1. Atomic Masses and Nuclear Composition

The nucleus of an atom consists of protons and neutrons, collectively called nucleons. Atomic masses are measured in atomic mass units (u), where 1 u is defined as 1/12th the mass of an unbound carbon-12 atom. The number of protons defines the element (atomic number, Z), while the total number of protons and neutrons defines the mass number (A). Isotopes of an element have the same atomic number but different mass numbers, meaning they have different numbers of neutrons. The nuclear composition is represented as $^A_Z\text{X}$.

2. Mass-Energy and Nuclear Binding Energy

According to Einstein's mass-energy equivalence, $E = mc^2$, mass and energy are interchangeable. The nuclear binding energy is the energy required to separate a nucleus into its constituent protons and neutrons. This energy corresponds to a "mass defect," the difference between the mass of the constituent nucleons and the mass of the nucleus itself. A higher binding energy per nucleon indicates a more stable nucleus. This concept explains why nuclear reactions release significant amounts of energy.

3. Nuclear Force

The nuclear force is the strong, short-range force that binds protons and neutrons together in the atomic nucleus. It is the strongest of the fundamental forces, overcoming the electrostatic repulsion between positively charged protons. This force is charge-independent, meaning it acts equally between proton-proton, neutron-neutron, and proton-neutron pairs, and is very strong at distances of about $10^{-15}$ meters (femtometers) but drops rapidly to negligible values at larger distances. It is responsible for the stability of atomic nuclei.

4. Radioactivity and Decay Laws

Radioactivity is the spontaneous disintegration of unstable atomic nuclei, accompanied by the emission of particles (alpha, beta) or electromagnetic radiation (gamma rays). Radioactive decay follows statistical laws; the rate of decay is proportional to the number of radioactive nuclei present ($R = \frac{dN}{dt} = -\lambda N$), where $\lambda$ is the decay constant. The half-life ($t_{1/2}$) of a radioactive substance is the time it takes for half of the nuclei to decay, related to the decay constant by $t_{1/2} = \frac{\ln 2}{\lambda}$.

5. Nuclear Energy and Reactions (Fission and Fusion)

Nuclear reactions involve transformations of atomic nuclei. Nuclear fission is the process where a heavy nucleus splits into lighter nuclei, releasing a large amount of energy. This is the principle behind nuclear power reactors and atomic bombs. Nuclear fusion is the process where light nuclei combine to form a heavier nucleus, also releasing immense energy. Fusion is the energy source of stars, including our Sun, and is being explored for clean energy generation on Earth. Both processes involve converting mass into energy, following $E = \Delta mc^2$. India is actively involved in research related to both nuclear fission power and fusion energy.

6. Additional: Nuclear Reactions and Q-value

In any nuclear reaction, energy is either released or absorbed. The Q-value of a nuclear reaction is the energy released or absorbed, calculated from the difference in the total rest mass energy of the reactants and the products. $Q = (\sum m_{\text{reactants}} - \sum m_{\text{products}})c^2$. If $Q > 0$, the reaction is exothermic (energy is released), and if $Q < 0$, it is endothermic (energy must be supplied for the reaction to occur). This is a direct application of mass-energy equivalence in nuclear processes.