If the mass numbers of two nuclei are in the ratio (5: 2 ) and their diameters are in ratio (2: 6 ), Then their nuclear densities will be in the ratio

Step-by-step solution

The nuclear radius R is related to the mass number A by the formula R = R₀ A^ 1/3 , where R₀ is a constant. The diameter D is proportional to the radius, so D A^ 1/3 . The nuclear density is defined as the ratio of the mass of the nucleus to its volume. The mass of a nucleus is approximately M = A m_ p , where m_ p is the mass of a nucleon. The volume of a nucleus is V = 4 3 R³ = 4 3 (R₀ A^ 1/3 )³ = 4 3 R₀³ A . The nuclear density is = M V = A m_ p 4 3 R₀³ A = m_ p 4 3 R₀³ . Since m_ p , R₀ , and are constants, the