Question

Which of the following statements are correct?
(A) The electrostatic repulsive force between the protons can be greater than the nuclear force to bind the nucleons together inside a nucleus.
(B) The repulsive electrostatic force between protons in smaller nuclei is much smaller than the nuclear force between nucleons inside a nucleus.
(C) The gravitational force between nucleons is much smaller than the nuclear force between the nucleons inside a nucleus.
(D) The binding energy per nucleon between nucleons is almost constant because the nuclear force is a long range force.
Choose the correct answer from the options given below:

• (A) and (D) only
• (B) and (C) only
• (C) and (D) only
• (A) only

Hint:

Key properties of the nuclear force to remember: 1. Strongest force at short distances. 2. Short-range (acts only over a few femtometers). 3. Charge-independent (acts equally between p-p, n-n, and p-n). 4. Saturation property (a nucleon interacts only with its nearest neighbors), which leads to nearly constant binding energy per nucleon.

Answer 1

The Correct Option is B

Step 1: Concept Understanding:
This question assesses understanding of the nuclear force's properties, its comparison to other fundamental forces, and its relation to nuclear stability and binding energy.

Step 2: Detailed Explanation:
(A) The electrostatic repulsive force between the protons can be greater than the nuclear force to bind the nucleons together inside a nucleus.
If electrostatic repulsion exceeds the attractive nuclear force, the nucleus becomes unstable and disintegrates. This statement describes a condition leading to fission or decay in large, proton-rich nuclei, not a general characteristic of all nuclei. For a stable nucleus, the nuclear force must be stronger. In the general context of a bound nucleus, this statement is false.
(B) The repulsive electrostatic force between protons in smaller nuclei is much smaller than the nuclear force between nucleons inside a nucleus.
The strong nuclear force is the most potent force at nuclear distances. In small, stable nuclei, the attractive nuclear force significantly outweighs the electrostatic repulsion between the protons, ensuring stability. This statement is correct.
(C) The gravitational force between nucleons is much smaller than the nuclear force between the nucleons inside a nucleus.
Gravitational force is the weakest of the four fundamental forces. At the nuclear scale, its attraction is negligible compared to both the strong nuclear and electrostatic forces. For instance, the strong force is approximately \(10^{38}\) times stronger than gravity. This statement is correct.
(D) The binding energy per nucleon between nucleons is almost constant because the nuclear force is a long range force.
The near-constant binding energy per nucleon (saturation) is due to the short-range nature of the nuclear force, where a nucleon primarily interacts with its immediate neighbours. If the force were long-range, binding energy would increase with mass number A as every nucleon interacts with all others. The provided reason is incorrect. This statement is incorrect.

Step 3: Final Answer:
Statements (B) and (C) accurately describe nuclear forces. Statement (D) incorrectly attributes the constant binding energy per nucleon to a long-range force. Statement (A) describes a condition for instability rather than a general property of bound nuclei. Therefore, (B) and (C) are the correct statements.