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: The mass defect (\( \Delta m \)) is the variance between the cumulative mass of individual nucleons (protons and neutrons) within a nucleus and the nucleus's experimentally determined mass. The formula is: \[ \Delta m = Z m_p + (A - Z) m_n - m_{\text{nucleus}} \] Here, \( Z \) denotes the proton count, \( A - Z \) represents the neutron count, \( m_p \) and \( m_n \) are the respective masses of a proton and a neutron, and \( m_{\text{nucleus}} \) is the observed nuclear mass.

Binding Energy: Binding energy (\( E_b \)) is the energy required to disassemble a nucleus into its constituent protons and neutrons, calculated via 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) and \( \Delta m \) is the mass defect. Fission Process and Binding Energy Per Nucleon: Nuclear fission, the splitting of a heavy nucleus into lighter ones, liberates substantial energy. This phenomenon is explained by binding energy per nucleon: \[ \text{Binding Energy per Nucleon} = \frac{E_b}{A} \] Heavy nuclei, such as Uranium-235, possess a lower binding energy per nucleon compared to medium-sized nuclei. Upon fission, the resultant smaller nuclei exhibit a higher binding energy per nucleon, indicating energy release. This liberated energy underpins nuclear power generation and the function of atomic bombs.