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

Time period of electron , `T=(2mpir)/(v)=((2pixxepsi_(0)n^(2)h^(2))/(pime^(2)))/((e^(2))/(2epsi_(0)nh))`
`T=(4epsi_(0^(2))n^(3)h^(3))/(me^(4))`
Current, `i=(e)/(T)=(e)/((4epsi_(0)^(2)n^(3)h^(3))/(me^(4)))rArri=(me^(5))/(4epsi_(0)^(2)n^(3)h^(3))i.e., iprope^(5)`