The average speed of gas molecules is equal to

Options

A. `((8 RT)/(pi M))^(1//2)`
B. `((3 RT)/( M))^(1//2)`
C. `((2 RT)/( M))^(1//2)`
D. `(( RT)/( M))^(1//2)`

Answer

A

Explanation

If there are `n` number of molecules in a sample and their individual speeds are `u_(1),u_(2),….u_(n)`, then the average speed of molecules `u_(av)` can be calculated as follows:
`u_(av) = (u_(1) + u_(2) + … + u_(n))/(n)`
According to the Maxwell-Boltzmann distribution of speeds, it is given as
`u_(av) = sqrt((8 RT)/(pi M))`
Option (2) is root mean square speed and option (3) is most probable speed.