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NEET Sample Paper NEET Sample Test Paper-10

  • question_answer
    In the hydrogen atomspectrum, \[{{\lambda }_{3}}=1\] 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)  \[\frac{27}{32}\]                                         

    B)  \[\frac{32}{27}\]

    C)  \[\frac{4}{9}\]                       

    D)  \[\frac{9}{4}\]

    Correct Answer: A

    Solution :

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


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