Question

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

Hint:

The higher the binding energy per nucleon, the more stable the nucleus. The most stable nucleus in nature is Iron-56.

Answer 1

Mass Defect: Mass defect (\( \Delta m \)) is the difference between the total mass of the individual nucleons (protons and neutrons) in a nucleus and the actual measured mass of the nucleus. It is given by: \[ \Delta m = Z m_p + (A - Z) m_n - m_{\text{nucleus}} \] where:
\( Z \) is the number of protons,
\( A - Z \) is the number of neutrons,
\( m_p \) and \( m_n \) are the masses of a proton and a neutron, respectively,
\( m_{\text{nucleus}} \) is the actual nuclear mass.

Binding Energy: Binding energy (\( E_b \)) is the energy required to break a nucleus into its constituent protons and neutrons. It is given by Einstein’s mass-energy equivalence: \[ E_b = \Delta m \cdot c^2 \] where: \( c \) is the speed of light (\( 3.0 \times 10^8 \) m/s),
\( \Delta m \) is the mass defect.
Fission Process and Binding Energy Per Nucleon: Nuclear fission occurs when a heavy nucleus splits into two or more lighter nuclei, releasing a significant amount of energy. This is explained using the concept of binding energy per nucleon: \[ \text{Binding Energy per Nucleon} = \frac{E_b}{A} \] For heavy nuclei (e.g., Uranium-235), the binding energy per nucleon is lower than that of medium-sized nuclei.
When a heavy nucleus splits, the resulting smaller nuclei have higher binding energy per nucleon, meaning energy is released in the process.
This released energy is the basis of nuclear power and atomic bombs.