Nuclei Notes for NEET and JEE Main 2027: Key Points and PDF

Nuclei is Chapter 13 of NCERT Class 12 Physics Part II and is in both the NEET UG and JEE Main syllabus under the unit Atoms and Nuclei. These notes cover atomic mass unit, composition and size of the nucleus, mass-energy relation, mass defect, binding energy per nucleon, nuclear force, fission and fusion, with a free notes PDF.

Nuclei Notes for NEET and JEE Main

Section-wise key points from NCERT Chapter 13, formula and comparison tables, high-yield facts and common mistakes for 2027 revision.

Nuclei at a Glance

The topic list follows the NEET UG 2026 syllabus notified by the National Medical Commission (NMC) on 22 December 2025 and the JEE Main 2026 syllabus released by the National Testing Agency (NTA). Both stay the reference until the 2027 syllabi are out. The full lists are on the NEET syllabus and JEE Main syllabus pages. Radioactivity appears only briefly in the rationalised NCERT chapter and is not named in either syllabus.

What is the nucleus made of?

A nucleus is made of protons and neutrons (together called nucleons); it holds more than 99.9% of the mass of an atom but is about 10⁴ times smaller in radius.

• The volume of a nucleus is about 10^-12 times the volume of the atom, so an atom is almost empty. If an atom were the size of a classroom, the nucleus would be the size of a pinhead.
• Atomic mass unit: 1 u = 1/12 of the mass of one ¹²C atom = 1.660539 × 10^-27 kg.
• Atomic masses are measured with a mass spectrometer, which revealed isotopes. Chlorine has isotopes of 34.98 u (75.4%) and 36.98 u (24.6%), giving a weighted average of 35.47 u.
• Hydrogen has three isotopes (1.0078 u, 2.0141 u, 3.0160 u). The nucleus of the lightest one (99.985% abundance) is the proton. Tritium is unstable and is produced artificially.
• Proton mass m_p = 1.00727 u = 1.67262 × 10^-27 kg, equal to the hydrogen atom mass (1.00783 u) minus one electron mass (0.00055 u).
• Electrons are not inside the nucleus; this was ruled out using quantum theory. Nuclear charge is +Ze, so the number of protons is exactly Z.
• James Chadwick discovered the neutron in 1932 by bombarding beryllium with alpha-particles, and won the 1935 Nobel Prize in Physics.
• Neutron mass m_n = 1.00866 u = 1.6749 × 10^-27 kg. A free neutron is unstable: it decays into a proton, an electron and an antineutrino with a mean life of about 1000 s, but it is stable inside the nucleus.
• Notation: Z = atomic number (protons), N = neutron number, A = mass number = Z + N. ¹⁹⁷₇₉Au has 79 protons and 118 neutrons; gold has 32 isotopes from A = 173 to A = 204.

Size of the Nucleus and Nuclear Density

Nuclear radius grows as the cube root of the mass number: R = R₀A^1/3, with R₀ = 1.2 fm (1 fm = 10^-15 m).

• Geiger and Marsden, at Rutherford’s suggestion, scattered alpha-particles from thin gold foil. A 5.5 MeV alpha-particle comes no closer than about 4.0 × 10^-14 m to a gold nucleus, so the nucleus must be smaller than that.
• Accurate nuclear sizes come from scattering fast electrons off targets of different elements.
• Since volume ∝ R³ ∝ A, nuclear density is the same for all nuclei, like a drop of liquid of constant density.
• Nuclear density is about 2.3 × 10¹⁷ kg m^-3, compared with 10³ kg m^-3 for water. Matter in neutron stars has a comparable density.
• Radius from electron scattering differs slightly from alpha scattering: electrons sense the charge distribution, alpha-particles sense nuclear matter.

Mass-energy Relation, Mass Defect and Binding Energy

The mass of a nucleus is always less than the total mass of its free protons and neutrons; this mass defect, converted by E = mc², is the binding energy.

