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Question

An electron of mass me, initially at rest, moves through a certain distance in a uniform electric field in time t1.A proton of mass mp , also initially at rest, takes time t2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t subscript 1 over t subscript 2 is nearly equal to..

  1. 1    
  2. open parentheses m subscript p over m subscript e close parentheses to the power of 1 half end exponent    
  3. open parentheses m subscript e over m subscript p close parentheses to the power of 1 half end exponent    
  4. 1836    

The correct answer is: open parentheses m subscript p over m subscript e close parentheses to the power of 1 half end exponent


    F subscript e end subscript equals e E
    a subscript e end subscript equals fraction numerator F subscript e end subscript over denominator m subscript e end subscript end fraction
    a subscript p end subscript equals fraction numerator F subscript p end subscript over denominator m subscript p end subscript end fraction
    S equals fraction numerator 1 over denominator 2 end fraction a subscript e end subscript t subscript 1 end subscript superscript 2 end superscript equals fraction numerator negative 1 over denominator 2 end fraction a subscript p end subscript t subscript 2 end subscript superscript 2 end superscript
    rightwards double arrow therefore fraction numerator t subscript 2 end subscript over denominator t subscript 1 end subscript end fraction equals square root of fraction numerator a subscript e end subscript over denominator a subscript p end subscript end fraction end root equals square root of fraction numerator m subscript p end subscript over denominator m subscript e end subscript end fraction end root

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