If an electron in a hydrogen atom jumps from an orbit of level $\mathrm{n}=3$ to orbit of level…

If an electron in a hydrogen atom jumps from an orbit of level $\mathrm{n}=3$ to orbit of level $\mathrm{n}=2$, then the emitted radiation frequency is (where $\mathrm{R}=$ Rydberg's constant, $\mathrm{C}=$ Velocity of light)
  1. $\frac{3 \mathrm{RC}}{27}$
  2. $\frac{\mathrm{RC}}{25}$
  3. $\frac{ \mathrm{8RC}}{9}$
  4. $\frac{ \mathrm{5RC}}{36}$

Solution

$\begin{array}{ll} & \frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right] \\ \therefore \quad & \frac{1}{\lambda}=\left[\frac{1}{2^2}-\frac{1}{3^2}\right]=\frac{5}{36} \mathrm{R} \\ \therefore \quad & \mathrm{f}=\frac{\mathrm{c}}{\lambda}=\frac{5}{36} \mathrm{Rc}\end{array}$

Asked in: MHT CET 2023 (09 May Shift 1)

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