Understanding the Universe: An Introduction to Physics and Astrophysics

James B. Seaborn

Chapter 18 The Sun Is a Nuclear Furnace - all with Video Answers

Educators

Chapter Questions

Problem 1

Neutrons and protons have mass and therefore exert an attractive gravitational force on each other. Explain clearly and completely why this force cannot be the force responsible for binding neutrons and protons together to form a stable nucleus.

Kayla Day

Numerade Educator

01:49

Problem 2

When the isotope ${ }^{214}$ Po emits a $\beta$-particle, it transforms into a new element. What is the new element? What is its mass number? What is its atomic (proton) number? Suppose this isotope emits an $\alpha$-particle instead of a $\beta$-particle. What is the new element in this case?

Mayank Tripathi

Numerade Educator

05:27

Problem 3

Complete the radioactive decays
$\begin{array}{llll}{ }^{211} \mathrm{Po} \xrightarrow{\alpha} & { }^{190} \mathrm{Au} \xrightarrow{\beta^{+}} & { }^{138} \mathrm{Cs} \xrightarrow{\beta^{-}} & { }^{234} \mathrm{U} \xrightarrow{\alpha} \\ { }^{131} \mathrm{Xe} \xrightarrow{\gamma} & { }^{40} \mathrm{~K} \xrightarrow{\beta^{-}} & { }^6 \mathrm{He} \xrightarrow{\beta^{-}} & { }^{89} \mathrm{Zr} \xrightarrow{\beta^{+}}\end{array}$

Mayank Tripathi

Numerade Educator

02:26

Problem 4

An isotope of strontium ${ }^{90} \mathrm{Sr}$ is a fairly long-lived (28-year half life) radioactive byproduct of nuclear fission that has found its way into the food chain through dairy products. Write the formula for $\beta^{-}$-decay of this isotope and calculate the energy released when it decays.

Salamat Ali

Numerade Educator

02:06

Problem 5

Calculate the energy released in the ordinary radiaoactive $\beta$-decay of the isotopes ${ }^{20} \mathrm{~F},{ }^{32} \mathrm{P}$, and ${ }^{14} \mathrm{C}$.

David Collins

Numerade Educator

01:24

Problem 6

Calculate the energy released in radioactive $\beta^{-}$-decay of each of the isotopes ${ }^3 \mathrm{H}$ and ${ }^{23} \mathrm{Ne}$.

Lisa Tarman

Numerade Educator

04:52

Problem 7

Calculate the average binding energy per nucleon for ${ }^{56} \mathrm{Fe}$.

Nicholas Majtenyi

Numerade Educator

09:13

Problem 8

Calculate the average binding energy per nucleon for each of the tin isotopes ${ }^{112} \mathrm{Sn},{ }^{116} \mathrm{Sn},{ }^{120} \mathrm{Sn}$, and ${ }^{124} \mathrm{Sn}$. Which of these isotopes is most strongly bound? Explain.

Laurent Bergeron

Numerade Educator

04:05

Problem 9

A sulfur atom is assembled from sixteen hydrogen atoms and sixteen neutrons. Calculate the energy released in assembly and the average binding energy per nucleon.

Zachary Warner

Numerade Educator

01:38

Problem 10

Calculate the average binding energy (in MeV ) per particle for each of the isotopes ${ }^{58} \mathrm{Mn}$. ${ }^{58}{ }^5 \mathrm{~F},{ }^{58} \mathrm{Co}$, und ${ }^{58} \mathrm{Ni}$. Calculate the energy released in ordinary $\beta$-decay of ${ }^{34} \mathrm{Mn}$. The onergy relensed in $\beta^{+\dagger}$-decny of ${ }^{58} \mathrm{Co}$ is 1.29 MeV . By means of a calculation, verify this result. Explain clearly your reasoning. (NOTE: It is important to remember that it is atomic masses of neutral atoms that we use to calculate nuclear binding energies. Hence, the number of electrons must be the same in initial and final states so that the electron contributions cancel. This is automatically achieved in $\beta^{-}$-decay but not in $\beta^{+}$-decay.)

Chai Santi

Numerade Educator

02:48

Problem 11

Calculate the average binding energy per nucleon for the uranium isotopes ${ }^{235} \mathrm{U}$ and ${ }^{238} \mathrm{U}$.

