The radius of a nucleus is related to the mass number (A) by the formula: R=R0⋅A1∕3 where: R0 is a constant (approximately 1.2×10−15 meters), and A is the mass number. Let's denote the radii of the nuclei of elements X and Y by R(X) and R(Y) respectively. Given the mass numbers: For element X:A(X)=232 For element Y:A(Y)=29 The radii are then:
‌R(X)=R0⋅(232)1∕3 ‌R(Y)=R0⋅(29)1∕3 We are asked to find the ratio of these radii: ‌
R(X)
R(Y)
=‌
R0⋅(232)1∕3
R0⋅(29)1∕3
=(‌
232
29
)1∕3 Calculating the cube root of the ratio: ‌‌
232
29
≈8 ‌81∕3=2 Hence, the ratio of the radii of the nuclei of elements X and Y is: 2:1 The correct option is Option D: 2:1.