The relation `p=(alpha)/(beta)e^((-alphaZ)/(ktheta)` , where `p` is pressure, `Z` is distance, `k` is Boltzmann constant and `theta` is 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

Dimension formula of Boltzman constant
`k rarr [M^(1)L^(2)T^(-2)theta^(-1)]`
`(alpha[L^(1)])/([M^(1)L^(2)T^(-2)theta^(-1)][theta^(-1)])=M^(0)L^(0)T^(0)theta^(0)`
`alpha=[M^(1)L^(1)T^(-2)], beta=([M^(1)L^(1)T^(-2)])/([M^(1)L^(-1)T^(-2)])=[L^(2)]`