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. $n_{1}=\text{8}\text{,}\textit{n}_{2}=1$
• B. $n_{1}=\text{4}\text{,}\textit{n}_{2}=2$
• C. $n_{1}=\text{2}\text{,}\textit{n}_{2}=4$
• D. $n_{1}=\text{1}\text{,}\textit{n}_{2}=8$

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 $n_2=2$