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

  • question_answer
    When a metallic surface is illuminated with radiation of wavelength \[\lambda \], the stopping potential is V. If the same surface is illuminated with radiation of wavelength \[2\lambda \] the stopping potential is \[\frac{V}{4}.\]The threshold wavelength for the metallic surface is:

    A) \[4\lambda \]     

    B) \[5\lambda \]

    C) \[\frac{5}{2}\lambda \]

    D) \[3\lambda \]

    Correct Answer: D

    Solution :

    [d] According to Einstein's photoelectric effect, \[eV=\frac{hc}{\lambda }-\frac{hc}{{{\lambda }_{0}}}\]                                     ?.(i) \[eV/4=\frac{hc}{2\lambda }-\frac{hc}{{{\lambda }_{0}}}\]                                ?(ii) Dividing equation (i) by (ii) by \[\Rightarrow 4=\frac{\frac{1}{\lambda }-\frac{1}{{{\lambda }_{0}}}}{\frac{1}{2\lambda }-\frac{1}{{{\lambda }_{0}}}}\]on solving we get, \[{{\lambda }_{0}}=3\lambda \]


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