Question

What is meant by mass-defect? In a nuclear fission reaction, find out the value of the fission energy \( Q \).

Hint:

The mass defect represents the difference between the mass of the individual particles and the mass of the nucleus. This difference is the energy released during nuclear reactions and is given by \( E = \Delta m . c^2 \).

Answer 1

Mass defect in a nuclear reaction refers to the difference in mass between the sum of the masses of the individual nucleons (protons and neutrons) and the mass of the entire nucleus. This difference in mass is converted into binding energy that holds the nucleus together, as per Einstein’s equation \( E = mc^2 \).
For the given nuclear fission reaction: \[ _{92}^{235}U + _{0}^{1}n ⇒ _{54}^{140}Xe + _{38}^{94}Sr + 2_{0}^{1}n + Q \] We need to calculate the fission energy \( Q \), which is given by the mass defect of the entire reaction. The formula for \( Q \) is: \[ Q = \left[ \text{(Mass of Reactants)} - \text{(Mass of Products)} \right] \times c^2 \] Given:
- Mass of \( _{92}^{235}U = 235.0439 \, \text{amu} \)
- Mass of \( _{54}^{140}Xe = 139.9054 \, \text{amu} \)
- Mass of \( _{38}^{94}Sr = 93.9063 \, \text{amu} \)
- Mass of \( _{0}^{1}n = 1.00867 \, \text{amu} \)
- \( 1 \, \text{amu} = 931 \, \text{MeV}/c^2 \)
Step 1: Find the mass of reactants and products
- Mass of reactants: \( 235.0439 + 1.00867 = 236.05257 \, \text{amu} \)
- Mass of products: \( 139.9054 + 93.9063 + 2(1.00867) = 235.829 \, \text{amu} \)
Step 2: Calculate the mass defect
Mass defect \( \Delta m = 236.05257 - 235.829 = 0.22357 \, \text{amu} \)
Step 3: Convert mass defect to energy
\[ Q = 0.22357 \times 931 \, \text{MeV} = 208.9 \, \text{MeV} \] Thus, the fission energy \( Q \) is approximately 208.9 MeV.