JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank Self Evaluation Test - Dual Nature of Radiation and Matter

  • question_answer
    Photoelectric emission is observed from a metallic surface for frequencies \[{{v}_{1}}\] and \[{{v}_{2}}\] of the incident light rays\[\left( {{v}_{1}}>{{v}_{2}} \right)\]. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of 1:k, then the threshold frequency of the metallic surface is

    A) \[\frac{{{v}_{1}}-{{v}_{2}}}{k-1}\]

    B) \[\frac{k{{v}_{1}}-{{v}_{2}}}{k-1}\]

    C) \[\frac{k{{v}_{2}}-{{v}_{1}}}{k-1}\]

    D) \[\frac{{{v}_{2}}-{{v}_{1}}}{k-1}\]

    Correct Answer: B

    Solution :

    [b] By using \[\Rightarrow h\left( {{v}_{1}}-{{v}_{0}} \right)={{K}_{1}}\]                              ....(i) \[\text{And }h\left( {{v}_{2}}-{{v}_{0}} \right)={{K}_{2}}\]                              ....(ii) \[\Rightarrow \frac{{{v}_{1}}-{{v}_{0}}}{{{v}_{2}}-{{v}_{0}}}=\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{1}{K'}\] \[\text{Hence }{{v}_{0}}=\frac{k{{v}_{1}}-{{v}_{2}}}{K-1}.\]


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