The mass number of two nuclei P and Q are 27 and 125 respectively. The ratio of their radii R_P: R_Q is given by:

Step-by-step solution

The radius R of a nucleus with mass number A is given by the relation R = R₀ A^ 1/3 , where R₀ is a constant. For nucleus P , A_P = 27 . Thus, R_P = R₀ (27)^ 1/3 = R₀ 3 . For nucleus Q , A_Q = 125 . Thus, R_Q = R₀ (125)^ 1/3 = R₀ 5 . The ratio of their radii is R_P R_Q = R₀ 3 R₀ 5 = 3 5 . Therefore, the ratio R_P : R_Q is 3 : 5 . Answer: 3 : 5