CBSE Class 12 Physics Revision Notes Chapter 13: Nuclei

The nucleus contains more than 99.9% of an atom’s mass within a region much smaller than the complete atom.
Nuclear binding energy, fission and fusion can be understood through Einstein’s mass-energy equivalence.

The chapter Nuclei explains the composition, mass, size and stability of atomic nuclei. It introduces protons, neutrons, isotopes and the strong nuclear force that holds nucleons together despite electrostatic repulsion between protons.

Use these CBSE Class 12 Physics Revision Notes Chapter 13 for the 2026–27 session. Begin with nuclear composition and radius. Then revise mass defect, binding energy, nuclear force, radioactivity, fission, fusion and energy production in stars.

Key Takeaways

• Nuclear radius: R = R₀A¹ᐟ³, where R₀ is approximately 1.2 fm.
• Mass-energy relation: E = mc² connects a change in mass with an equivalent change in energy.
• Binding energy: Eb = ΔMc² measures the energy required to separate a nucleus into its nucleons.
• Nuclear energy: Energy is released when nuclei move towards a state with greater binding energy per nucleon.

Access Class 12 Physics Chapter 13 Nuclei Notes in 30 Minutes

Divide the chapter into three revision blocks:

• First 10 minutes: Nuclear composition, nuclide notation, nuclear radius and density
• Next 10 minutes: Mass defect, binding energy, binding-energy curve and nuclear force
• Final 10 minutes: Radioactivity, nuclear fission, nuclear fusion and stellar energy

While solving nuclear-mass questions, check whether the given value is an atomic mass or a nuclear mass. Atomic masses include electron masses, while nuclear masses do not.

Need help revising mass-defect calculations, binding-energy graphs and nuclear reactions?
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Composition of Nucleus in Class 12 Physics Chapter 13 Notes

The nucleus is the small central part of an atom.

It contains:

• Protons
• Neutrons

Protons and neutrons together are called nucleons.

The nucleus:

• Carries positive charge
• Contains nearly the complete mass of the atom
• Occupies a very small part of the atomic volume
• Is held together by nuclear forces

All atomic electrons remain outside the nucleus.

Proton

A proton carries one unit of positive charge.

Its mass is approximately:

mp = 1.00727 u

or:

mp = 1.67262 × 10⁻²⁷ kg

A free proton is stable.

Neutron

A neutron has no electric charge.

Its mass is:

mn = 1.00866 u

or approximately:

mn = 1.6749 × 10⁻²⁷ kg

The neutron was discovered by James Chadwick in 1932.

A free neutron is unstable and may decay into:

• A proton
• An electron
• An antineutrino

Its mean life is about 1000 seconds. A neutron can remain stable inside many nuclei.

Atomic Mass Unit in Nuclei Class 12 Notes

The kilogram is inconvenient for expressing atomic and nuclear masses.

Therefore, atomic masses are measured in the atomic mass unit, represented by u.

One atomic mass unit is defined as one-twelfth of the mass of one carbon-12 atom.

1 u = 1.660539 × 10⁻²⁷ kg

The energy equivalent of one atomic mass unit is:

1 u = 931.5 MeV/c²

Therefore, a mass defect of 1 u corresponds to an energy of:

931.5 MeV

Electron Mass

The electron mass is:

me = 0.00055 u

or:

me = 9.1 × 10⁻³¹ kg

The electron is much lighter than a proton or neutron.

Mass Number and Atomic Number in Class 12 Physics Nuclei Notes

The composition of a nucleus is described using Z, N and A.

Atomic Number

The atomic number Z is the number of protons in a nucleus.

It also determines:

• Nuclear charge, +Ze
• Identity of the element
• Number of electrons in a neutral atom

Neutron Number

The neutron number N is the number of neutrons in the nucleus.

Mass Number

The mass number A is the total number of nucleons.

Therefore:

A = Z + N

Hence:

N = A − Z

Nuclide Notation

A nuclear species is represented as:

ᴬZX

Here:

• X is the chemical symbol.
• A is the mass number.
• Z is the atomic number.

