The atomic nucleus is an incredibly dense region at the centre of an atom, containing protons (positively charged) and neutrons (neutral). Together, protons and neutrons are called nucleons. The number of protons (Z) is the atomic number, which determines the element. The total number of nucleons (Z + N) is the mass number A. Atoms of the same element with different numbers of neutrons are called isotopes.

The nucleus is held together by the strong nuclear force — one of the four fundamental forces of nature. The strong force is extremely powerful at short range (up to ~3 fm) but drops to zero beyond that range. It is this force that overcomes the electrostatic repulsion between protons and keeps the nucleus stable. The strong nuclear force does not distinguish between protons and neutrons — it is charge-independent.

Experimental scattering experiments (Rutherford-type and electron scattering) have shown that the radius of a nucleus follows a simple empirical relation:

This means the nuclear radius is proportional to A^1/3. Taking the cube to find volume:

This is a crucial NEET fact: radius ∝ A^1/3 but volume ∝ A. Students often confuse the two. Since volume is proportional to mass number, and mass is also proportional to A (each nucleon has roughly the same mass), the nuclear density is constant — the same for all nuclei regardless of size or element.

Nuclear density ρ = mass/volume = (A × m_u) / ((4/3)πR₀³ × A) = m_u / ((4/3)πR₀³)

Since A cancels, nuclear density is the same for all nuclei! This extraordinary result means that gold, carbon, hydrogen — all have the same nuclear density of approximately 2.3 × 10¹⁷ kg/m³. This is about 10¹⁴ times denser than ordinary matter (like water at 10³ kg/m³). A teaspoon of nuclear matter would weigh about 500 million tonnes!

When protons and neutrons combine to form a nucleus, the actual mass of the nucleus is always less than the sum of the individual masses of the separate protons and neutrons. This "missing" mass is called the mass defect (Δm):

This mass defect is NOT the difference between the mass of an atom and its nucleus (that would simply give the mass of the electrons: Z × m_e). The mass defect specifically refers to the difference between the total mass of FREE nucleons and the BOUND nucleus. This distinction is frequently tested in NEET — Statement C in this problem incorrectly defines it as atom minus nucleus.

By Einstein's famous mass-energy equivalence (E = mc²), the mass defect corresponds to an amount of energy called the binding energy:

The binding energy is the energy released when free nucleons come together to form the nucleus — or equivalently, the energy you would need to supply to break the nucleus apart into its individual nucleons. A larger binding energy means a more stable nucleus — the nucleons are more tightly bound together.

The binding energy per nucleon (B.E./A) is a measure of nuclear stability. When plotted against mass number A, this curve reveals fundamental insights about nuclear physics:

Unstable nuclei spontaneously transform into more stable configurations through radioactive decay. There are three main types of nuclear decay:

Alpha (α) decay: Nucleus emits an alpha particle (₂He⁴ — 2 protons + 2 neutrons). Mass number decreases by 4, atomic number by 2. Example: ₉₂U²³⁸ → ₉₀Th²³⁴ + ₂He⁴

Beta (β⁻) decay: A neutron converts to a proton, emitting an electron and an antineutrino. Mass number unchanged, atomic number increases by 1. Example: ₆C¹⁴ → ₇N¹⁴ + e⁻ + ν̄

Gamma (γ) decay: Nucleus in excited state releases energy as a high-energy photon (gamma ray). No change in mass number or atomic number. Often accompanies alpha or beta decay.

The number of undecayed nuclei N at time t follows exponential decay:

The half-life is the time for half the radioactive nuclei to decay. It is characteristic of each isotope and cannot be changed by any chemical or physical means (temperature, pressure, etc.). After n half-lives, fraction remaining = (1/2)ⁿ.

Nuclear Fission: A heavy nucleus (like U-235 or Pu-239) splits into two medium-sized nuclei when struck by a neutron. Example: ₉₂U²³⁵ + n → ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + 3n + energy. The three released neutrons can trigger further fissions — a chain reaction. Nuclear reactors control this chain reaction; nuclear weapons (atom bombs) allow it to run uncontrolled. Energy released ≈ 200 MeV per fission event.

Nuclear Fusion: Light nuclei combine to form a heavier nucleus. Example: ₁H² + ₁H³ → ₂He⁴ + n + 17.6 MeV. This is the reaction powering the sun and stars. Requires extremely high temperatures (millions of Kelvin) to overcome electrostatic repulsion between positive nuclei. Fusion releases more energy per unit mass than fission. Thermonuclear weapons (hydrogen bombs) use uncontrolled fusion. Controlled fusion (as in ITER project) is still being developed as a future energy source.