In the relation `P=(alpha)/(beta)e^(-alpha z//ktheta)`
where `{:(P="pressure"),(z= "distance"), (k = "Boltzman's constant"), (theta = "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

As exponential expression is dimensionless
`(alphaz)/(ktheta)=M^(0)L^(0)T^(0)`
`alpha=(ktheta)/(z)=(ML^(2)T^(-2)theta^(-1)xxtheta^(1))/(L^(1))`
`:.alpha=ML^(1)T^(-2).`
Now `(alpha)/(beta)` will have dimension of `P`.
`:.beta=(alpha)/(P)=(ML^(1)T^(-2))/(ML^(-1)T^(-2))=L^(2).`
Hence correct choice is `(a)`.