We separate U-235 from U-238 by fluorinating a sample of uranium to form UF₆ (which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes. Calculate the ratio of effusion rates for ²³⁸UF₆ and ²³⁵UF₆. The atomic mass of U-235 is 235.054 amu and that of U-238 is 238.051 amu.

Key Concepts

Effusion and Diffusion

Effusion is the process by which gas molecules escape through a tiny hole into a vacuum, while diffusion is the spreading of gas molecules throughout a space. The rates of these processes depend on the mass of the gas molecules, with lighter molecules effusing and diffusing faster than heavier ones, as described by Graham's law.

Graham's Law of Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means that if two gases have different molar masses, the lighter gas will effuse more quickly than the heavier gas, allowing for the calculation of effusion rates based on their respective masses.

Isotopes and Atomic Mass

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. In this case, U-235 and U-238 are isotopes of uranium, and their differing atomic masses are crucial for calculating the ratio of their effusion rates, as lighter isotopes will effuse more rapidly.