Monoatomic gases helium (He), argon (Ar), and xenon (Xe) are isolated from the atmosphere and placed in the same tank. How does the root-mean-square speed vary between these three species?

Brownian motion refers to the random motion of particles as they collide with fluid particles. A dust particle of mass 2.15 × 10^-17 kg is suspended in air whose temperature is 308 K. Determine the root mean square speed of its Brownian motion.

The molar mass of Nitrogen is 28.01 g/mol. If the root-mean-square speed of the nitrogen molecules is 509 m/s, how many molecules with this speed moving between the left and right faces of a cube of length 0.2 m are required to produce a pressure of 1.5 atm?

A sample of 15 nitrogen molecules has speeds ranging from 36 m/s, 37 m/s, 38 m/s, ....., and 50 m/s. Determine the i) average speed and ii) the root-mean-square speed of the nitrogen molecules in the sample.

A sample of hydrogen gas contains hydrogen (¹₁H) and deuterium (²₁H) atoms. A scientist developed a method to separate the two isotopes based on the technique of isotope separation by gas diffusion. The sample of hydrogen is introduced into a series of diffusion-permeable porous cells at a fixed temperature T. ¹₁H diffuses through the porous membrane more rapidly than ²₁H, resulting in a separation of the two isotopes. The scientist collects the enriched gas stream, which contains ²₁H. Calculate the ratio of the root mean square velocities of ¹₁H and ²₁H (v_rms(¹₁H)/v_rms(²₁H)). ¹₁H has a mass of 1.008 u, and ²₁H has a mass of 2.014 u.

The root-mean-square speed of molecules in a gas is 700 m/s. If the volume of the gas is suddenly doubled, what will be the new rms speed of the molecules, assuming the pressure remains constant?