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Nuclear Physics: Principles and Applications

J. S. Lilley

Chapter 1

Introduction And Basic Concepts - all with Video Answers

Educators

Chapter Questions

01:41

Problem 1

Assuming that a nucleus is a sphere of nuclear matter of radius $1.2 \times A^{1 / 3} \mathrm{fm}$, express the average nuclear density in SI units.

Narayan Hari
Narayan Hari
Numerade Educator
01:35

Problem 2

Calculate the wavelengths of $1 \mathrm{MeV}, 10 \mathrm{eV}$ and thermal $(0.025 \mathrm{eV}) \gamma$ rays, electrons, neutrons and fission fragments $(A=100)$.

What is the ratio of the momenta of a $10-\mathrm{MeV}{ }^{13} \mathrm{C}$ ion and a $10-\mathrm{MeV}$ photon?

Sheh Lit Chang
Sheh Lit Chang
University of Washington
01:43

Problem 3

Use the uncertainty principle to estimate the minimum kinetic energy of an electron confined within a nucleus of size $10 \mathrm{fm}$. Hint: Assume the electron is fully relativistic.

Nicholas Mogoi
Nicholas Mogoi
Numerade Educator
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Problem 4

Before the discovery of the neutron, it was proposed that the penetrating radiation produced when beryllium was bombarded with $\alpha$ particles consisted of high-energy $\gamma$ rays (up to $50 \mathrm{MeV}$ ) produced in reactions such as $\alpha+{ }^{9} \mathrm{Be} \rightarrow{ }^{13} \mathrm{C}+\gamma$.
(a) Calculate the $Q$ value for this reaction.
(b) If $5-\mathrm{MeV} \alpha$ particles are incident on ${ }^{9} \mathrm{Be}$, calculate the energy of the ${ }^{13} \mathrm{C}$ nucleus and, hence, determine the energy of $\gamma$ radiation assuming it is emitted as a single photon. Hint: You may neglect the momentum of the $\gamma$ ray relative to the ${ }^{13} \mathrm{C}$ nucleus (see Problem 1.2). Masses: $m\left({ }^{4} \mathrm{He}\right)=4.0026 \mathrm{u}, \quad m\left({ }^{9} \mathrm{Be}\right)=9.0122 \mathrm{u}, m\left({ }^{13} \mathrm{C}\right)=13.0034 \mathrm{u}$.

Tanvi Garg
Tanvi Garg
Numerade Educator
03:20

Problem 5

(a) If the kinetic energy of a neutron, confined inside a cubic box, is $10 \mathrm{MeV}$ in its ground state, calculate the size of the box.
(b) What are the energies of the next three excited states?

Anand Jangid
Anand Jangid
Numerade Educator
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Problem 6

Calculate the $Q$ value for the $\alpha$ decay of ${ }^{234} \mathrm{U}$. Compare this with the $Q$ values for ${ }^{234} \mathrm{U}$ to decay by emitting a deuteron, triton or ${ }^{3} \mathrm{He}$ particle. Use atomic mass data given in Appendix $\mathrm{F}$.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:57

Problem 7

The $\alpha$ -active nucleus ${ }^{212}$ Po in its ground state decays to the ground state of ${ }^{208} \mathrm{~Pb}$ by emitting an $8.784-\mathrm{MeV} \alpha$ particle. Calculate the energy of the recoiling ${ }^{208} \mathrm{~Pb}$ nucleus and, hence, the mass (in atomic mass units) of ${ }^{212}$ Po. Use mass data from Appendix $\mathrm{F}$.

Zachary Warner
Zachary Warner
Numerade Educator
03:04

Problem 8

$^{36} \mathrm{Cl}$ decays into ${ }^{36} \mathrm{~S}(35.967081 \mathrm{u})$ and ${ }^{36} \mathrm{Ar}$. If the energy release is $1.142 \mathrm{MeV}$ to ${ }^{36} \mathrm{~S}$
and $0.709 \mathrm{MeV}$ to ${ }^{36} \mathrm{Ar}$, calculate the masses of ${ }^{36} \mathrm{Cl}$ and ${ }^{36} \mathrm{Ar}$. Describe the modes of decay.

Jenna Nikles
Jenna Nikles
Numerade Educator
03:22

Problem 9

An initial number $N_{\mathrm{A}}(0)$ of nuclei A decay into daughter nuclei $\mathrm{B}$, which are also radioactive. The respective decay probabilities are $\lambda_{\mathrm{A}}$ and $\lambda_{\mathrm{B}}$. If $\lambda_{\mathrm{B}}=2 \lambda_{\mathrm{A}}$, calculate the time (in terms of $\left.\lambda_{A}\right)$ when $N_{B}$ is at its maximum. Calculate $N_{B}$ (max) in terms of $N_{\mathrm{A}}(0)$

Yujian Zeng
Yujian Zeng
Numerade Educator
01:44

Problem 10

Derive the formula $N(t)=P\left(1-\mathrm{e}^{-\lambda t}\right) / \lambda$ for the production of a radioactive nuclide (decay constant $\lambda$ ) as a function of time, given that the production rate is constant at $P$ nuclei per second.

Estimate the time it will take to produce a $100 \mu \mathrm{Ci}$ source of ${ }^{36} \mathrm{Cl}$ by irradiating $1 \mathrm{~g}$ of natural nickel chloride (molecular weight $129.6$ ) in a neutronflux of $10^{14} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}$. The cross section for the neutron capture reaction ${ }^{35} \mathrm{Cl}(\mathrm{n}, \gamma)^{36} \mathrm{Cl}$ is $43 \mathrm{~b}$ and the halflife of ${ }^{36} \mathrm{Cl}$ is long $\left(3 \times 10^{5}\right.$ years). $75.8 \%$ of natural chlorine consists of ${ }^{35} \mathrm{Cl}$.

David Collins
David Collins
Numerade Educator
00:58

Problem 11

Using the information given in Problem $1.10$, calculate the fraction of ${ }^{35} \mathrm{Cl}$ which is transformed if $1 \mathrm{~g}$ of nickel chloride is irradiated for 1 day.

Nicole Mabante
Nicole Mabante
Numerade Educator
05:11

Problem 12

A thin $\left(1 \mathrm{mg} / \mathrm{cm}^{2}\right)$ target of ${ }^{48} \mathrm{Ca}$ is bombarded with a 10 -n A beam of $\alpha$ particles. A detector, subtending a solid angle of $2 \times 10^{-3}$ steradians, records 15 protons per second. If the angular distribution is measured to be isotropic, determine the total cross section (in $\mathrm{mb}$ ) for the ${ }^{48} \mathrm{Ca}(\alpha, \mathrm{p})$ reaction. Take the atomic mass of ${ }^{48} \mathrm{Ca}$ to be $48 \mathrm{u}$.

Mayank Tripathi
Mayank Tripathi
Numerade Educator