What is the wave number of photon emitted during transition from orbit, $\mathrm{n}=4$ to $\mathrm{n}=2$ in…

What is the wave number of photon emitted during transition from orbit, $\mathrm{n}=4$ to $\mathrm{n}=2$ in hydrogen atom $\left[\mathrm{R}_{\mathrm{H}}=109677 \mathrm{~cm}^{-1}\right]$
  1. $20564.44 \mathrm{~cm}^{-1}$
  2. $23032.17 \mathrm{~cm}^{-1}$
  3. $15354.78 \mathrm{~cm}^{-1}$
  4. $\quad 25225.7 \mathrm{~cm}^{-1}$

Solution

$\begin{aligned} \bar{v} & =109677\left[\frac{1}{2^2}-\frac{1}{4^2}\right] \mathrm{cm}^{-1} \\ & =109677\left[\frac{1}{4}-\frac{1}{16}\right] \mathrm{cm}^{-1} \\ & =109677\left[\frac{12}{64}\right] \mathrm{cm}^{-1} \\ & =20564.44 \mathrm{~cm}^{-1}\end{aligned}$

Asked in: MHT CET 2023 (09 May Shift 2)

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