For example, gold-197 is represented as:

¹⁹⁷₇₉Au

It contains:

• 79 protons
• 118 neutrons
• 197 nucleons

Isotopes, Isobars and Isotones in Physics Chapter 13 Revision Notes

Isotopes

Isotopes are nuclei with:

• The same atomic number Z
• Different mass numbers A
• Different neutron numbers N

Examples of hydrogen isotopes are:

• Protium, ¹₁H
• Deuterium, ²₁H
• Tritium, ³₁H

Their chemical properties are almost identical because they have the same electronic structure.

Isobars

Isobars have:

• The same mass number A
• Different atomic numbers Z

For example:

³₁H and ³₂He

Both have mass number 3.

Isotones

Isotones have:

• The same neutron number N
• Different atomic numbers Z
• Different mass numbers A

For example:

¹⁹⁸₈₀Hg and ¹⁹⁷₇₉Au

Each contains 118 neutrons.

Isotopes, Isobars and Isotones Comparison

Average Atomic Mass in Chapter 13 Physics Notes

Most elements occur naturally as a mixture of isotopes.

The atomic mass listed for an element is the weighted average of the masses of its isotopes.

For isotopes with masses m₁ and m₂ and percentage abundances P₁ and P₂:

Average atomic mass = (P₁m₁ + P₂m₂)/100

For chlorine:

• One isotope has mass about 34.98 u and abundance 75.4%.
• Another has mass about 36.98 u and abundance 24.6%.

Its weighted average is close to:

35.47 u

This explains why atomic masses are not always whole numbers.

Nuclear Radius in CBSE Class 12 Physics Chapter 13 Notes

Scattering experiments show that the radius of a nucleus depends on its mass number.

The empirical relation is:

R = R₀A¹ᐟ³

Here:

• R is the nuclear radius.
• A is the mass number.
• R₀ is approximately 1.2 × 10⁻¹⁵ m.

Since:

1 fm = 10⁻¹⁵ m

we may write:

R₀ = 1.2 fm

Dependence on Mass Number

Nuclear radius varies as:

R ∝ A¹ᐟ³

Therefore, the ratio of the radii of two nuclei is:

R₁/R₂ = (A₁/A₂)¹ᐟ³

A nucleus with eight times the mass number has twice the radius.

Nuclear Volume

Since nuclear volume is proportional to R³:

V ∝ R³

Using R ∝ A¹ᐟ³:

V ∝ A

Therefore, nuclear volume is directly proportional to the number of nucleons.

Nuclear Density in Class 12 Nuclei Revision Notes

The mass of a nucleus is approximately proportional to its mass number A.

Since:

Mass ∝ A

and:

Volume ∝ A

the density is:

Density = Mass/Volume

Therefore:

Nuclear density is nearly independent of A.

All nuclei have approximately the same density.

The nuclear density is of the order of:

2.3 × 10¹⁷ kg/m³

This is extremely high compared with ordinary matter.

For comparison:

Density of water ≈ 10³ kg/m³

The density inside neutron stars is comparable to nuclear density.

Mass-Energy Equivalence in CBSE Class 12 Nuclei Notes

Einstein showed that mass is a form of energy.

The mass-energy equivalence relation is:

E = mc²

Here:

• E is energy.
• m is mass.
• c is the speed of light in vacuum.

Since:

c ≈ 3 × 10⁸ m/s

a small amount of mass corresponds to a very large amount of energy.

Energy Equivalent of One Gram

For:

m = 1 g = 10⁻³ kg

E = 10⁻³ × (3 × 10⁸)²

Therefore:

E = 9 × 10¹³ J

Complete conversion of one gram of mass would release an enormous amount of energy.

Unified Conservation Law

Mass and energy should not be treated as completely separate conserved quantities.

The correct principle is conservation of total mass-energy.

This principle is important in nuclear decays and reactions.

Mass Defect in Nuclei Revision Notes

A nucleus contains Z protons and A − Z neutrons.

The expected mass of its separate nucleons is:

Zmₚ + (A − Z)mₙ

However, the measured nuclear mass M is smaller than this sum.

The difference is called the mass defect.

