What will be the ratio of radii of two nuclei having their mass numbers in the ratio of 64 : 125?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 4 : 5 \)
The radius of a nucleus depends on its mass number \( A \) as \( R = R_{0}A^{1/3} \), so the nuclear radius varies as the cube root of \( A \).
\( \displaystyle \frac{R_{1}}{R_{2}} = \left(\frac{A_{1}}{A_{2}}\right)^{1/3} = \left(\frac{64}{125}\right)^{1/3} = \frac{4}{5} \)
So the ratio of radii is \( 4 : 5 \).