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

  • question_answer
    In the hydrogen atom spectrum \[{{\lambda }_{3-1}}\] and \[{{\lambda }_{2-1}}\] represent wavelengths emitted due to transition from second and first excited states to the ground. state respectively. The value of \[\frac{{{\lambda }_{3-1}}}{{{\lambda }_{2-1}}}\]is

    A)   27/32

    B)  32/27

    C)  4/9

    D)  9/4

    Correct Answer: A

    Solution :

    [a] \[\frac{1}{{{\lambda }_{3-1}}}=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{3}^{2}}} \right)=\frac{8R}{9}\] \[\frac{1}{{{\lambda }_{2-1}}}=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)=\frac{3R}{4}\Rightarrow \frac{{{\lambda }_{3-1}}}{{{\lambda }_{2-1}}}=\frac{27}{32}\]


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