A hydrogen atom falls from $\mathrm{n}^{\text {th }}$ higher energy orbit to first energy orbit (…

A hydrogen atom falls from $\mathrm{n}^{\text {th }}$ higher energy orbit to first energy orbit ( $\mathrm{n}=1$ ). The energy released is equal to 12.75 ev . The $n^{\text {th }}$ orbit is
  1. $n=4$
  2. $n=3$
  3. $n=6$
  4. $n=5$

Solution

In hydrogen atom, $\begin{aligned} & \Delta \mathrm{E}=13.6\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right) \\ & \Rightarrow 12.75=13.6\left(\frac{1}{1^2}-\frac{1}{\mathrm{n}^2}\right) \\ & \therefore \mathrm{n}=4 .\end{aligned}$

Asked in: AP EAMCET 2024 (19 May Shift 2)

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