Chapter 22, Problem 30A

Which atoms have the greater average speed in a mixture, U-238 or U-235? How would this affect diffusion through a porous membrane of otherwise identical gases made from these isotopes?

To determine

To explain: If U-238 or U-235 has the greater average speed in a mixture. The effect on diffusion through a porous membrane of otherwise identical gases made from these isotopes.

Explanation of Solution

Introduction:

Kinetic energy is given by,

  $\text{KE}=\frac{1}{2}m{v}^2$

Hence, kinetic energy depends on mass and speed of a body.

For kinetic energy to be same, U-235 should have greater velocity (as it has less mass) and U-238 should have lesser velocity (as it has more mass). When mixed together, both will attain the same temperature and thus same kinetic energy. Therefore, for kinetic energy to be same, U-235 has a greater speed than U-238.

Conclusion:

U-235 has a greater average speed than U-238.