ΔM = [Zmₚ + (A − Z)mₙ] − M

The missing mass has been converted into binding energy during formation of the nucleus.

Using Atomic Masses

When atomic masses are used, the hydrogen-atom mass may be used instead of the proton mass so that electron masses cancel correctly.

Then:

ΔM = [ZmH + (A − Z)mₙ] − Matom

Here:

• mH is the mass of a hydrogen atom.
• Matom is the measured atomic mass.

This form is convenient in numerical problems based on tabulated atomic masses.

Nuclear Binding Energy in Class 12 Physics Chapter 13 Notes

The nuclear binding energy is the energy required to separate a nucleus completely into its individual protons and neutrons.

It is also equal to the energy released when the free nucleons combine to form the nucleus.

Binding energy is:

Eb = ΔMc²

If ΔM is given in atomic mass units:

Eb = ΔM × 931.5 MeV

A larger binding energy generally means that more energy is required to break the nucleus apart.

Physical Meaning of Binding Energy

When nucleons form a bound nucleus:

• Energy is released.
• The mass of the bound system decreases.
• The final nucleus has lower total mass-energy.
• The nucleus becomes more stable than the separate nucleons.

To separate the nucleus again, the same amount of energy must be supplied.

Binding Energy per Nucleon in Chapter 13 Physics Notes

The binding energy per nucleon is:

Ebn = Eb/A

It gives the average energy required to remove one nucleon from a nucleus.

Binding energy per nucleon is a better measure of nuclear stability than total binding energy.

A nucleus with a higher binding energy per nucleon is generally more tightly bound.

Binding-Energy Curve

The graph of binding energy per nucleon against mass number has the following features:

• It rises quickly for light nuclei.
• It reaches a maximum near A = 56.
• The maximum value is about 8.75 MeV per nucleon.
• It remains near 8 MeV for medium-mass nuclei.
• It decreases slowly for very heavy nuclei.
• Uranium-238 has a value of about 7.6 MeV per nucleon.

Nuclei near iron are among the most tightly bound.

Important Mass Ranges

Binding-Energy Curve and Nuclear Stability Revision Notes

The binding-energy curve explains why both fission and fusion release energy.

Heavy Nuclei

Very heavy nuclei have lower binding energy per nucleon than medium-mass nuclei.

If a heavy nucleus splits:

• Medium-mass fragments are formed.
• Binding energy per nucleon increases.
• The products are more tightly bound.
• Energy is released.

This process is nuclear fission.

Light Nuclei

Very light nuclei also have lower binding energy per nucleon.

If light nuclei combine:

• A heavier nucleus is formed.
• Binding energy per nucleon increases.
• The final nucleus is more tightly bound.
• Energy is released.

This process is nuclear fusion.

Nuclear Force in Class 12 Physics Nuclei Notes

The nucleus contains positively charged protons.

These protons repel each other through the electrostatic force.

A stronger attractive force is therefore required to hold the nucleus together.

This force is called the nuclear force or strong nuclear force.

Properties of Nuclear Force

The main properties are:

• It is much stronger than electrostatic and gravitational forces at nuclear distances.
• It acts between protons and neutrons.
• It is attractive over normal nuclear separations.
• It becomes strongly repulsive at extremely small separations.
• It is a short-range force.
• Its effect becomes negligible beyond a few femtometres.
• It is nearly independent of electric charge.
• Proton-proton, neutron-neutron and proton-neutron nuclear forces are approximately similar.

Attractive and Repulsive Regions

The potential energy of two nucleons is minimum at a separation of about:

r₀ ≈ 0.8 fm

For separations greater than about 0.8 fm:

• The force is mainly attractive.

For separations smaller than about 0.8 fm:

• The force becomes strongly repulsive.

The repulsive part prevents the nucleus from collapsing into an extremely small volume.

Saturation Property

A nucleon interacts strongly only with nearby nucleons.

It does not interact equally with every other nucleon in a large nucleus.

This property is called the saturation property of nuclear force.

It explains why binding energy per nucleon remains nearly constant for medium and heavy nuclei.

Radioactivity in Physics Chapter 13 Revision Notes

Radioactivity is the spontaneous transformation of an unstable nucleus into another nucleus with the emission of radiation.

