The electron of a hydrogen atom revolves the proton in a circuit nth of radius `r_(0) = (in_(0) n^(2)h^(2))/(pi m e^(2)) ` with a speed `upsilon_(0) =(e^(2))/(2 in_(0) nh)` The current the to circulating charge is proportional to

Options

A. `e^2`
B. `e^3`
C. `e^5`
D. `e^6`

Answer

C

Explanation

`T=(2pir_n)/v_n= (2pixxepsilon_0n^2h^2)/(pi me^2) xx(2epsilon_0nh)/(e^2) = (4 epsilon_0^2n^3h^3)/(me^4)`
Current `(I_n)=q/T=e/((4epsilon_0^2n^3h^3)/(me^4))=(me^5)/(4epsilon_0^2n^3h^3)`
`I_n prop e^5`