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?

Homework Equations

ρ=m/v
V=4/3∏r²
v_rms=√(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

v_rms=√(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?

 

[voko]

Check the volume of a sphere.

 

[nlingraham]

Thank you very much