Narayan Hari

Numerade Educator

04:37

Problem 12

The mass- 39 isotope of potassium $(\mathrm{K})$ is stable. This isotope is produced in the $\beta^{-}$-decay of a radioactive isotope in which the energy released is 0.565 MeV . Identify this radioactive isotope and calculate its mass and its average binding energy per nucleon.

Km Neeraj

Numerade Educator

05:04

Problem 13

The average binding energy per nucleon for ${ }^{16} \mathrm{~N}$ is 7.374 MeV . Calculate the atomic mass of this isotope. Use your result to calculate the energy released in radioactive $\beta^{-}$-decay of this isotope. Give the symbolic representation of this radioactive decay.

Ren Jie Tuieng

Numerade Educator

01:18

Problem 14

In ${ }^{209} \mathrm{Bi}$, the average binding energy per nucleon is 7.848 MeV . Calculate the atomic mass of this isotope. From your result, calculate the energy released in $\beta^{-}$-decay of ${ }^{209} \mathrm{~Pb}$. Express this decay process symbolically.

Khoobchandra Agrawal

Numerade Educator

02:40

Problem 15

The mass of a ${ }^{234} \mathrm{Th}$ atom is 234.04358 u . Calculate the average nuclear binding energy per nucleon for this isotope. Calculate the energy released in the radioactive alpha decay of ${ }^{238} \mathrm{U}$.

Lisa Tarman

Numerade Educator

05:27

Problem 16

The nuclei of the isotopes ${ }^{23} \mathrm{Na}$ and ${ }^{23} \mathrm{Mg}$ are called "mirror" nuclei, because the proton number of each is equal to the neutron number of the other. Calculate the difference in binding energy (in MeV ) for these two nuclei. Which is the more tightly bound system? Give a physical reason why you would expect it to be more tightly bound.

Yujian Zeng

Numerade Educator

02:55

Problem 17

Calculate the energy released in radioactive $\beta^{+}$-decay of ${ }^{39} \mathrm{Ca}$. (See note on Exercise 18.10.)

Zulfiqar Ali

Numerade Educator

01:07

Problem 18

There are five stable isotopes of the element calcium: ${ }^{40} \mathrm{Ca},{ }^{42} \mathrm{Ca},{ }^{43} \mathrm{Ca}$, ${ }^{44} \mathrm{Ca}$, and ${ }^{46} \mathrm{Ca}$. Calculate the average binding energy per nucleon for each of these. Which has the most tightly bound nucleus? Explain.

David Collins

Numerade Educator

01:49

Problem 19

Each of the isotopes ${ }^{16} \mathrm{O},{ }^{32} \mathrm{~S},{ }^{75} \mathrm{As},{ }^{109} \mathrm{Ag},{ }^{150} \mathrm{Sm},{ }^{197} \mathrm{Au}$, and ${ }^{209} \mathrm{Bi}$ is stable. Calculate the average binding energy per nucleon for each of these.
Based on your results, write a general statement regarding the relationship between the average nuclear binding energy per nucleon and the mass number for stable isotopes.

Vishal Gupta

Numerade Educator

01:14

Problem 20

All isotopes of radium are radioactive. The longest-lived isotope is ${ }^{226} \mathrm{Ra}$, an $\alpha$-particle emitter with a half-life of 1,620 years. Write the decay formula and calculate the energy released in the radioactive decay of this isotope.

Narayan Hari

Numerade Educator

03:41

Problem 21

Natural lithium is a mixture of two isotopes, ${ }^6 \mathrm{Li}$ and ${ }^7 \mathrm{Li}$. Calculate the natural relative abundance of each of these isotopes.

Nicole Smina

Numerade Educator

01:44

Problem 22

There are two stable isotopes of boron. One has mass 10.01294 u and the other 11.00931 u . The chemically determined mass of natural boron is 10.811 u . In a sample of natural boron, what fraction of the atoms will be ${ }^{10} \mathrm{~B}$ atoms?

Ajay Singhal

Numerade Educator

04:34

Problem 23

What fraction of the mass of a sample of natural chlorine is the ${ }^{35} \mathrm{Cl}$ isotope?

