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College Physics 2017

Educators

Problem 1

Natural uranium ore contains about 0.720$\%$ of the fissile uranium $-235$ isotope. Suppose a sample of uranium ore contains $2.50 \times 10^{28}$ uranium nuclei. Determine the number of uranium-235 nuclei in the sample.

Ren Jie T.

Problem 2

A typical uranium-234 fission event releases 208 $\mathrm{MeV}$ of energy. Determine (a) the energy released per event in joules and (b) the change in mass during the event.

Ren Jie T.

Problem 3

If the average energy released in a fission event is 208 MeV, find the total number of fission events required to operate a 100. - W lightbulb for 1.0 h.

Ren Jie T.

Problem 4

Find the energy released in the fission reaction
$$\mathrm{n}+_{92}^{235} \mathrm{U} \quad \rightarrow \quad_{40}^{98} \mathrm{Zr}+\frac{135}{52} \mathrm{Te}+3 \mathrm{n}$$
The atomic masses of the fission products are 97.9120 u for 98 Zr and 134.9087 u for $_{52}^{135} \mathrm{Te}$ .

Ren Jie T.

Problem 5

Find the energy released in the fission reaction
$$_{0}^{1} \mathrm{n}+_{92}^{295} \mathrm{U} \rightarrow_{38}^{88} \mathrm{Sr}+\frac{136}{54} \mathrm{Xe}+12_{0}^{1} \mathrm{n}$$

Ren Jie T.

Problem 6

According to one estimate, the first atomic bomb released an energy equivalent to $20 .$ kilotons of TNT. If 1.0 ton of TNT releases about $4.0 \times 10^{9} \mathrm{J}$ , how much uranium was lost through fission in this bomb? (Assume 208 MeV released per fission.)

Ren Jie T.

Problem 7

Assume ordinary soil contains natural uranium in amounts of 1 part per million by mass. (a) How much uranium is in the top 1.00 $\mathrm{m}$ of soil on a 1 -acre $\left(43560-\mathrm{ft}^{2}\right)$ plot of ground, assuming the specific gravity of soil is 4.00$?(\mathrm{b})$ How much of the isotope 235 $\mathrm{U}$ , appropriate for nuclear reactor fuel, is in this soil? Hint: See Appendix $\mathrm{B}$ for the percent abundance of $^{235} \mathrm{U}$

Ren Jie T.

Problem 8

A typical nuclear fission power plant produces about 1.00 GW of electrical power. Assume the plant has an overall efficiency of 40.0% and each fission produces 200. MeV of thermal energy. Calculate the mass of $^{235} \mathrm{U}$ consumed each day.

Ren Jie T.

Problem 9

In order to minimize neutron leakage from a reactor, the ratio of the surface area to the volume must be as small as possible. Assume that a sphere of radius a and a cube both have the same volume. Find the surface - to - volume ratio for (a) the sphere and (b) the cube. (c) Which of these reactor shapes would have the minimum leakage?

Ren Jie T.

Ren Jie T.

Problem 45

(a) Show that about $1.0 \times 10^{10} \mathrm{J}$ would be released by the fusion of the deuterons in 1.0 gal of water. Note that 1 of every 6500 hydrogen atoms is a deuteron. (b) The average energy consumption rate of a person living in the United States is about $1.0 \times 10^{4} \mathrm{J} / \mathrm{s}(\text { an average power of } 10 . \mathrm{kW}) .$ At this rate, how long would the energy needs of one person be supplied by the fusion of the deuterons in 1.0 gal of water? Assume the energy released per deuteron is 1.64 $\mathrm{MeV}$

Ren Jie T.

Problem 46

The oceans have a volume of 317 million cubic miles and con- $\operatorname{tain} 1.32 \times 10^{21} \mathrm{kg}$ of water. Of all the hydrogen nuclei in this water, 0.0156$\%$ are deuterium. (a) If all of these deuterium nuclei were fused to helium via the first reaction in Equation 30.4 , determine the total amount of energy that could be released. (b) Present world electric power consumption is about $7.00 \times 10^{12} \mathrm{W}$ . If consumption were 100 times greater, how many years would the energy supply calculated in (a) last?

Ren Jie T.

Problem 47

A $\pi$ -meson at rest decays according to
$$\pi^{-} \rightarrow \mu^{-}+\overline{\nu}_{\mu}$$
What is the energy carried off by the neutrino? Assume the neutrino has no mass and moves off with the speed of light. Take $m_{\pi} c^{2}=139.6 \mathrm{MeV}$ and $m_{\mu} c^{2}=105.7 \mathrm{MeV.}$ Note: Use relativity; see Equation 26.13 .

Ren Jie T.

Problem 48

The reaction $\pi^{-}+\mathrm{p} \rightarrow \mathrm{K}^{0}+\Lambda^{0}$ occurs with high probability, whereas the reaction $\pi^{-}+\mathrm{p} \rightarrow \mathrm{K}^{0}+\mathrm{n}$ never occurs. Analyze these reactions at the quark level. Show that the first reaction conserves the total number of each type of quark and the second reaction does not.

Ren Jie T.

Problem 49

The sun radiates energy at the rate of $3.85 \times 10^{26} \mathrm{W} .$ Suppose the net reaction
$$4 \mathrm{p}+2 \mathrm{e}^{-} \rightarrow \alpha+2 \nu_{\mathrm{e}}+6 \gamma$$
accounts for all the energy released. Calculate the number of
protons fused per second. Note: Recall that an alpha particle is
a helium-4 nucleus.

Ren Jie T.
A $\mathrm{K}^{0}$ particle at rest decays into a $\pi^{+}$ and a $\pi^{-} .$ The mass of the $\mathrm{K}^{0}$ is 497.7 $\mathrm{MeV} / c^{2}$ and the mass of each pion is 139.6 $\mathrm{MeV} / c^{2} .$ What will be the speed of each of the pions?