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Chapter 43: Q7P (page 1331)

At what rate must ${}^{235}U$ nuclei undergo fission by neutron bombardment to generate energy at the rate of 1.00 W? Assume that Q=200 MeV.

Short Answer

Expert verified

The rate at which nuclei undergo fission by neutron bombardment. $3.12 脳 10^{10} s^{- 1}$ .

Step by step solution

01

Given data

The generated energy, P =1 W

The released energy, Q =200 MeV

02

Determine the formulas to calculate the rate at which nuclei undergo fission by neutron bombardment.

The expression to calculate the fission ratio is given as follows.

$R = \frac{P}{Q}$ ...(i)

03

Calculate the rate at which nuclei undergo fission by neutron bombardment.

Calculate the fission ratio.

Substitute 1W forP and 200 MeV for into equation (i).

$R = \frac{1 W}{200 MeV} R = \frac{1 W}{200 脳 10^{6} eV} R = \frac{1 W}{200 脳 10^{6} 脳 1.6 脳 10^{19} J} R = \frac{1}{3.2 脳 10^{11}}$

Solve further as,

$R = \frac{10^{11}}{3.2} R = \frac{10 脳 10^{10}}{3.2} R = 3.12 脳 10^{10} s^{- 1}$

Hence the rate at which nuclei undergo fission by neutron bombardment $3.12 脳 10^{10} s^{- 1}$ .

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Most popular questions from this chapter

In an atomic bomb, energy release is due to the uncontrolled fission of plutonium ${}^{239}{Pu}$ (or ${}^{235}U$ ). The bomb鈥檚 rating is the magnitude of the released energy, specified in terms of the mass of TNT required to produce the same energy release. One megaton of TNT releases $2.6 脳 10^{28} MeV$ of energy. (a) Calculate the rating, in tons of TNT, of an atomic bomb containing 95 kg of ${}^{239}{Pu}$ , of which 2.5 kg actually undergoes fission. (See Problem 4.) (b) Why is the other 92.5 kg of ${}^{239}{Pu}$ needed if it does not fission?

The neutron generation time $t_{g e n}$ in a reactor is the average time needed for a fast neutron emitted in one fission event to be slowed to thermal energies by the moderator and then initiate another fission event. Suppose the power output of a reactor at timeis $t = 0$ is $P_{0}$ . Show that the power output a time tlater is $P (t)$ , whererole="math" localid="1661757074768" $P (t) = P_{0} t^{t / t_{g e n}}$ and kis the multiplication factor. For constant power output, $k = 1$ .

Expressions for the Maxwell speed distribution for molecules in a gas are given in Chapter 19. (a) Show that the most probable energyis given by

$K_{P} = \frac{1}{2} kT$

Verify this result with the energy distribution curve of Fig. 43-10, for which $T = 1.5 脳 10 K$ . (b) Show that the most probable speedis given by

$v_{P} = \sqrt{\frac{2 kT}{m}}$

Find its value for protons at $T = 1.5 脳 10^{7} K$ . (c) Show that the energy corresponding to the most probable speed(which is not the same as the most probable energy) is

$K_{V, P} = kT$

Locate this quantity on the curve of Fig. 43-10.

(a) 鈥� (d) Complete the following table, which refers to the generalized fission reaction

${}^{235}{U + n 鈫� X + Y + bn}$

Some uranium samples from the natural reactor site described in Module 43-3 were found to be slightly enrichedin $^{235} U$ , rather than depleted. Account for this in terms of neutron absorption by the abundant isotope $^{238} U$ and the subsequent beta and alpha decay of its products.

See all solutions

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