The Schrodinger equation for a free electron of mass m and energy W written in terms of the wave function `Psi` is `(d^(1)Psi)/(dx^(2))+(8pi^(2)mE)/(h^(2))Psi=0`. The dimensions of the coefficient of `Psi` in the second term must be

Options

A. `[M^(1)L^(1)]`
B. `[L^(2)]`
C. `[L^(-2)]`
D. `[M^(1)L^(-1)T^(1)]`

Answer

C

Explanation

`h = (E lamda)/(C)`
`(mEC^(2))/((E lamda)^(2))=(mEC^(2))/(E^(2)lamda^(2))=(M^(1)(L^(1)T^(-1))^(2))/(M^(1)L^(2)T^(-2)L^(2))=(L^(2)T^(-2))/(L^(2)T^(-2)L^(2))=L^(-2)`