AIIMS AIIMS Solved Paper-2011

  • question_answer
    The wavelength of a spectral line emitted by hydrogen atom in the Lyman series is \[\frac{16}{15R}\]. What is the value of \[{{n}_{2}}\]? (R = Rydberg constant)

    A)  2                            

    B)         3                            

    C)         4                            

    D)         1

    Correct Answer: C

    Solution :

    For Lyman series, \[\frac{1}{\lambda }=R\left[ \frac{1}{{{1}^{2}}}-\frac{1}{n_{2}^{2}} \right]\] \[\frac{15R}{16}=R\left[ \frac{1}{{{1}^{2}}}-\frac{1}{n_{2}^{2}} \right]\] \[\frac{15R}{16R}=R\left[ \frac{n_{2}^{2}-1}{n_{2}^{2}} \right]\] \[\frac{15}{16}=\frac{n_{2}^{2}-1}{n_{2}^{2}}\] \[15n_{2}^{2}=16n_{2}^{2}-16\] \[n_{2}^{2}=16\] \[{{n}_{2}}=4\]


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