Question

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

• A. \( 27:125 \)
• B. \( 9:25 \)
• C. \( 3:5 \)
• D. \( 1:1 \)

Hint:

For nuclei, the mass number ratio follows the cube of the radius ratio.

Answer 1

The Correct Option is A

Step 1: Relationship Between Surface Area and Mass Number The surface area of a nucleus is proportional to the square of its radius: \[ A \propto R^2 \] Since nuclear radius is related to mass number: \[ R \propto A^{1/3} \] Step 2: Compute the Mass Number Ratio \[ \frac{R_1}{R_2} = \sqrt{\frac{9}{25}} = \frac{3}{5} \] \[ \left(\frac{M_1}{M_2}\right)^{1/3} = \frac{3}{5} \] Cubing both sides: \[ \frac{M_1}{M_2} = \left(\frac{3}{5}\right)^3 = \frac{27}{125} \] Thus, the correct answer is \( 27:125 \).