Question

Define 'Mass defect' and 'Binding energy' of a nucleus. Describe 'Fission process' on the basis of binding energy per nucleon.

Hint:

The fission process is driven by the increase in binding energy per nucleon as large nuclei split into smaller ones, releasing energy.

Answer 1

Mass Defect, Binding Energy, and Fission Process

1. Mass Defect 

The mass defect of a nucleus is the difference between the total mass of the individual nucleons (protons and neutrons) that make up the nucleus and the actual mass of the nucleus itself. Mathematically, it is expressed as:

\[ \Delta m = \text{Mass of nucleons} - \text{Mass of nucleus} \]

2. Binding Energy

The binding energy of a nucleus is the energy required to separate the nucleus into its constituent protons and neutrons. It is related to the mass defect by Einstein’s equation:

\[ E = \Delta m c^2 \]

Where \( \Delta m \) is the mass defect, \( c \) is the speed of light, and \( E \) is the binding energy.

3. Fission Process

Nuclear fission is the process in which a heavy nucleus, such as uranium-235, splits into two or more smaller nuclei, releasing a large amount of energy. This occurs when a nucleus absorbs a neutron and becomes unstable. During fission:

• The nucleus splits into smaller fragments.
• A large amount of energy is released due to the increased binding energy per nucleon in the fission products.
• The binding energy per nucleon increases as the nucleus splits, resulting in energy release.

Answer 2

1. Mass Defect:

The mass defect is the difference between the mass of a nucleus and the sum of the masses of its constituent protons and neutrons. When nucleons (protons and neutrons) bind together to form a nucleus, they lose a small amount of mass, which is converted into binding energy. The mass defect can be expressed as:

\[ \text{Mass Defect} = \text{(Mass of Protons + Neutrons)} - \text{Mass of the Nucleus} \]

The mass defect is responsible for the binding energy of the nucleus, which holds the nucleus together and prevents it from flying apart due to the repulsive forces between the protons.

2. Binding Energy:

Binding energy is the energy required to separate a nucleus into its constituent protons and neutrons. It is equal to the energy released when the nucleus is formed from its nucleons. The binding energy is related to the mass defect by Einstein’s mass-energy equivalence principle:

\[ E = \Delta m \cdot c^2 \]

where \(\Delta m\) is the mass defect, and \(c\) is the speed of light. Binding energy is a measure of the stability of a nucleus. The higher the binding energy, the more stable the nucleus.

3. Fission Process based on Binding Energy per Nucleon:

Fission is the process in which a heavy nucleus splits into two lighter nuclei, releasing a large amount of energy. The energy released during fission is primarily due to the change in the binding energy per nucleon before and after the fission process.

For heavy nuclei (like Uranium-235), the binding energy per nucleon is relatively low compared to the binding energy per nucleon of lighter elements such as Iron. This difference in binding energy per nucleon is the key to the fission process.

When a nucleus of Uranium-235 absorbs a neutron, it becomes highly unstable and splits into two lighter nuclei (such as Barium and Krypton), along with the release of neutrons and a huge amount of energy. The total binding energy of the resulting fragments is higher than that of the original nucleus, and this excess energy is released in the form of kinetic energy of the fission products, gamma radiation, and energy carried by neutrons. The binding energy per nucleon increases as the nucleus splits into smaller, more tightly bound fragments.

The following graph explains the relationship between binding energy per nucleon and atomic number:

Conclusion: The fission process occurs because the binding energy per nucleon of the fission fragments is higher than that of the original nucleus, and energy is released as a result of this difference in binding energy.