Question

If the volume of nucleus having mass number 2 is V, then that for the nucleus having mass number 8 is

• A. 2V
• B. 3V
• C. 4V
• D. 6V
• E. 9V

Hint:

Nuclear density is constant because volume is proportional to mass number.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The volume of a nucleus is proportional to its mass number (A). \(V \propto A\).

Step 2: Detailed Explanation:
The radius of a nucleus is given by \(R = R_0 A^{1/3}\), where \(R_0\) is a constant. Volume, \(V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi R_0^3 A\). Thus, \(V \propto A\). Given: For \(A_1 = 2\), \(V_1 = V\). For \(A_2 = 8\), \(V_2 = V_1 \times \frac{A_2}{A_1} = V \times \frac{8}{2} = 4V\).

Step 3: Final Answer:
The volume of the nucleus with mass number 8 is \(4V\).