Four statements regarding the properties of a nucleus are given below (where A is the mass number) : A. The nuclear density is independent of the mass number A . B. The nuclear density increases linearly with the mass number A . C. The radius of a nucleus is proportional to A^ 2/3 . D. The radius of a nucleus is proportional to A^ 1/3 . Choose the correct answer from the options given below :

Step-by-step solution

The radius of a nucleus is given by the relation R = R₀ A^ 1/3 , where R₀ is a constant and A is the mass number. Thus, the radius of a nucleus is proportional to A^ 1/3 . Statement D is true and Statement C is false. The volume of the nucleus is V = 4 3 R^3 = 4 3 R₀^3 A . The mass of the nucleus is approximately M = m A , where m is the average mass of a nucleon. The nuclear density is given by = M V = m A 4 3 R₀^3 A = m 4 3 R₀^3 . Since the mass number A cancels out, the nuclear density is independent of A . Stat