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Question: Answered & Verified by Expert
What is the wave number of photon emitted during transition from orbit, $\mathrm{n}=4$ to $\mathrm{n}=2$ in hydrogen atom $\left[\mathrm{R}_{\mathrm{H}}=109677 \mathrm{~cm}^{-1}\right]$
ChemistryStructure of AtomMHT CETMHT CET 2023 (09 May Shift 2)
Options:
  • A $20564.44 \mathrm{~cm}^{-1}$
  • B $23032.17 \mathrm{~cm}^{-1}$
  • C $15354.78 \mathrm{~cm}^{-1}$
  • D $\quad 25225.7 \mathrm{~cm}^{-1}$
Solution:
2326 Upvotes Verified Answer
The correct answer is: $20564.44 \mathrm{~cm}^{-1}$
$\begin{aligned} \bar{v} & =109677\left[\frac{1}{2^2}-\frac{1}{4^2}\right] \mathrm{cm}^{-1} \\ & =109677\left[\frac{1}{4}-\frac{1}{16}\right] \mathrm{cm}^{-1} \\ & =109677\left[\frac{12}{64}\right] \mathrm{cm}^{-1} \\ & =20564.44 \mathrm{~cm}^{-1}\end{aligned}$

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