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?

A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare (b) the root-mean-square speeds. (Hint: Appendix D shows the molar mass (in g/mol) of each element under the chemical symbol for that element.)

You are watching a science fiction movie in which the hero shrinks down to the size of an atom and fights villains while jumping from air molecule to air molecule. In one scene, the hero's molecule is about to crash head-on into the molecule on which a villain is riding. The villain's molecule is initially 50 molecular radii away and, in the movie, it takes 3.5 s for the molecules to collide. Estimate the air temperature required for this to be possible. Assume the molecules are nitrogen molecules, each traveling at the rms speed. Is this a plausible temperature for air?

Eleven molecules have speeds 15, 16, 17, …, 25 m/s. Calculate (a) vₐᵥ₉ and (b) vᵣₘₛ.

b. A gas cylinder has a piston at one end that is moving outward at speed vₚᵢₛₜₒₙ during an isobaric expansion of the gas. Find an expression for the rate at which vᵣₘₛ is changing in terms of vₚᵢₛₜₒₙ, the instantaneous value of vᵣₘₛ, and the instantaneous value L of the length of the cylinder.

A cylinder contains gas at a pressure of 2.0 atm and a number density of 4.2 x 10²⁵ m⁻³. The rms speed of the atoms is 660 m/s. Identify the gas.

The rms speed of molecules in a gas is 600 m/s. What will be the rms speed if the gas pressure and volume are both halved?

By what factor does the rms speed of a molecule change if the temperature is increased from 10℃ to 1000℃?

Dust particles are ≈ 10 μm in diameter. They are pulverized rock, with p ≈ 2500 kg/m³. If you treat dust as an ideal gas, what is the rms speed of a dust particle at 20℃?