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Wave Optics

Question
CBSEENPH12040070
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If the nucleus Al presubscript 13 presuperscript 27 has a nuclear radius of about 3.6 fm, then Te presubscript 52 presuperscript 125 would have its radius approximately as: 

  • 6.0 fm

  • 9.6 fm

  • 12.0 fm

  • 4.8 fm

Solution

A.

6.0 fm

If R is the radius of the nucleus, the corresponding volume 4πR3/3 has been found to be proportional to A.
This relationship is expressed in inverse form as
 R = Ro A1/3
The value of Ro is 1.2 x 10-15 m, ie, 1.2 fm

straight R subscript Al over straight R subscript Te space equals space fraction numerator R subscript o left parenthesis A subscript A l end subscript right parenthesis to the power of 1 divided by 3 end exponent over denominator R subscript o left parenthesis A subscript T e end subscript right parenthesis to the power of 1 divided by 3 end exponent end fraction straight R subscript Al over straight R subscript Te space equals space fraction numerator left parenthesis A subscript A l end subscript right parenthesis to the power of 1 divided by 3 end exponent over denominator left parenthesis A subscript T e end subscript right parenthesis to the power of 1 divided by 3 end exponent end fraction space equals space fraction numerator left parenthesis 27 right parenthesis to the power of 1 divided by 3 end exponent over denominator left parenthesis 125 right parenthesis to the power of 1 divided by 3 end exponent end fraction space equals space 3 over 5 straight R subscript Te space equals space 5 over 3 space straight x space straight R subscript Al space equals space 5 over 3 straight x space 3.6 6 space fm

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