Question

The electron in a hydrogen atom makes a transition from $n=n_1$ to $n=n_2$ state. The time period of the electron in the initial state $\left(n_1\right)$ is eight times that in the final state $\left(n_2\right)$ . The possible values of $n_1$ and $n_2$ are

• A. $n_1=\text{8}\text{,}{\text{n}}_2=1$
• B. $n_1=\text{4}\text{,}{\text{n}}_2=2$
• C. $n_1=\text{2}\text{,}{\text{n}}_2=4$
• D. $n_1=\text{1}\text{,}{\text{n}}_2=8$

Answer 1

Answer: (B)

In a hydrogen atom, the time period is given by $T\propto n^3$
$\frac{T_1}{T_2}={\left(\frac{n_1}{n_2}\right)}^3\Rightarrow \frac{8}{1}={\left(\frac{n_1}{n_2}\right)}^3$
$\Rightarrow \frac{n_1}{n_2}=\frac{2}{1}$
Thus, $n_1=4$ and $n_2=2$