Question

Four statements are given (A is mass number):
A. The volume of a nucleus is proportional to A.
B. The volume of a nucleus is proportional to A$^{1/3$.}
C. The difference in mass of an atom and its nucleus is called the mass defect.
D. The difference in mass of a nucleus and its constituents is called the mass defect.
Choose the correct answer from the options given below:

• A. A and D are true, but B and C are false
• B. B and D are true, but A and C are false
• C. B and C are true, but A and D are false
• D. A and C are true, but B and D are false

Hint:

Since Volume $\propto$ A and Mass $\propto$ A, the density of a nucleus (Mass/Volume) is constant for all elements!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Nuclear physics defines specific relationships between the number of nucleons (A) and physical properties like radius, volume, and mass.

Step 2: Detailed Explanation:
1. Nuclear Radius and Volume: The radius $R = R_0 A^{1/3}$. Since a nucleus is spherical, $\text{Volume} = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi (R_0 A^{1/3})^3 = \frac{4}{3}\pi R_0^3 A$. Thus, Volume $\propto$ A. (A is True, B is False). 2. Mass Defect: By definition, mass defect ($\Delta m$) is the difference between the sum of the masses of the individual protons and neutrons (constituents) and the actual measured mass of the nucleus. (D is True, C is False). Note that C describes the mass of electrons, not mass defect.

Step 3: Final Answer:
Statements A and D are true; B and C are false.