Binding Energy Per Nucleon and Strong Nuclear Force

Correct Answer

Options (B) and (D)

Understanding Binding Energy Per Nucleon

The binding energy of a nucleus is the energy required to separate all the nucleons (protons and neutrons) completely. When this energy is divided by the total number of nucleons, we obtain the binding energy per nucleon.

A larger binding energy per nucleon means that the nucleons are held together more tightly and the nucleus is more stable.

The graph of binding energy per nucleon versus mass number is one of the most important graphs in nuclear physics. It rises rapidly for light nuclei, reaches a maximum around iron (mass number approximately 56), remains nearly constant for medium-mass nuclei, and decreases gradually for very heavy nuclei.

Why Does the Binding Energy Remain Nearly Constant for Medium Nuclei?

For nuclei with mass numbers approximately between 30 and 150, each nucleon interacts mainly with its nearby neighbours because the strong nuclear force has a very short range. Adding more nucleons does not significantly increase the attractive force experienced by each nucleon, so the binding energy per nucleon remains nearly constant.

This behaviour is called the saturation property of nuclear forces. It is one of the strongest pieces of evidence that the strong nuclear force acts only over very short distances, comparable to the size of a nucleon.

Why Is the Binding Energy Lower for Very Light Nuclei?

Light nuclei contain only a small number of nucleons. Each nucleon has fewer neighbouring nucleons with which it can interact. As a result, the attractive nuclear force is smaller, leading to a lower binding energy per nucleon.

When two light nuclei combine to form a heavier nucleus, the resulting nucleus has a higher binding energy per nucleon. The increase in binding energy appears as released energy. This process is known as nuclear fusion.

Why Is the Binding Energy Lower for Very Heavy Nuclei?

In very heavy nuclei, although the strong nuclear force continues to act between neighbouring nucleons, the electrostatic repulsion between the large number of positively charged protons becomes significant. This repulsive force reduces the overall stability of the nucleus and decreases the binding energy per nucleon.

If such a heavy nucleus splits into two medium-sized nuclei, the products have a higher binding energy per nucleon. The difference in binding energy is released as energy. This process is called nuclear fission.

Analysis of Each Option

Option (A): The Strong Nuclear Force Oscillates with Distance

This statement is incorrect. Experimental evidence shows that the strong nuclear force decreases rapidly with distance and does not oscillate. It remains attractive over the typical distances found inside the nucleus and does not exhibit periodic variations.

Option (B): Fusion of Light Nuclei and Fission of Heavy Nuclei Release Energy

This statement is correct.

Light nuclei with very small mass numbers have lower binding energy per nucleon. When they fuse to form heavier nuclei, the binding energy per nucleon increases, releasing energy.

Similarly, very heavy nuclei have lower binding energy per nucleon than medium-sized nuclei. Splitting them into lighter nuclei increases the binding energy per nucleon, and the excess energy is released.

This is the principle behind the energy produced in the Sun through nuclear fusion and in nuclear reactors through nuclear fission.

Option (C): Strong Nuclear Force Is Long-Ranged

This statement is incorrect. If the strong nuclear force were long-ranged, every nucleon would interact significantly with every other nucleon in the nucleus. In that case, the binding energy per nucleon would continue increasing with mass number, which is not observed experimentally.

The nearly constant binding energy per nucleon for medium-sized nuclei proves that the force is not long-ranged.

Option (D): Strong Nuclear Force Is Short-Ranged

This statement is correct.

The saturation of the binding energy curve clearly shows that each nucleon interacts only with nearby nucleons. The force becomes negligible beyond a distance of about 1–2 femtometres. This short-range nature explains why the binding energy per nucleon remains almost constant for medium-mass nuclei.

The Saturation Property of Nuclear Forces

One of the most important properties of the strong nuclear force is saturation. Unlike gravitational or electrostatic forces, which act over long distances, the strong nuclear force acts only between neighbouring nucleons. Therefore, each nucleon contributes almost the same amount to the total binding energy regardless of how large the nucleus becomes.

This saturation property is responsible for the nearly flat portion of the binding energy curve between mass numbers approximately 30 and 150.

Applications of the Binding Energy Curve

The binding energy curve explains several important natural and technological phenomena. It explains why stars produce energy through nuclear fusion, why nuclear reactors generate electricity using uranium fission, why iron is among the most stable elements in nature, and why energy is released whenever nuclei move toward the region of maximum binding energy per nucleon.

Important Points

• Binding energy per nucleon is maximum near iron (A ≈ 56).
• Fusion of light nuclei releases energy.
• Fission of heavy nuclei releases energy.
• Strong nuclear force is attractive and extremely short-ranged.
• The saturation property proves that each nucleon interacts mainly with its nearest neighbours.

Final Answer

The correct conclusions are:

Option (B) – Fusion of light nuclei and fission of heavy nuclei release energy.

Option (D) – The strong nuclear force is short-ranged and decreases rapidly with distance.

Correct Answer: (B) and (D)