In the relation `P= (alpha)/(beta)e^(-(alphaz)/(ktheta))` is pressure, z is distance, k is Boltzmann constant and `theta` is the temperature. The dimensional formula of `beta` will be

Options

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

Answer

A

Explanation

In the given equation, should be dimensionless.
`alpha= (ktheta)/(z)` or `[alpha]= ([ML^(2)T^(-2)K^(-1)][K])/([L])= [MLT^(-2)]`
`P= (alpha)/(beta)` or `[beta]= [(alpha)/(P)]= ([MLT^(-2)])/([ML^(-1)T^(-2)])= [M^(0)L^(2)T^(0)]`