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.

Answer 1

Mass-Energy Conversion in Nuclear Reactions Concept: In every nuclear reaction, the total number of nucleons may remain conserved, but the total mass of the system before and after the reaction is generally not the same. The difference arises because a part of the mass is associated with the binding energy of the nucleus. Einstein's mass-energy equivalence relation \[ E=\Delta mc^2 \] explains the conversion of mass into energy and vice versa.

Step 1: Understand nucleon conservation. In a nuclear reaction, \[ \text{Total number of protons before reaction} = \text{Total number of protons after reaction} \] and \[ \text{Total number of neutrons before reaction} = \text{Total number of neutrons after reaction}. \] Thus, nucleon number is conserved. However, conservation of nucleon number does not imply conservation of total mass.

Step 2: Introduce the concept of mass defect. The actual mass of a nucleus is less than the sum of the masses of its constituent nucleons. The difference is called mass defect. \[ \Delta m = (Zm_p+Nm_n)-M_{\text{nucleus}}. \] This mass defect corresponds to the binding energy of the nucleus.

Step 3: Explain energy release. When the products formed have greater binding energy than the reactants, the total mass of the products becomes smaller. The decrease in mass appears as released energy according to \[ E=\Delta mc^2. \] Similarly, if a nuclear reaction requires energy, the supplied energy is converted into additional mass. Thus, mass and energy are interchangeable. Conclusion: Although the numbers of protons and neutrons remain conserved, the total binding energy of the nuclei changes during a nuclear reaction. This change in binding energy appears as a change in mass, and the relation \[ \boxed{E=\Delta mc^2} \] accounts for the conversion of mass into energy or energy into mass.