In the relaction ` p = (a)/(beta) e ^((aZ)/(k theta )`, p is pressure Z is distance .k is Boltamann constant and `theta` is the teperations . 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

`[(aZ)/(ktheta)] = [M^(0) L^(0) T^(0) ]`
`[a] = [(k theta )/(Z)]`
`[p] = [(a )/(beta)]`
`[beta] = [(a )/(p)] = [(k theta )/(Zp)]`
Demension of k theta are that to energy ,.Hence ,
` [beta] = [(ML^(2)T^(-2))/(LML^(-1)T^(-2))] `
` = [M^(0)L^(2)T^(0)]`