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Hydrogen-like ion: frequency for one transition to n = 1 given the frequency for another transition to n = 1

The same question, asked 2 times: 2021 Paper 18*, 1 Feb 2024. Every wording below, oldest first.

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  1. Question 1

    2021 Paper 18

    10
    A particular hydrogen like ion emits radiation of frequency 2.92×1015 Hz2.92 \times10^{15}\text{ }Hz when it makes transition from n=3n = 3 to n=1n = 1. The frequency in HzHz of radiation emitted in transition from n=2n= 2 to n=1n= 1 will be:

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  2. Question 2

    1 Feb 2024

    115
    A particular hydrogen - like ion emits the radiation of frequency 3×1015 Hz3 \times10^{15}\text{ }Hz when it makes transition from n=2n = 2 to n=1n = 1. The frequency of radiation emitted in transition from n=3n = 3 to n=1n = 1 is x9×1015 Hz\frac{x}{9}\times10^{15}\text{ }Hz, when x=x = ________ .