The velocity of 4 gas molecules are given by 1km/s , 3km/s , 5 km/s and 7km/s . Calculate the difference between average and RMS velocity .

Options

A. 0.338
B. 0.438
C. 0.538
D. 0.638

Answer

C

Explanation

The average volocity
`v_("av")=(v_(1)+v_(2)+v_(3)....v_(n))/(N)=(1+3+5+7)/(4)=4"km//s"`
Root mean square velocity
`v"rms"=sqrt((v_(1)^(2)+v_(2)^(2)+v_(3)^(2)+v_(4)^(2)+...+v_(n)^(2))/(N))`
`v"rms"=sqrt((1+(3)^(2)+(5)^(2)+(7)^(2))/(4)`
`sqrt21=4.583"kms"^(-1)`
Differnce between average velocity and root mean square velocity =4.583-4=0.583 `kms^(-1)`