Q88 / 90 · JEE Main 2024 (01 Feb Shift 2) · Physics

A particular hydrogen - like ion emits the radiation of frequency $3 \times 10^{15} Hz$ when it makes transition from $n = 2$ to $n = 1 .$ The frequency of radiation emitted in transition from $n =3$ to $n = 1$ is $\frac{x}{9} \times 10^{15} Hz,$ when $x =$ _____.

Correct answer: 32

Solution

For Hydrogen like atom, energy emitted is $E = - 13.6 Z^{2} (\frac{1}{n_{i}^{2}} - \frac{1}{n_{f}^{2}})$

$\Rightarrow E = C (\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}})$

$\Rightarrow h ν = C [\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}]$

Therefore, the ratio $\frac{v_{1}}{v_{2}} = \frac{{[\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}]}_{2 - 1}}{{[\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}]}_{3 - 1}}$

$= \frac{[\frac{1}{1} - \frac{1}{4}]}{[\frac{1}{1} - \frac{1}{9}]} = \frac{\frac{3}{4}}{\frac{8}{9}}$

$= \frac{3}{4} \times \frac{9}{8}$

$\Rightarrow \frac{v_{1}}{v_{2}} = \frac{27}{32}$

$\Rightarrow v_{2} = \frac{32}{27} v_{1} = \frac{32}{27} \times 3 \times 10^{15} Hz = \frac{32}{9} \times 10^{15} Hz$

Hence, $x = 32$ .

Hence, the correct answer is 32.

A particular hydrogen - like ion emits the radiation of frequency 3×1015 Hz when it makes transition from n=2 to n=1. The frequency of radiation emitted in transition from n=3 to n=1 is x9×1015 Hz, when x= _____.

Solution

Relevant Questions

A particular hydrogen - like ion emits the radiation of frequency $3 \times 10^{15} Hz$ when it makes transition from $n = 2$ to $n = 1 .$ The frequency of radiation emitted in transition from $n =3$ to $n = 1$ is $\frac{x}{9} \times 10^{15} Hz,$ when $x =$ _____.