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JEE Main & Advanced Physics Atomic Physics Question Bank Self Evaluation Test - Atoms

  • question_answer
    In a hydrogen like atom electron make transition from an energy level with quantum number n to another with quantum number (n-1). If n>>1, the frequency of radiation emitted is proportional to:

    A)          \[\frac{1}{n}\]

    B)  \[\frac{1}{{{n}^{2}}}\]

    C)  \[\frac{1}{{}^{{{n}^{3}}}/{}_{2}}\]

    D)  \[\frac{1}{{{n}^{3}}}\]

    Correct Answer: D

    Solution :

    [d] \[\Delta E=hv\] \[v=\frac{\Delta E}{h}=k\left[ \frac{1}{{{\left( n-1 \right)}^{2}}}-\frac{1}{{{n}^{2}}} \right]=\frac{k\left( 2n-1 \right)}{{{n}^{2}}\left( {{n}^{2}}-1 \right)}\] \[\approx \frac{2k}{{{n}^{3}}}\text{ or, }v\propto \frac{1}{{{n}^{3}}}\]


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