Class 12 Physics Chapter 13 Nuclei – Revision Notes

Quick revision notes for Class 12 Physics Chapter 13 – Nuclei, covering nuclear size and composition, mass defect and binding energy, the binding-energy-per-nucleon curve, and nuclear fission and fusion — ideal for last-minute board exam revision.

Composition and Size of the Nucleus

A nucleus contains protons (charge +e) and neutrons (uncharged) — together called nucleons. The number of protons is the atomic number Z; the total number of nucleons is the mass number A. Nuclei with the same Z but different A (i.e. a different number of neutrons) are called isotopes. The nuclear radius follows R=R₀A^1/3 (R₀≈1.2fm), so nuclear volume is proportional to A — which means nuclear density is essentially the same for every nucleus, regardless of size (NCERT Exercise 13.10).

Mass Defect and Binding Energy

A nucleus’s actual mass is always slightly less than the sum of the masses of its separate protons and neutrons; this shortfall is the mass defect, Δm=Zm_H+(A−Z)m_n−M. By Einstein’s mass-energy relation, this missing mass corresponds to the nucleus’s binding energy, BE=Δm×c², conventionally computed as BE(MeV)=Δm(u)×931.5. Binding energy is the energy that would need to be supplied to completely separate a nucleus into free protons and neutrons.

The Binding-Energy-per-Nucleon Curve

Plotting BE/A against mass number A gives a curve that rises steeply for light nuclei, peaks at about 8.7–8.8MeV around A≈56 (the iron region — the most stable nuclei), and then declines slowly for heavier nuclei. This single curve explains why both fusion of very light nuclei and fission of very heavy nuclei release energy: both processes move the resulting nuclei toward the peak, increasing total binding energy, with the difference released as energy.

Nuclear Fission

Fission is the splitting of a heavy nucleus (e.g. uranium-235, plutonium-239) into two lighter nuclei, usually triggered by neutron absorption, releasing a large amount of energy (typically ≈180–200MeV per event) along with more free neutrons that can sustain a chain reaction. This is the basis of nuclear power plants. Not every split releases energy, though — splitting a nucleus already near the peak of the BE/A curve (like iron) requires energy rather than releasing it (NCERT Exercise 13.6).

Nuclear Fusion and the Coulomb Barrier

Fusion is the combining of two light nuclei (e.g. isotopes of hydrogen) into a heavier one, releasing energy because the product moves closer to the BE/A peak. Because both nuclei are positively charged, they must overcome a repulsive Coulomb barrier (of order a few hundred keV for light nuclei) before the short-range attractive nuclear force can bind them — which is why fusion requires extremely high temperatures (as in the Sun’s core) and remains difficult to sustain in a controlled way on Earth.

One-Line Summary

Chapter 13 explains nuclear structure and the mass-energy relationship behind binding energy, and uses the binding-energy-per-nucleon curve to show why splitting heavy nuclei (fission) and combining light nuclei (fusion) are the two processes that release nuclear energy.