Q157 / 160 · AP EAMCET 2024 (21 May Shift 2) · Physics
The surface areas of two nuclei are in the ratio $9: 25$. The mass numbers of the nuclei are in the ratio
- Correct answerA$27: 125$
- B$9: 25$
- C$3: 5$
- D$1: 1$
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,
$\frac{R_1}{R_2}=\left(\frac{A_1}{A_2}\right)^{\frac{1}{3}} \Rightarrow \frac{A_1}{A_2}=\left(\frac{R_1}{R_2}\right)^3=\left(\frac{3}{5}\right)^3=\frac{27}{125}$
$\therefore \quad$ Ratio of radii,
$\frac{R_1}{R_2}=\left(\frac{A_1}{A_2}\right)^{\frac{1}{3}} \Rightarrow \frac{A_1}{A_2}=\left(\frac{R_1}{R_2}\right)^3=\left(\frac{3}{5}\right)^3=\frac{27}{125}$
Hence, the correct answer is option: 'A'.