An electron in a hydrogen atom makes a transition `n_(l) rarr n_(2)`, where `n_(1) and n_(2)` are principal quantum numbers of the states. Assume the Bohr's model to be valid. The time period of the electron in the initial state is eight times to that of final state. What is ratio of `n_(2)//n_(2)`

Explanation

Since, T `prop n^(3)`
`therefore (T_(1))/(T_(2)) = (n_(1)^(3))/(n_(2)^(3)) " As" T_(1) = 8T_(2), ((n_(1))/(n_(2)))^(3) = 8 " (or)" n_(2) = 2n_(2)`.
Thus the possible values of `n_(1) and n_(2)` are
`n_(1) = 2, n_(2) = 1 , n_(1) = 4 , n_(2) = 2 , n_(1) = 6, n_(2) = 3 `, and so on .....