According to Maxwell`-`distribution law, the probability function representing the ratio of molecules at a particular velocity to the total number of molecules is given by
`f(v)=k_(1)sqrt(((m)/(2piKT^(2))))4piv^(2)e^(-(mv^(2))/(2KT))`
Where `m` is the mass of the molecule, `v` is the velocity of the molecule, `T` is the temperature `k` and `k_(1)` are constant. The dimensional formulae of `k_(1)` is

Options

A. `L^(2)T^(-2)`
B. `L^(1)T^(-1)K^(-3//2)`
C. `L^(1)T^(-1)K^(+3//2)`
D. `L^(2)T^(-1)K^(+3//2)`

Answer

C

Explanation

Here `f(v)` is dimensionless and `[mv^(2)]=[kt]`
`[k_(i)]=[((2pikT^(2))/(m))^( 1.5)(1)/(4piv^(2))]=[vT^(1.5)]=[L^(1)T^(-1)K^(1.5)]`