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
Radius of a nucleus: $R = R_0 A^{1/3}$, where A is the mass number
Let the mass numbers of the two nuclei be $A_1 : A_2 = 64 : 125$
Then, the ratio of radii:
$\frac{R_1}{R_2} = \left(\frac{A_1}{A_2}\right)^{1/3} = \left(\frac{64}{125}\right)^{1/3}$
$\frac{R_1}{R_2} = \frac{4}{5}$
∴ Ratio of radii = 4 : 5