Particle physics / ideal gas problem

[greenskyy]

Homework Statement

Dust particles are approximately 11.0 micrometers in diameter. They are pulverized rock, with density 2500 kg/m^3. If you treat dust as an ideal gas, what is the rms speed of a dust particle at 23.0 degrees C?

Homework Equations

I have no idea.
The only one I would bet money on is:

$$v_{rms}=\sqrt{\frac{3k_{B}T}{m}}$$

The Attempt at a Solution

I made a couple of far-reached guesses at this problem and came to the wrong answer. One method was to use the ideal gas law with pressure = 101325 Pa, and getting the number of particles to be 2.48*10^25. My main issue here is going from density and radius of a particle to a molecular mass or a correct number of particles. I am completely stumped by the problem and getting nowhere. If anyone could offer help, I would greatly appreciate it.

 

[jgens]

Well, show us your work for what you've done so far and maybe we'll be able to offer more help! I'll give you a couple of hints though: The absolute temperature of an ideal gas is proportional to its random translational kinetic energy. How might this help you solve the problem?

 

[ehild]

Your starting formula is OK,

$$v_{rms}=\sqrt{\frac{3k_{B}T}{m}}$$

but why do you want the number of he particles? In the formula, m means the mass of a single particle. Given the diameter and density, it is easy to get.

ehild