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Question

Photoelectric emission is observed from a metallic surface for frequencies nu subscript 1 end subscript and nu subscript 2 end subscript of the incident light rays left parenthesis nu subscript 1 end subscript greater than nu subscript 2 end subscript right parenthesis. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of 1 colon k, then the threshold frequency of the metallic surface is

  1. fraction numerator nu subscript 1 end subscript minus nu subscript 2 end subscript over denominator k minus 1 end fraction    
  2. fraction numerator k nu subscript 1 end subscript minus nu subscript 2 end subscript over denominator k minus 1 end fraction    
  3. fraction numerator k nu subscript 2 end subscript minus nu subscript 1 end subscript over denominator k minus 1 end fraction    
  4. fraction numerator nu subscript 2 end subscript minus nu subscript 1 end subscript over denominator k end fraction    

The correct answer is: fraction numerator k nu subscript 1 end subscript minus nu subscript 2 end subscript over denominator k minus 1 end fraction


    By using h nu minus h nu subscript 0 end subscript equals K subscript m a x end subscript
    rightwards double arrow h left parenthesis nu subscript 1 end subscript minus nu subscript 0 end subscript right parenthesis equals K subscript 1 end subscript….(i)
    And h left parenthesis nu subscript 2 end subscript minus nu subscript 0 end subscript right parenthesis equals K subscript 2 end subscript….(ii)
    rightwards double arrow fraction numerator nu subscript 1 end subscript minus nu subscript 0 end subscript over denominator nu subscript 2 end subscript minus nu subscript 0 end subscript end fraction equals fraction numerator K subscript 1 end subscript over denominator K subscript 2 end subscript end fraction equals fraction numerator 1 over denominator K end fraction, Hence nu subscript 0 end subscript equals fraction numerator K nu subscript 1 end subscript minus nu subscript 2 end subscript over denominator K minus 1 end fraction.

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