The energy (in J) released when an excited electron of $5^{\text {th }}$ orbit of hydrogen atom returns to…

The energy (in J) released when an excited electron of $5^{\text {th }}$ orbit of hydrogen atom returns to its ground state is
  1. $2.091 \times 10^{-18}$
  2. $4.182 \times 10^{-18}$
  3. $6.273 \times 10^{-18}$
  4. $8.364 \times 10^{-18}$

Solution

$\begin{aligned} & \text { } \mathrm{E}=2.18 \times 10^{-18}\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right) \\ & =2.18 \times 10^{-18}\left(\frac{1}{5^2}-\frac{1}{1^2}\right)=2.18 \times 10^{-18}(-0.96) \\ & =-2.091 \times 10^{-18} \mathrm{~J}\end{aligned}$

Asked in: AP EAMCET 2023 (18 May Shift 2)

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