Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 43, Problem 30P

(a)

To determine

The ratio of surface area to volume of a sphere to produce minimum neutron leakage.

(b)

To determine

The ratio of surface area to volume of a cube to produce minimum neutron leakage.

(c)

To determine

The ratio of surface area to volume of a parallelepiped of dimensions a×a×2a to produce minimum neutron leakage.

(d)

To determine

Identify the shape with minimum and maximum leakage and give reason.

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To minimize neutron leakage from a reactor, the ratio of the surface area to the volume should be a minimum. For a given volume V, calculate this ratio for (a) a sphere, (b) a cube, and (c) a parallelepiped of dimensions a x a x 2a. (d) Which of these shapes would have minimum leakage? Which would have maximum leakage? Explain your answers.
Control rods are usually made of an alloy of indium. The absorption cross-section of indium for thermal neutron is 71 b, and the mass density of solid indium is 7.31 g cm-3. Estimate the neutron transmission ratio of a 1-cm thick indium slab. (a) 0.07 (b)0.7 (c) 0.01 (d) 0.1
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