Uranium has two naturally occurring isotopes. ²³⁸U has a natural abundance of 99.3% and ²³⁵U has an abundance of 0.7%. It is the rarer ²³⁵U that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, UF₆, which is a gas, then allowing it to diffuse through a series of porous membranes. ²³⁵UF₆ has a slightly larger rms speed than ²³⁸UF₆ and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of ²³⁵UF₆ to that of ²³⁸UF₆?

Key Concepts

Root Mean Square Speed

The root mean square (rms) speed is a measure of the average speed of particles in a gas, calculated as the square root of the average of the squares of the speeds of the particles. It is directly related to the temperature and molar mass of the gas, with lighter gases having higher rms speeds. This concept is crucial for understanding how different isotopes of uranium behave when diffusing through membranes.

Diffusion

Diffusion is the process by which particles spread from areas of high concentration to areas of low concentration. In the context of gases, lighter molecules diffuse faster than heavier ones due to their higher average speeds. This principle is essential for separating isotopes, as it explains why ²³⁵UF₆, being lighter, diffuses more quickly than ²³⁸UF₆.

Isotopes and Their Properties

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. The properties of isotopes, such as their mass and stability, influence their behavior in physical processes like diffusion. Understanding the differences between ²³⁵U and ²³⁸U is key to solving the problem of their separation in nuclear applications.