AIIMS AIIMS Solved Paper-2009

  • question_answer
    Let \[{{k}_{1}}\] be the maximum kinetic energy of photoelectrons emitted by light of wavelength \[{{\lambda }_{1}}\] and \[{{K}_{2}}\] corresponding to wavelength\[{{\lambda }_{2}}\]. If \[{{\lambda }_{1}}=2{{\lambda }_{2}},\] then

    A) \[2{{k}_{1}}={{k}_{2}}\]

    B)                       \[{{k}_{1}}=2{{k}_{2}}\]

    C)                       \[{{k}_{1}}<{{k}_{2}}/2\]              

    D)       \[{{k}_{1}}>2{{k}_{2}}\]

    Correct Answer: C

    Solution :

    Here, \[{{K}_{1}}=\frac{hc}{{{\lambda }_{1}}}-W\]                      ???.(i) and \[{{K}_{2}}=\frac{hc}{{{\lambda }_{2}}}-W\]                ??..(ii) Substituting \[{{\lambda }_{1}}=2{{\lambda }_{2}}\] in Eq. (i), we get \[{{K}_{1}}=\frac{hc}{2{{\lambda }_{2}}}-W\] \[{{K}_{1}}=\frac{1}{2}\left( \frac{hc}{{{\lambda }_{2}}} \right)-W\] \[=\frac{1}{2}({{K}_{2}}+W)-W\] \[{{K}_{1}}=\frac{{{K}_{2}}}{2}-\frac{W}{2}\] or  \[{{K}_{1}}<\frac{{{K}_{2}}}{2}\]


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