Question

Dust particles in air have a typical mass of 5.0 x 10-16 kg. They undergo irregular motion due to collisions with air molecules. a) Find the root-mean-square speed of the dust particle in air at 27 0 C.

Answer 1

Rms speed of the particle will be
`38.68* 10^8m/sec`

Step-by-step explanation:

We have given mass of the air particle
`m=5* 10^(-16)kg`

Gas constant R = 8.314 J/mol-K

Temperature is given T =
`27^(\circ)C=273+27=300K`

We have to find the root mean square speed of the particle

Which is given by
`v_(rms)=\sqrt{(3RT)/(m)}=\sqrt{(3* 8.314* 300)/(5* 10^(-16))}=38.68* 10^8m/sec`

So rms speed of the particle will be
`38.68* 10^8m/sec`