• Worked NCERT example: for ¹⁶₈O the expected mass of 8 protons and 8 neutrons is larger than the measured nuclear mass (15.99053 u) by ΔM = 0.13691 u, which equals 127.5 MeV/c². That much energy is needed to split it into its nucleons.
• Binding energy per nucleon is the average energy needed to separate a nucleus into its nucleons, and it is a better measure of how tightly a nucleus is held than total binding energy.

Binding Energy per Nucleon Curve

• E_bn is practically constant (about 8 MeV) for middle mass numbers, 30 < A < 170.
• The curve peaks at about 8.75 MeV near A = 56 and falls to about 7.6 MeV at A = 238.
• E_bn is lower for light nuclei (A < 30) and heavy nuclei (A > 170).
• The flat region shows that the nuclear force is short-ranged: a nucleon feels only its near neighbours (saturation property).
• A heavy nucleus (A = 240) splitting into two A = 120 nuclei becomes more tightly bound, so fission releases energy. Two very light nuclei (A ≤ 10) joining also become more tightly bound, so fusion releases energy.
• The curve is smooth but shows small peaks at nuclides like ⁴He and ¹⁶O, seen as evidence of a shell structure in nuclei.

Nuclear Force: Key Properties

The nuclear force is a strong, short-range, charge-independent attraction that holds nucleons together against the Coulomb repulsion between protons.

• It is much stronger than the Coulomb force, which in turn is much stronger than gravity.
• It falls rapidly to zero when nucleons are more than a few femtometres apart, which causes saturation and the near-constant binding energy per nucleon.
• The potential energy of a pair of nucleons is minimum at r₀ ≈ 0.8 fm. The force is attractive beyond 0.8 fm and strongly repulsive below it.
• The force between neutron-neutron, proton-neutron and proton-proton pairs is about the same; it does not depend on electric charge.
• Unlike Coulomb’s law or Newton’s law of gravitation, the nuclear force has no simple mathematical form.

Radioactivity in Brief

Radioactivity is the decay of an unstable nucleus; A. H. Becquerel discovered it by accident in 1896 while studying uranium-potassium sulphate.

• Stable light nuclei have a neutron to proton ratio of about 1:1; for heavy nuclei it rises to about 3:2. Nuclei far from this ratio are unstable.
• Only about 10% of known isotopes are stable.
• The law of radioactive decay and half-life calculations are not in the rationalised NCERT text, and radioactivity is not named in the 2026 NEET UG or JEE Main syllabus.

Nuclear Energy: Fission and Fusion

Energy is released whenever less tightly bound nuclei change into more tightly bound ones, either by splitting a heavy nucleus (fission) or joining light nuclei (fusion).

• Chemical reactions involve energies of a few eV; nuclear reactions release energies of the order of MeV, about a million times more for the same mass.
• Fission of 1 kg of uranium gives about 10¹⁴ J, against about 10⁷ J from burning 1 kg of coal.

Nuclear Fission

• A neutron-induced example: ¹₀n + ²³⁵₉₂U → ²³⁶₉₂U → ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 3 ¹₀n.
• The same reaction can give other pairs, such as ¹³³₅₁Sb + ⁹⁹₄₁Nb + 4n, or ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + 2n.
• The fragments are radioactive and emit beta particles in succession to reach stable products.
• Energy released is about 200 MeV per fission. Estimate: E_bn rises from about 7.6 MeV (A = 240) to about 8.5 MeV (A = 120), a gain of about 0.9 MeV per nucleon, so 240 × 0.9 ≈ 216 MeV.
• This energy first appears as kinetic energy of fragments and neutrons, then as heat. Nuclear reactors use controlled fission; an atom bomb is uncontrolled fission.