Ahmed Ali

Numerade Educator

06:36

Problem 24

Complete the following nuclear processes:

$$
\begin{gathered}
\alpha+{ }^{90} \mathrm{Zr} \longrightarrow+p \\
p+{ }^{37} \mathrm{Cl} \longrightarrow{ }^{34} \mathrm{~S}+ \\
+{ }^{28} \mathrm{Si} \longrightarrow{ }^{55} \mathrm{Fe}+{ }^3 \mathrm{He} \\
n+{ }^{99} \mathrm{Ru} \longrightarrow+\alpha \\
{ }^{12} \mathrm{C}+{ }^{28} \mathrm{Si} \longrightarrow{ }^{40} \mathrm{Ca}+
\end{gathered}
$$

$$
\begin{aligned}
{ }^{12} \mathrm{C}+{ }^{16} \mathrm{O} & \longrightarrow+\gamma \\
{ }^7 \mathrm{Li}+{ }^{10} \mathrm{~B} & \longrightarrow{ }^{14} \mathrm{C}+ \\
{ }^2 \mathrm{H}+{ }^{123} \mathrm{Sb} & \longrightarrow+{ }^3 \mathrm{He} \\
p+{ }^{11} \mathrm{~B} & \longrightarrow+n \\
\alpha+{ }^{65} \mathrm{Cu} & \longrightarrow{ }^{68} \mathrm{Zn}+
\end{aligned}
$$

Dr. Satish Ingale

Numerade Educator

02:47

Problem 25

Calculate the energy released in each of the nuclear reactions

$$
{ }^3 \mathrm{H}+{ }^{14} \mathrm{~N} \longrightarrow \quad{ }^{16} \mathrm{O}+n \quad \text { and } \quad{ }^3 \mathrm{He}+{ }^{14} \mathrm{~N} \longrightarrow \quad{ }^{16} \mathrm{O}+p
$$

Sanat Mukherjee

Numerade Educator

01:20

Problem 26

The nucleus of an atom of ${ }^{27} \mathrm{Al}$ is struck by an $\alpha$-particle. The products of the ensuing nuclear reaction are a proton and the nucleus of another atom. Write the complete equation for this nuclear process.

Abdel Osman

Numerade Educator

00:50

Problem 27

No element has a stable isotope with mass number equal to eight. When a proton is incident on a ${ }^7 \mathrm{Li}$ nucleus at rest, two $\alpha$-particles are produced. By how much does the combined kinetic energy of the $\alpha$-particles exceed the kinetic energy of the incoming proton?

Keshav Singh

Numerade Educator

01:49

Problem 28

A nuclenr renction occurs when a ${ }^3 \mathrm{He}$ nucleus strikes $\mathrm{a}^{88} \mathrm{Sr}$ target nucleus. One of the two reaction products is a proton. Write the complete equation for this mueleur reaction. The product nucleus is radionctive and decays by ordinary beta decay. Write the nuclear radioactive equation for the decay process. Calculate the energy released in the radioactive decay.

Jorge Villanueva

Numerade Educator

02:03

Problem 29

In the fission of ${ }^{235} \mathrm{U}$ by slow neutrons, an average energy of about 200 MeV is released in each fission. The energy released in the Hiroshima nuclear explosion in August of 1945 was about $8 \times 10^{13} \mathrm{~J}$ (roughly equivalent to the explosive energy of 20,000 tons of TNT). Estimate the mass of ${ }^{235} \mathrm{U}$ that fissioned in the Hiroshima bomb. If $18 \%$ of the ${ }^{235} \mathrm{U}$ fissioned, estimate the mass of ${ }^{235} \mathrm{U}$ used in constructing the bomb.

Surendra Kumar

Numerade Educator

06:18

Problem 30

Explain clearly why fission fragments (nuclei produced in the fission of a heavy element) are usually highly radioactive.

Shubham Kumar

Numerade Educator

01:20

Problem 31

There is one stable isotope of fluorine, ${ }^{19} \mathrm{~F}$. When a beam of slow neutrons falls on a sample of natural fluorine, $\beta^{-}$particles are detected. Write the two nuclear equations that represent the complete process of formation and decay of the radioactive nucleus. Calculate the energy released in the radioactive decay.

David Collins

Numerade Educator

00:59