An electron in a hydrogen atom makes a transition n₁→n₂, where n₁ and n₂ are principal quantum numbers of the states. The time period of the electron in the initial state is eight times to that of final state. What is the ratio of n₁/n₂?

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8 : 1

2 : 1

1 : 2

4 : 1

answer is C.

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Detailed Solution

$\begin{array}{l} T \propto n^{3} \Rightarrow \frac{T_{1}}{T_{2}} = {(\frac{n_{1}}{n_{2}})}^{3} \Rightarrow \frac{8 T}{T} = {(\frac{n_{1}}{n_{2}})}^{3} \\ ∴ n_{1} : n_{2} = 2 : 1 \end{array}$

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