In the relation, `P=alpha/beta e^((alphaZ)/(ktheta))P` 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

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)]`