# Find the rms speed of a dust particle.

nlingraham

## Homework Statement

Dust particles are 13.0 micrometers in diameter. They are pulverized rock, with ρ=2540 kg/m3 . If you treat dust as an ideal gas, what is the rms speed of a dust particle at 18.0 C?

ρ=m/v
V=4/3∏r2
vrms=√(3kT/m)

## The Attempt at a Solution

OK:

13 micrometers = 1.3*10-5 m, which makes radius 6.5*10-6 m

Then, V=(4/3)∏(6.5*10-6)2=1.7697*10-10 m3

m=ρv=(2540)(1.7697*10-10 m3)=4.495*10-7 kg

vrms=√(3*(1.38*10-23)*(273+18))/(4.495*10-7 kg))
=1.63*10-7 m/s

This isn't right though, anyone see where I went wrong?