electrons are completely absorbed in $100 \mathrm{~g}$ of tissue.

Declan Nell

Numerade Educator

Problem 46

A particular radioactive source produces 100 mrad of 2-MeV gamma rays per hour at a distance of $1.0 \mathrm{~m}$.
(a) How long could a person stand at this distance before accumulating an intolerable dose of 1 rem? (b) Assuming the gamma radiation is emitted uniformly in all directions, at what distance would a person receive a dose of $10 \mathrm{mrad} / \mathrm{h}$ from this source?

Lisa Tarman

Numerade Educator

Problem 47

A radioactive sample contains $3.50 \mu \mathrm{g}$ of pure ${ }^{11} \mathrm{C}$, which has a half-life of $20.4$ min. (a) How many moles of ${ }^{11} \mathrm{C}$ are present initially? (b) Determine the number of nuclei present initially. What is the activity of the sample (c) initially and (d) after $8.00 \mathrm{h?}$ ?

Lisa Tarman

Numerade Educator

Problem 48

How much time elapses before $90.0 \%$ of the radioactivity of a sample of ${ }_{3}^{\prime 2}$ As disappears, as measured by its activity? The half-life of ${ }_{33}^{2} \mathrm{~A}$ s is $26 \mathrm{~h}$.

Mayank Tripathi

Mayank Tripathi

Numerade Educator

Problem 49

A $200.0-\mathrm{mCi}$ sample of a radioactive isotope is purchased by a medical supply house. If the sample has a half-life of $14.0$ days, how long will it keep before its activity is reduced to $20.0 \mathrm{mCi?}$

Lisa Tarman

Numerade Educator

Problem 50

(a) Why is the beta decay $\mathrm{p} \rightarrow \mathrm{n}+\mathrm{e}^{+}+\nu$ forbidden for a free proton? (b) Why is the same reaction possible if the proton is bound in a nucleus, as in the reaction ${ }^{13} \mathrm{~N} \rightarrow{ }_{6}^{18} \mathrm{C}+\mathrm{e}^{+}+\nu ?$ (c) How much energy is released in
the reaction given in part (b)? Suggestion: Add seven electrons to both sides of the reaction and write it for neutral atoms.

Sam Stansfield

Numerade Educator

Problem 51

In a piece of rock from the Moon, the ${ }^{87} \mathrm{Rb}$ content is assayed to be $1.82 \times 10^{10}$ atoms per gram of material and the $^{87} \mathrm{Sr}$ content is found to be $1.07 \times 10^{9}$ atoms per gram. (The relevant decay is ${ }^{\mathrm{B} 7} \mathrm{Rb} \rightarrow{ }^{87} \mathrm{Sr}+\mathrm{e}^{-} .$ The half-life of the decay is $4.8 \times 10^{10}$ yr.) (a) Determine the age of the rock. (b) Could the material in the rock actually be much older? What assumption is implicit in using the radioactive-dating method?

Eduard Sanchez

Numerade Educator

Problem 52

$\mathrm{e}$
(a) Can $^{57}$ Co decay by e emission? Explain.
(b) $\mathrm{Can}$ ${ }^{14} \mathrm{C}$ decay by $\mathrm{e}^{-}$ emission? Explain. (c) If either answer is yes, what is the range of kinetic energies available for the beta particle? Atomic masses: ${ }^{57} \mathrm{Co}: 56.936294 \mathrm{u} ;{ }^{57} \mathrm{Fe}$ :
$56.995396 \mathrm{u}$

Mayukh Banik

Numerade Educator

Problem 53

A medical laboratory stock solution is prepared with an initial activity due to ${ }^{24} \mathrm{Na}$ of $2.5 \mathrm{mCi} / \mathrm{ml}$, and $10.0 \mathrm{ml}$ of the stock solution is diluted at $t_{0}=0$ to a working solution whose total volume is $250 \mathrm{ml}$. After $48 \mathrm{~h}$, a $5.0$ -ml sample of the working solution is monitored with a counter. What is the measured activity? Nole: $1 \mathrm{ml}=1$ milliliter.

Eduard Sanchez

Numerade Educator

Problem 54

After the sudden release of radioactivity from the Chernobyl nuclear reactor accident in 1986 , the radioactivity of milk in Poland rose to $2000 \mathrm{~Bq} / \mathrm{L}$ due to iodine131 , with a half-life of $8.04$ days. Radioactive iodine is particularly hazardous because the thyroid gland concentrates iodine. The Chernobyl accident caused a measurable increase in thyroid cancers among children in Belarus.
(a) For comparison, find the activity of milk due to potassium. Assume 1 liter of milk contains $2.00 \mathrm{~g}$ of potassium, of which $0.0117 \%$ is the isotope ${ }^{40} \mathrm{~K}$, which has a half-life of $1.28 \times 10^{9} \mathrm{yr}$. (b) After what length of time would the activity due to iodine fall below that due to potassium?

Eduard Sanchez

Numerade Educator

Problem 55

During the manufacture of a steel engine component, radioactive iron $\left({ }^{59} \mathrm{Fe}\right)$ is included in the total mass of $0.20 \mathrm{~kg}$. The component is placed in a test engine when the activity due to the isotope is $20.0 \mu$ Ci. After a $1000-h$ test period, oil is removed from the engine and is found to contain enough ${ }^{59} \mathrm{Fe}$ to produce 800 disintegrations/min per liter of oil. The total volume of oil in the engine is $6.5 \mathrm{~L}$. Calculate the total mass worn from the engine component per hour of operation. (The halflife of $^{\text {i9 }} \mathrm{Fe}$ is $45.1$ days.)

Shahab Ullah

Numerade Educator