Question

An electron in a hydrogen atom makes a transition $n_1\to n_2$ where $n_1$ and $n_2$ are principal quantum numbers of the states. Assume the Bhor's model to be valid. The time period of the electron in the initial states is eight times to that of final state. What is ratio of $\frac{n_1}{n_2}$

• A. 8 : 1
• B. 4 : 1
• C. 2 : 1
• D. 1 : 2

Answer 1

The correct option is C 2 : 1

$T_n\propto n^3$ $n\propto T^{\frac{1}{3}}$
$\frac{n_1}{n_2}={\left[\frac{T_1}{T_2}\right]}^{\frac{1}{3}}={\left[\frac{8}{1}\right]}^{\frac{1}{3}}$
$n_1:n_2=2:1$