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CMC Medical CMC-Medical Ludhiana Solved Paper-2009

  • question_answer
    If \[{{\lambda }_{1}}\,\,and\,\,{{\lambda }_{2}}\]are the wavelengths of the first members of the Lyman and Paschen series respectively, then \[{{\lambda }_{1}}:{{\lambda }_{2}}\]is

    A)  1 : 3                                      

    B)  1 : 30

    C)  7 : 50                                    

    D)  7 : 308

    Correct Answer: D

    Solution :

                     For first line ofLyman series, \[{{n}_{1}}=1\] and \[{{n}_{2}}=2\] \[\therefore \]  \[\frac{1}{{{\lambda }_{1}}}=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)=R\left( 1-\frac{1}{4} \right)=\frac{3R}{4}\] For first line of Paschen series \[{{n}_{1}}=3\] and \[{{n}_{2}}=4\] \[\therefore \]  \[\frac{1}{{{\lambda }_{2}}}=R\left( \frac{1}{{{3}^{2}}}-\frac{1}{{{4}^{2}}} \right)=R\left( \frac{1}{9}-\frac{1}{16} \right)\] \[=\frac{7R}{144}\] \[\therefore \]  \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{7R}{144}\times \frac{4}{3R}=\frac{7}{108}\]


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