# 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….

Q: The electron in a hydrogen atom makes a transition n1 → n2 where n1 and n2 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 n1 and n2 ?

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

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

As , T1 = 8 T2

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

n1 = 2 n2

Thus the possible values of n1 and n2 are n1 = 2 , n2 = 1. n1 = 4, n2 = 2 , n1 = 6 , n2 = 3; and so on.