A particular hydrogen like ion emits radiation of frequency $2.92 \times 10^{15} \mathrm{~Hz}$ when it makes transition from $n=3$ to $n=1$. The frequency in Hz of radiation emitted in transition from $n=2$ to $n=1$ will be :

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Modern Physics

A particular hydrogen like ion emits radiation of frequency

2.92 \times 1 0^{15} Hz

when it makes transition from

n = 3

n = 1

. The frequency in Hz of radiation emitted in transition from

n = 2

n = 1

will be :

Answer: (A)

For a hydrogen-like ion the emitted frequency is

ν = R c Z^{2} (\frac{1}{n _{f}^{2}} - \frac{1}{n _{i}^{2}})

For the

3 \to 1

transition

ν_{31} = R c Z^{2} (1 - \frac{1}{9}) = \frac{8}{9} R c Z^{2} = 2.92 \times 1 0^{15}

Hz, and for

2 \to 1

ν_{21} = R c Z^{2} (1 - \frac{1}{4}) = \frac{3}{4} R c Z^{2}

. The unknown

Z

cancels on dividing:

ν_{21} = \frac{3/4}{8/9} ν_{31} = \frac{27}{32} \times 2.92 \times 1 0^{15} = 2.46 \times 1 0^{15} Hz

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Single correct option