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Question
CBSEENPH12040099
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The radius of germanium (Ge) nuclide is measured to be twice the radius of Be presubscript 4 presuperscript 9. The number of nucleons in Ge are

  • 73

  • 74

  • 75

  • 72

Solution

D.

72

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

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