In the relation ` p = (a)/(beta) e ^((aZ)/(k theta )`, p is pressure Z is distance .k is Boltzman constant and `theta` is the temperature . The dimensional formula of `beta` will be

Options

A. `M^(1)L^(2)T^(2)`
B. `M^(0)L^(2)T^(0)`
C. `M^(2)L^(0)T^(1)`
D. None of these

Answer

B

Explanation

Here, `ax"/"k theta` is power raised to exponent hence it must be dimensionless.
`[a][x]=[k][theta]`
`implies [a]=(ML^(2)T^(-2)K^(-1)xxK)/(L)`
`implies [a]= MLT^(-2)`
Now we can understand that `a"/"b` must have same dimensions as that of pressure.
`([a])/([b])=[P]`
`implies (MLT^(-2))/([b])=ML^(-1)T^(-2)`
`implies [b]= M^(0)L^(2)T^(0)`.