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 to circulating charge is proportional to

Options

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

Answer

C

Explanation

`T = ("distance")/("speed") = (2pir_(n))/(v_(d))`
`= (2pi in_(0) h^(2) xx 2 in_(0) nh)/(pi m e^(2) xx e^(2)) = (4 in_(0)^(2) n^(3)h^(3))/(m e^(4))`
Current `I =(e)/(T) = ( e xx me^(4))/(4 in_(0)^(2)n^(2)h^(3)) = (m e^(5))/(4 in_(0)^(2)n^(2)h^(3))`
so `I prop e^(5)`