Nuclear Fusion and Energy in Stars

• Examples: ¹H + ¹H → ²H + e⁺ + ν + 0.42 MeV; ²H + ²H → ³He + n + 3.27 MeV; ²H + ²H → ³H + ¹H + 4.03 MeV.
• Nuclei must overcome the Coulomb barrier, about 400 keV for two protons. Setting (3/2)kT ≈ 400 keV gives T ≈ 3 × 10⁹ K. Fusion driven by high temperature is called thermonuclear fusion.
• The sun’s interior is at about 1.5 × 10⁷ K, well below that estimate, so solar fusion involves protons with energies much above the average.
• The proton-proton cycle burns hydrogen into helium; the net result is 4 ¹H + 2e⁻ → ⁴He + 2ν + 6γ + 26.7 MeV.
• When core hydrogen runs out, the core contracts and heats to about 10⁸ K and helium fuses into carbon. Elements beyond the peak of the binding energy curve cannot be made this way.
• The sun is about 5 × 10⁹ years old and has hydrogen for about another 5 billion years; it will then become a red giant.
• Controlled thermonuclear fusion needs fuel at about 10⁸ K as a plasma; confining the plasma is the main challenge. Several countries, including India, are developing such techniques.

• In a nuclear reaction the numbers of protons and of neutrons are each conserved, so the energy comes from the difference in binding energies of the nuclei on the two sides.
• Chemical reactions also involve a mass defect, but it is about a million times smaller than in nuclear reactions.

Most-asked Facts for NEET and JEE Main: Nuclei

Revise these one-line facts from the NCERT chapter just before the exam.

• 1 u = 1.660539 × 10^-27 kg = 931.5 MeV/c².
• m_p = 1.00727 u, m_n = 1.00866 u, m_e = 0.00055 u.
• Neutron discovered by Chadwick (1932); a free neutron has a mean life of about 1000 s.
• R = R₀A^1/3, R₀ = 1.2 fm; nuclear density about 2.3 × 10¹⁷ kg m^-3, independent of A.
• Isotopes: same Z; isobars: same A; isotones: same N.
• ΔM = [Zm_p + (A − Z)m_n] − M; E_b = ΔMc².
• Binding energy per nucleon: about 8 MeV for 30 < A < 170, peak about 8.75 MeV at A = 56, about 7.6 MeV at A = 238.
• Nuclear force: short range, charge independent, attractive beyond about 0.8 fm and repulsive below.
• Fission of U-235 releases about 200 MeV per nucleus.
• Coulomb barrier for two protons is about 400 keV; the matching temperature is about 3 × 10⁹ K.
• Proton-proton cycle: four hydrogen atoms give one helium atom and 26.7 MeV.
• Nuclear energies are about a million times chemical energies (MeV against eV).

Common Mistakes to Avoid

Watch for these mix-ups when you answer questions on this chapter.

• Writing R ∝ A. The radius goes as A^1/3; it is the volume that is proportional to A.
• Saying heavier nuclei are denser. Nuclear density is the same for all nuclei.
• Judging stability by total binding energy. Use binding energy per nucleon; it peaks near A = 56, not for uranium.
• Mixing up isobars and isotones: isobars share A, isotones share N.
• Calling the nuclear force attractive at all distances. Below about 0.8 fm it is strongly repulsive.
• Thinking the nuclear force acts only between protons, or is weaker between neutrons. It is about the same for n-n, n-p and p-p pairs.
• Mixing atomic and nuclear masses in a mass defect sum. With atomic masses, use the hydrogen atom mass in place of m_p so the electron masses cancel.
• Treating 931.5 as a conversion for kilograms. It converts atomic mass units: 1 u = 931.5 MeV/c².
• Assuming the sun’s core is hot enough for every proton to fuse. Its 1.5 × 10⁷ K is far below the 3 × 10⁹ K estimate; only the fastest protons fuse.
• Saying a neutron is stable everywhere. A free neutron decays; it is stable only inside the nucleus.

Nuclei Notes PDF and Related Pages

Download the AglaSem Class 12 Physics notes for Dual Nature of Radiation and Matter, Atoms and Nuclei (key notes and important questions with answers) free: View PDF. It is an older combined set, so it also covers the Atoms and Dual Nature chapters and some radioactivity questions that are outside the current syllabus.

• All chapters: Physics notes for NEET and JEE Main
• Full topic list: NEET syllabus and JEE Main syllabus
• Practice: NEET question papers and JEE Main question papers
• Source text: NCERT Chapter 13 (NCERT, Class 12 Physics Part II)

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