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NEET Sample Paper NEET Sample Test Paper-84

  • question_answer
    A doubly ionised Li atom is excited from its ground state \[(n\,\,=\,\,1)\] to \[n\,\,=\,\,3\] state. The wavelengths of the spectral lines are given by \[{{\lambda }_{32,}}{{\lambda }_{31}}\]and\[{{\lambda }_{21}}\]. The ratio a \[{{\lambda }_{32}}{{\lambda }_{31}}\]and \[{{\lambda }_{21}}{{\lambda }_{31}}\]are, respectively

    A) 8.1, 0.67          

    B)        8.1, 1.2

    C) 6.4, 1.2

    D)        6.4, 0.67

    Correct Answer: C

    Solution :

    [c] \[\frac{1}{\lambda }=R\left( \frac{1}{{{n}_{1}}^{2}}-\frac{1}{{{n}_{2}}^{2}} \right)\] where R = Rydberg constant             \[\frac{1}{{{\lambda }_{32}}}=\left( \frac{1}{4}-\frac{1}{9} \right)=\frac{5}{36}\] \[\Rightarrow \]   \[{{\lambda }_{32}}=\frac{36}{5}\] Similarly solving for \[{{\lambda }_{31}}and\,{{\lambda }_{21}}\]             \[{{\lambda }_{31}}=\frac{9}{8}\]and\[{{\lambda }_{21}}=\frac{4}{3}\] \[\therefore \]      \[\frac{{{\lambda }_{32}}}{{{\lambda }_{31}}}=6.4\] and \[\frac{{{\lambda }_{21}}}{{{\lambda }_{31}}}\simeq 1.2\]            


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