Pressure depends on distance as, `P = (alpha)/(beta)exp((-alpha z)/(k theta))`, where `alpha, beta` are constants, z is distance, k is Boltzmann's constant and `theta` is temperature. The dimensions of `beta` are :

Options

A. `[M^(0)L^(0)T^(0)]`
B. `[M^(-1)L^(-1)T^(-1)]`
C. `[M^(0)L^(2)T^(0)]`
D. `M^(-1)L^(1)T^(2)]`

Answer

c

Explanation

Unit of K is joules per kelvin or the dimensional formula of K is `[ML^(2)T^(-2) theta^(-1)]. Alpha z//k theta` should be dimensionless.
So, dimensional formula of `alpha=([ML^(2)T^(-2)])/([L])=[MLT^(-2)]`
dimensional formula of `P= [ML^(-1) T^(-2)]`
`rArr beta=[alpha/P]=([MLT^(-2)])/([ML^(-1)T^(-2)])=[M^(0)L^(0)T^(0)]`