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Two nuclei have mass numbers 27 and 125 respectively. What is the ratio of their nuclear radii and the ratio of their nuclear densities?

Options

  1. A27 : 125 and 1 : 1
  2. B3 : 5 and 1 : 1
  3. C3 : 5 and 3 : 5
  4. D3 : 5 and 27 : 125

Correct answer

B. 3 : 5 and 1 : 1

Step-by-step solution

The radius of a nucleus is related to its mass number A by the formula R = R₀ A^ 1/3 . For the two nuclei with mass numbers A₁ = 27 and A₂ = 125 , the ratio of their radii is: R₁ R₂ = ( A₁ A₂ )^ 1/3 = ( 27 125 )^ 1/3 = 3 5 Therefore, the ratio of their radii is 3 : 5 . The nuclear density is approximately constant for all nuclei and is independent of the mass number A . Therefore, the ratio of their nuclear densities is 1 : 1 . Answer: 3 : 5 and 1 : 1

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