Question

An electron in hydrogen atom makes a transition $n_1\to n_2$ where $n_1$ and $n_2$ are principal quantum numbers of the two states. Assuming Bohr's model to be valid, the time period of the electron in the initial state is eight times that in the final state. The possible values of $n_1$ and $n_2$ are

• A. $n_1=6$ and $n_2=2$
• B. $n_1=8$ and $n_2=1$
• C. $n_1=8$ and $n_2=2$
• D. $n_1=4$ and $n_2=2$

Answer 1

Answer: (D)

$n_1=4$ and $n_2=2$

$\begin{array}{c}\text{Given- * An electron makes transition}{n}_1⟶n_2\\ \text{such that Time period in initial state is}\\ 8\text{times the final state.}[T_1=8T_2]\end{array}$

$\text{We know that in a single}{e}^{-}\text{model-}$

$T\propto \frac{n^3}{z^2}$

$\Rightarrow \frac{T_1}{T_2}=\frac{n_1^3}{n_2^3}=\frac{8}{1}$

$\begin{array}{cc}\Rightarrow \frac{n_1}{n_2}=2\Rightarrow n_1=4n_2=2& \\ & \text{is one of a possible value.}\end{array}$