Calculate the wave number of photon emitted during transition from the orbit $\mathrm{n}=2$ to…

Calculate the wave number of photon emitted during transition from the orbit $\mathrm{n}=2$ to $\mathrm{n}=1$ in hydrogen atom $\left(\mathrm{R}_{\mathrm{H}}=109677 \mathrm{~cm}^{-1}\right)$
  1. $72740 \mathrm{~cm}^{-1}$
  2. $92820 \mathrm{~cm}^{-1}$
  3. $82258 \mathrm{~cm}^{-1}$
  4. $83560 \mathrm{~cm}^{-1}$

Solution

$\begin{aligned} & \overline{\mathrm{V}}=\mathrm{R}_{\mathrm{H}}\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right) \\ & =109677\left(\frac{1}{1^2}-\frac{1}{2^2}\right) \\ & =82,257.75 \mathrm{~cm}^{-1}\end{aligned}$

Asked in: MHT CET 2022 (05 Aug Shift 1)

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