Calculate the rms speed of smoke particles of mass `5 xx 10^(-17) kg` in their Brownian motion in air at NTP. Given `k_(B) = 1.38 xx 10^(-23) J//K`

Options

A. `3xx10^(-2)ms^(-1)`
B. `1.5xx10^(-2)ms^(-1)`
C. `3xx10^(-3)ms^(-1)`
D. `1.5xx10^(-3)ms^(-1)`

Answer

B

Explanation

According to Kinetic therory,
average K.E. of a gas molecule `=1/2mv_(rms)^(2)=3/2k_(B)T`
`thereforev_(rms)=sqrt((3k_(B)T)/(m))=sqrt((3xx1.38xx10^(-23)xx273)/(5xx10^(17)))`
`=1.5xx10^(-2)m s^(-1)`