The ratio of the radii of the nucleus of two element X and Y having the mass numbers 232 and 29 is:

Step-by-step solution

The radius of a nucleus is given by the formula R = R₀ A^ 1/3 , where R₀ is a constant and A is the mass number of the nucleus. For the two elements X and Y, the ratio of their radii is given by R_ X R_ Y = R₀ A_ X ^ 1/3 R₀ A_ Y ^ 1/3 = ( A_ X A_ Y )^ 1/3 . Given A_ X = 232 and A_ Y = 29 , we substitute these values into the ratio: R_ X R_ Y = ( 232 29 )^ 1/3 . Since 232 = 29 8 , we have 232 29 = 8 . Therefore, R_ X R_ Y = (8)^ 1/3 = 2 . The ratio is 2 : 1 . Answer: 2 : 1