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

Answer:

Rms speed of the particle will be  $38.68\times 10^8m/sec$

Explanation:

We have given mass of the air particle $m=5\times 10^{-16}kg$

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 $v_{rms}=\sqrt{\frac{3RT}{m}}=\sqrt{\frac{3\times 8.314\times 300}{5\times 10^{-16}}}=38.68\times 10^8m/sec$

So rms speed of the particle will be $38.68\times 10^8m/sec$