The electron in a hydrogen atom makes a transition from `n = n_(1) to n = n_(2)` state. The time period of the electron in the initial state `(n_(1))` is eight times that in the final state `(n_(2))`The possible values of `n_(1)` and `n_(2)` are

Options

A. `n_(1) = 8,n_(2)=1`
B. `n_(1) = 4, n_(2) = 2`
C. `n_(1) = n_(2) = 4`
D. `n_(1) = 1, n_(2) = 8`

Answer

b

Explanation

`E=(-e)/(2xx4piepsilon_(0)).(1)/(r)=-(13.6)(Z^(2))/(n^(2))`
`:.rpropn^(2)=k.n^(2)`
`mr^(2)omega=nhimpliesomega=(2pi)/(T)=(nh)/(mr^(2))=(nh)/(mk.n^(4))`
`:.Tpropn^(3)T_(1)=8T_(2)impliesn_(1)^(3)=8n_(2)^(3)`
`impliesn_(1)=2n_(2):.n_(1):n_(2)=4:2`