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Chapter 4: Q20Q (page 165)

Uranium-238 ( U238) has three more neutrons than uranium-235 ( U235). Compared to the speed of sound in a bar of U235, is the speed of sound in a bar of U238 higher, lower, or the same? Explain your choice, including justification for assumptions you make.

Short Answer

Expert verified

Speed of sound in U238 is lower than speed of sound in U235 because speed of sound is inversely proportional to the root of atomic mass.

Step by step solution

01

Given data

Bars of U235 and U238.

It is given that the uranium U238has three more neutrons as compared to uranium U235.

02

Speed of sound in solid

Speed of sound in a solid of stiffness constant k, atomic mass mand interatomic bond length d is given by,

v=kmd....i

03

Comparing speed of sound in U238 to that in U235

U238has three more neutrons in its nucleus than U235. Thus the atomic mass of U238is greater than that of U235. Their stiffness constant and interatomic distance are the same. From equation (i), it is seen that the speed of sound in a solid is inversely proportional to the root of its atomic mass. Thus a solid with greater atomic mass will have lower speed of sound in it. Hence speed of sound in U238is lower than that of U235

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(Figure 4.56)

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