Q: The electron in a hydrogen atom makes a transition n_{1} → n_{2} where n_{1} and n_{2} are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the

initial state is eight times that in the final state. What are the possible values of n_{1} and n_{2} ?

Sol: $\large T \propto n^3 $

$\large \frac{T_1}{T_2} = \frac{n_1^3}{n_2^3} $

As , T_{1} = 8 T_{2}

$\large 8 = \frac{n_1^3}{n_2^3} $

n_{1} = 2 n_{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.