The distribution of the molecular velocities of gas molecules at any temperature `T` is shown below. (The plot below is known as Maxwell's distribution of molecular speeds.)

where
`v` is molecular velocity
`n` is number of molecules having velocity `v`
Let us define `Delta N_(v)`, which is equal to the number of molecules between the velocity range `v` and `v+ Delta v`, given by
`Delta N_(v)=4piNa^(3)e^(-bv^(2))v^(2)Deltav`
where
`N` is total number of molecules
`a=sqrt((M_(0))/(2piRT))` and `b=(M_(0))/(2RT)`
`R` is universal gas constant
`T` is temperature of the gas
`M_(0)` is molecular weight of the gas
Answer the following question:
`SI` units of `a` are

Options

A. `M^(3)`
B. `m^(-1)s`
C. `m^(2)s^(-2)`
D. `m s^(2)`

Explanation

`m^(-1)s`