Question

In the releation `p=(alpha)/(beta) e^(-)(az)/(ktheta)`, where `p` is the pressure `z` is distance `k` is Boltzmann constant and `theta` is the temperature the dimensional formula `beta` will be
A. `[M^(0)L^(2)T^(0)]`
B. `[ML^(2)T]`
C. `[ML^(0)T^(-1)]`
D. `[ML^(2)T^(-1)]`

Answer 1

(a) In given equation `(alphaz)/(ktheta)` should be dimensionless.
L `:. alpha=(ktheta)/z`
`implies[a]=([ML^(2)T^(-2)K^(-1)xxK])/([L])=[MLT^(-2)]`
and `p=(alpha)/(beta)implies[rho]=[(alpha)/(beta)]=[(MLT^(-2))/(ML^(-1)T^(-2))]=[M^(0)L^(2)T^(0)]`