Question

The relation between the nuclear radius \( R \) and the mass number \( A \), given by \( R = 1.2 A^{1/3} \) fm, implies that

• A. The central density of nuclei is independent of \( A \)
• B. The volume energy per nucleon is a constant
• C. The attractive part of the nuclear force has a long range
• D. The nuclear force is charge dependent

Hint:

In nuclear physics, the nuclear radius and central density of a nucleus are related to the mass number \( A \). The relation \( R \propto A^{1/3} \) implies constant central density.

Answer 1

The Correct Option is A, B

Step 1: Understanding the relation between nuclear radius and mass number.
The relation \( R = 1.2 A^{1/3} \) fm implies that the nuclear radius increases with the cube root of the mass number \( A \). This formula is often used to estimate the size of nuclei. The radius depends on the mass number but is not significantly affected by it for large nuclei.

Step 2: Analyzing the options.
(A) The central density of nuclei is independent of \( A \): Correct. Since the volume of a nucleus increases with \( A \) and the mass number is proportional to the volume, the central density of nuclei remains constant as \( A \) increases.
(B) The volume energy per nucleon is a constant: Incorrect. The volume energy per nucleon does not remain constant and depends on various factors, including the nuclear force and surface effects.
(C) The attractive part of the nuclear force has a long range: Incorrect. The nuclear force is short-range, typically acting only over distances of a few femtometers.
(D) The nuclear force is charge dependent: Incorrect. The nuclear force is mostly charge-independent, although electromagnetic effects can cause minor variations.

Step 3: Conclusion.
The correct answer is (A) because the central density of nuclei remains roughly the same as \( A \) increases.