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Question

In order to coincide the parabolas formed by singly ionised ions in one spectrograph and doubly ionized ions in the other Thomson’s mass spectrograph, the electric fields and magnetic fields are kept in the ratios 1 : 2 and 3 : 2 respectively. Then the ratio of masses of the ions is

  1. 3 : 4    
  2. 1 : 3    
  3. 9 : 4    
  4. None of these    

The correct answer is: 9 : 4


    Using Z to the power of 2 end exponent equals k open parentheses fraction numerator q over denominator m end fraction close parentheses y semicolon where k equals fraction numerator B to the power of 2 end exponent L D over denominator E end fraction. For parabolas to coincide in the two photographs, the fraction numerator k q over denominator m end fraction should be same for the two cases. Thus, fraction numerator B subscript 1 end subscript superscript 2 end superscript   L D e over denominator E subscript 1 end subscript m subscript 1 end subscript end fraction equals fraction numerator B subscript 2 end subscript superscript 2 end superscript L D left parenthesis 2 e right parenthesis over denominator E subscript 2 end subscript m subscript 2 end subscript end fraction
    Þ fraction numerator m subscript 1 end subscript over denominator m subscript 2 end subscript end fraction equals open parentheses fraction numerator B subscript 1 end subscript over denominator B subscript 2 end subscript end fraction close parentheses to the power of 2 end exponent cross times open parentheses fraction numerator E subscript 2 end subscript over denominator E subscript 1 end subscript end fraction close parentheses cross times fraction numerator 1 over denominator 2 end fraction equals fraction numerator 9 over denominator 4 end fraction cross times fraction numerator 2 over denominator 1 end fraction cross times fraction numerator 1 over denominator 2 end fraction equals fraction numerator 9 over denominator 4 end fraction

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