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The radius of germanium (G e) nuclide is measured to be twice the radius of scriptbase B e end scriptbase presubscript 4 end presubscript presuperscript 9 end presuperscript. The number of nucleons in Ge are

  1. 73    
  2. 74    
  3. 75    
  4. 72    

The correct answer is: 72


    Let radius of scriptbase B e end scriptbase presubscript 4 end presubscript presuperscript 9 end presuperscript nucleus be r. Then radius of germanium (Ge) nucleus will be2 r.
    Radius ofnucleus is given by
    R equals R subscript 0 end subscript A to the power of 1 divided by 3 end exponent
    therefore fraction numerator R subscript 1 end subscript over denominator R subscript 2 end subscript end fraction equals open parentheses fraction numerator A subscript 1 end subscript over denominator A subscript 2 end subscript end fraction close parentheses to the power of 1 divided by 3 end exponent
    rightwards double arrow fraction numerator r over denominator 2 r end fraction equals open parentheses fraction numerator 9 over denominator A to the power of 2 end exponent end fraction close parentheses to the power of 1 divided by 3 end exponent left parenthesis because A subscript 1 end subscript equals 9 right parenthesis
    rightwards double arrow blank open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 3 end exponent equals fraction numerator 9 over denominator A to the power of 2 end exponent end fraction
    Hence,A subscript 2 end subscript equals 9 blank cross times blank open parentheses 2 close parentheses to the power of 3 end exponent blank equals 9 cross times 8 equals 72
    Thus, in germanium (G e) nucleus number of nucleons is 72.

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