If the nuclear radius of 27Al is 3.6 fm, the radius of the nucleus of element having mass number 125 is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 6 fm
The nuclear radius follows \( R = R_0A^{1/3} \), because the nuclear volume is proportional to the mass number: the nuclear density is nearly the same for all nuclei. So the ratio of the radii needs only the ratio of the mass numbers.
\( \displaystyle \frac{R_2}{R_1} = \left(\frac{A_2}{A_1}\right)^{1/3} = \left(\frac{125}{27}\right)^{1/3} = \frac{5}{3} \)
\( R_2 = 3.6\,\mathrm{fm} \times 5/3 = 6\,\mathrm{fm} \)