Question

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.

Hint:

Nucleon number conserved ≠ mass conserved. Mass defect accounts for nuclear energy via \( E = mc^2 \).

Answer 1

Mass-Energy Conversion in Nuclear Reactions
In a nuclear reaction, even if the number of protons and neutrons is conserved, the total mass of the nucleus before and after the reaction may not be exactly the same. This difference in mass, called the mass defect, is converted into energy according to Einstein’s mass-energy equivalence principle:
\[ E = \Delta m \, c^2 \]
where \( \Delta m \) is the mass defect and \( c \) is the speed of light.
Explanation:
- When nucleons (protons and neutrons) bind together to form a nucleus, the total mass of the bound nucleus is slightly less than the sum of the individual masses of the separate nucleons. The “lost” mass appears as binding energy that holds the nucleus together.
- Conversely, in nuclear fission or fusion, a small fraction of mass is converted into energy, which is released as kinetic energy of the products and radiation.
- Thus, even though the number of protons and neutrons remains the same, the conversion of mass into energy occurs due to changes in nuclear binding energy.
Example:
- In the fusion of hydrogen nuclei to form helium, the helium nucleus has slightly less mass than the combined mass of four hydrogen nuclei. The missing mass is released as energy, which powers stars.
Conclusion:
Mass is converted into energy (or vice versa) in nuclear reactions through changes in nuclear binding energy, despite the conservation of the number of protons and neutrons. This principle underlies the enormous energy output of both nuclear fission and fusion reactions.