The surface areas of two nuclei are in the ratio $9: 25$. The mass numbers of the nuclei are in the ratio

The surface areas of two nuclei are in the ratio $9: 25$. The mass numbers of the nuclei are in the ratio
  1. $27: 125$
  2. $9: 25$
  3. $3: 5$
  4. $1: 1$

Solution

For two nuclei, $\frac{A_1}{A_2}=\frac{9}{25} \Rightarrow \frac{R_1^2}{R_2^2}=\frac{9}{25} \Rightarrow \frac{R_1}{R_2}=\frac{3}{5}$
$\therefore \quad$ Ratio of radii,
$\frac{R_1}{R_2}=\left(\frac{A_1}{A_2}\right)^{\frac{1}{3}} \Rightarrow \frac{A_1}{A_2}=\left(\frac{R_1}{R_2}\right)^3=\left(\frac{3}{5}\right)^3=\frac{27}{125}$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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