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

Uranium has two naturally occurring isotopes. ${}^{238}\text{U}$ has a natural abundance of $99.3\%$ and ${}^{235}\text{U}$ has an abundance of $0.7\%$. It is the rarer ${}^{235}\text{U}$ that is needed for nuclear reactors. The isotopes are separated by forming uranium hexafluoride, ${\text{UF}}_6$, which is a gas, then allowing it to diffuse through a series of porous membranes. ${}^{235}U{F}_6$ has a slightly larger rms speed than ${}^{238}U{F}_6$ and diffuses slightly faster. Many repetitions of this procedure gradually separate the two isotopes. What is the ratio of the rms speed of ${}^{235}U{F}_6$ to that of ${}^{238}U{F}_6$?

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℃?

(II) A group of 25 particles have the following speeds: two have speed 10 m/s, seven have 15 m/s, four have 20 m/s, three have 25 m/s, six have 30 m/s, one has 35 m/s, and two have 40 m/s. Determine the rms speed.

(I) By what factor will the rms speed of gas molecules increase if the temperature is increased from 0°C to 160°C?

(I) Calculate the rms speed of helium atoms near the surface of the Sun at a temperature of about 6000 K.

Estimate the rms speed of an amino acid, whose molecular mass is 89 u, in a living cell at 37°C.