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. `0.583`
D. `0.683`

Answer

C

Explanation

The average velocity
`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))`
`=sqrt((1 + (3)^(2) + (5)^(2) + (7)^(2))/(4))`
`= sqrt(21)` = 4.583 km/s
Difference between average velocity and root mean square velocity = 4.583 -4
`= 0.583` km/s