Final answer:
The root-mean-square speeds of O₂ and UF₆ at 65°C can be compared using the Urms formula from kinetic theory. The speeds depend on the absolute temperature and inversely on the molar mass. Gas diffusion enrichment techniques rely on these speed differences, though they present challenges due to small mass variations.
Step-by-step explanation:
The question compares the root-mean-square (Urms) speeds of oxygen gas (O₂) and uranium hexafluoride (UF₆) at a specific temperature of 65°C. The Urms speed is a measure of the average speed of particles in a gas, which is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass of the gas.
To compare O₂ and UF₆, we can use the formula for Urms speed derived from the kinetic theory of gases:
Urms = √(3kT/M)
Where k is the Boltzmann constant, T is the absolute temperature, and M is the molar mass of the gas.
Given that the molar mass of O₂ is 32.0 g/mol, and the molar mass of UF₆ varies slightly depending on the isotope of uranium, we can calculate the Urms for each gas. However, the efficiency of gas diffusion separation techniques, such as those used in uranium enrichment, relies on these differences in molecular speeds.
The techniques for enrichment exploit the slight variations in Urms speeds to separate isotopes, which can be a challenge due to the subtle differences in mass and consequently in velocity.