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Wave Optics

Question
CBSEENPH12040063
Wired Faculty App

Two nuclei have their mass number in the ratio of 1:3. The ratio of their nuclear densities would be

  • 1:3

  • 3:1

  • (3)1/3 : 1

  • 1:1

Solution

D.

1:1

Density of nuclear matter is independent of mass number, so the required ratio is 1:1
Alternative :
A1 : A2 = 1:3
Their radii will be in the ratio
straight R subscript straight o straight A subscript 1 superscript 1 divided by 3 end superscript space colon space straight R subscript straight o straight A subscript 2 superscript 1 divided by 3 end superscript space equals space 1 colon space 3 to the power of 1 divided by 3 end exponent Density space equals space fraction numerator straight A over denominator begin display style 4 over 3 end style πR cubed end fraction therefore comma space straight rho subscript straight A subscript 1 space end subscript colon space straight rho subscript straight A subscript 2 end subscript space space equals space fraction numerator 1 over denominator begin display style 4 over 3 end style πR subscript 0 cubed.1 cubed end fraction space equals fraction numerator 1 over denominator begin display style 4 over 3 πR subscript 0 cubed. left parenthesis 3 to the power of 1 divided by 3 right parenthesis end exponent right parenthesis cubed end style end fraction
Their nuclear densities will be the same.

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