Question

When the number of nucleons in a nuclues increases the binding energy per nucleons ?

• A. Increase continuously with mass number
• B. Decreases continuously with mass number
• C. Remains constant with mass number
• D. First increases and then decreases with increase in mass number

Answer 1

The Correct Option is D

The binding energy per nucleon is a critical concept in nuclear physics that relates to the stability of a nucleus. It indicates how tightly the nucleons (protons and neutrons) are held together in the nucleus. Let's explore how the binding energy per nucleon changes as the mass number (the total number of protons and neutrons) increases.

1. The binding energy per nucleon E_b/A, where E_b is the binding energy and A is the mass number, initially increases with the increase in mass number for lighter elements. This is because adding more nucleons leads to greater binding energy due to nuclear forces becoming more effective as nucleons attract each other.
2. However, this trend does not continue indefinitely. As we reach elements with intermediate mass numbers, the binding energy per nucleon reaches its peak around iron (Fe), which has one of the highest binding energies per nucleon owing to its favorable nuclear configuration.
3. Beyond iron, as the mass number continues to increase, the binding energy per nucleon gradually decreases. This is because the repulsive forces between protons in larger nuclei become increasingly significant, overpowering the attractive nuclear forces, and the nucleus becomes less stable.

This explanation shows that the correct answer is: "First increases and then decreases with increase in mass number". The other options can be ruled out because:

• "Increase continuously with mass number" is incorrect because the binding energy per nucleon does not continually increase for heavier elements.
• "Decreases continuously with mass number" is incorrect because the binding energy per nucleon increases initially for lighter elements.
• "Remains constant with mass number" is incorrect because there is a notable change in the binding energy per nucleon with varying mass numbers.

In summary, the variation in binding energy per nucleon first increases to a peak in stable middle-mass elements and then decreases as the nucleus becomes larger due to competing forces within the nucleus.