Question

There are two important isotopes of uranium— [Math Processing Error] and [Math Processing Error]; these isotopes are nearly identical chemically but have different atomic masses. Only [Math Processing Error] is very useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different average velocities [Math Processing Error] of uranium hexafluoride gas, [Math Processing Error]. (a) The molecular masses for [Math Processing Error][Math Processing Error] and [Math Processing Error][Math Processing Error] are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their average velocities?

a. 1:1
b. 349:352
c. 352:349
d. None

Answer 1

The ratio of the average velocities of uranium-235 and uranium-238 in UF6 gas is closest to 1:1. The calculation is based on their molecular masses and the inverse proportionality of rms velocity to the square root of molar mass.

Step-by-step explanation:

The average velocity ratio of two isotopes of uranium, uranium-235 and uranium-238, in their uranium hexafluoride gas form (UF6) can be found using the kinetic molecular theory of gases. The root-mean-square (rms) velocity (Vrms) is inversely proportional to the square root of molar mass (M), given by the equation Vrms = (3RT/M)^0.5, where R is the gas constant and T is temperature.

Given the molecular masses for 235U UF6 and 238U UF6 are 349.0 g/mol and 352.0 g/mol respectively, the ratio of their rms velocities is the square root of the inverse ratio of their masses. Hence:

• Ratio of average velocities, v235/v238 = (M238/M235)^0.5
• Ratio = (352.0/349.0)^0.5
• Ratio ≈ 1.0043

Therefore, the ratio of their average velocities is closest to 1:1, which means option a is correct. However, from a practical standpoint, the difference in average velocities is very small, making the gas diffusion technique challenging for separating these isotopes.