The electron in a hydrogen atom makes a transition `n_1 to n_2` , where `n_1 and n_2` are the principal quantum numbers of the two states. According to the Bohr model , the time period of revolution of electron in initial state is 8 times that in the final state. Which are possible values of `n_1 and n_2 `?
A `4,2`, B `8,2`, C `8,1`,D `6,3`.

Answer

either of A 4,2 or D 6,3 is possible .

Explanation

If the orbital frequency of the electron in the n -th orbit be `f_n` , then
`f_n prop 1/(n_3)`
So, time period `(=1/f) is T_n prop n^3 or, n prop (T_n)^(1//3)`
In the given question,
`T_1=8T_2 or, (T_1)/(T_2)=8`
`therefore (n_1)/(n_2) =((T_1)/(T_2))^(1//3) =(8)^(1//3) =2`
`therefore n_1=2n_2`
So, for the given values of `n_1 and n_2` , either of A 4,2 or D 6,3 is possible .