Answer the following questions:
$(a)$ Are the equations of nuclear reactions 'balanced' in the sense a chemical equation (e.g.,$2H_2 + O_2 \rightarrow 2H_2O$) is? If not,in what sense are they balanced on both sides?
$(b)$ If both the number of protons and the number of neutrons are conserved in each nuclear reaction,in what way is mass converted into energy (or vice-versa) in a nuclear reaction?
$(c)$ $A$ general impression exists that mass-energy interconversion takes place only in nuclear reactions and never in chemical reactions. This is strictly speaking,incorrect. Explain.

(N/A) chemical equation is balanced in the sense that the number of atoms of each element is the same on both sides. $A$ chemical reaction merely alters the combinations of atoms. In a nuclear reaction,elements may be transmuted,so the number of atoms of each element is not necessarily conserved. However,the total number of protons and the total number of neutrons are separately conserved in a nuclear reaction. Thus,nuclear reactions are balanced in terms of the total number of protons and neutrons.
$(b)$ The binding energy of a nucleus contributes negatively to its mass (mass defect). While the total number of protons and neutrons is conserved,the total binding energy of the nuclei on the reactant side may differ from that on the product side. This difference in binding energy manifests as energy released or absorbed. Since binding energy contributes to the mass,the difference in the total mass of the nuclei on both sides is converted into energy or vice-versa.
$(c)$ In principle,chemical reactions are similar to nuclear reactions regarding mass-energy interconversion. Energy released or absorbed in chemical reactions arises from the difference in chemical binding energies of atoms and molecules. Because chemical binding energy also contributes to the total mass (mass defect),the mass difference between reactants and products is converted into energy. However,these mass defects in chemical reactions are approximately a million times smaller than those in nuclear reactions,leading to the incorrect impression that mass-energy interconversion does not occur in chemical reactions.