If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.
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Nucleon number conserved ≠ mass conserved.
Mass defect accounts for nuclear energy via \( E = mc^2 \).
Total number of nucleons (protons + neutrons) is conserved.
But total mass is not conserved exactly.
This is explained using Einstein’s mass–energy relation:
\[
E = mc^2
\]
Step 1: Mass defect.
The mass of a nucleus is less than the sum of the masses of its individual nucleons.
This difference is called mass defect.
\[
\Delta m = (\text{sum of individual masses}) - (\text{actual nuclear mass})
\]
Step 2: Binding energy.
The missing mass appears as binding energy:
\[
E_b = \Delta m \, c^2
\]
This energy holds nucleons together inside the nucleus.
Step 3: During nuclear reactions.
In fission or fusion:
Products have different binding energies compared to reactants.
If final nuclei have higher binding energy per nucleon:
Total mass decreases
Excess mass released as energy
Step 4: Energy–mass conversion.
If mass decreases → energy released
If energy supplied → mass can increase
Thus, even though nucleon number is conserved, a small amount of mass is converted into energy (or vice versa).
Conclusion:
Mass is converted into energy in nuclear reactions due to changes in binding energy.
The difference in mass between reactants and products appears as energy according to:
\[
E = \Delta m \, c^2
\]