It was discovered by Henri Becquerel in 1896.

Radioactivity is:

• A nuclear phenomenon
• Spontaneous
• Unaffected by ordinary physical and chemical conditions
• Associated with unstable nuclei

The three main types of radioactive decay are:

• Alpha decay
• Beta decay
• Gamma decay

Alpha Decay in CBSE Class 12 Physics Chapter 13 Notes

In alpha decay, the unstable nucleus emits an alpha particle.

An alpha particle is a helium nucleus:

⁴₂He

It contains:

• Two protons
• Two neutrons
• Charge +2e

The general alpha-decay equation is:

ᴬZX → ᴬ⁻⁴Z⁻²Y + ⁴₂He + energy

After alpha decay:

• Mass number decreases by 4.
• Atomic number decreases by 2.
• A new element is formed.

Alpha particles have strong ionising power but relatively low penetrating power.

Beta Decay in Class 12 Nuclei Revision Notes

In beta decay, a nucleus emits an electron or positron.

Beta-Minus Decay

In beta-minus decay, a neutron changes into:

• A proton
• An electron
• An antineutrino

The general change is:

n → p + e⁻ + antineutrino

For the nucleus:

ᴬZX → ᴬZ+1Y + e⁻ + antineutrino

After beta-minus decay:

• Mass number remains unchanged.
• Atomic number increases by 1.

Beta-Plus Decay

In beta-plus decay, a proton changes into:

• A neutron
• A positron
• A neutrino

The general nuclear change is:

ᴬZX → ᴬZ−1Y + e⁺ + neutrino

After beta-plus decay:

• Mass number remains unchanged.
• Atomic number decreases by 1.

Gamma Decay in CBSE Class 12 Nuclei Notes

Gamma decay involves the emission of a high-energy photon.

The nucleus usually emits gamma radiation when it changes from an excited state to a lower-energy state.

The general equation is:

ᴬZX* → ᴬZX + γ

After gamma emission:

• Mass number remains unchanged.
• Atomic number remains unchanged.
• Nuclear energy decreases.

Gamma radiation has:

• No electric charge
• No rest mass
• Very high penetrating power
• Lower ionising power than alpha radiation

Alpha, Beta and Gamma Radiation Comparison

Nuclear Energy in Chapter 13 Physics Notes

Nuclear energy is released when a nuclear process produces more tightly bound nuclei.

The energy released in a nuclear reaction is often millions of times greater than the energy released in a chemical reaction involving a similar quantity of matter.

Typical energy scales are:

• Chemical reactions: a few eV per event
• Nuclear reactions: several MeV per event

For example:

• Fission of 1 kg of uranium can release about 10¹⁴ J.
• Burning 1 kg of coal releases about 10⁷ J.

This large difference arises because nuclear binding energies are much greater than chemical binding energies.

Q-Value of a Nuclear Reaction in Nuclei Revision Notes

The energy released or absorbed in a nuclear reaction is called its Q-value.

For a reaction:

A + b → C + d

the Q-value is:

Q = (mA + mb − mC − md)c²

Using atomic mass units:

Q = Mass difference × 931.5 MeV

Meaning of Q-Value

If:

Q > 0

the reaction releases energy and is exothermic.

If:

Q < 0

the reaction absorbs energy and is endothermic.

The Q-value may also be written as:

Q = Final kinetic energy − Initial kinetic energy

Total mass-energy and electric charge must be conserved in a nuclear reaction.

Nuclear Fission in Class 12 Physics Chapter 13 Notes

Nuclear fission is the splitting of a heavy nucleus into two or more medium-mass nuclei.

It is commonly initiated by neutron absorption.

An example is:

¹₀n + ²³⁵₉₂U → ²³⁶₉₂U* → ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 3¹₀n + energy

Other fragment combinations are also possible.

Why Fission Releases Energy

A heavy nucleus has a lower binding energy per nucleon than its medium-mass fission products.

After fission:

• The products are more tightly bound.
• Their total mass is lower.
• The lost mass appears as energy.

The energy released per uranium fission is of the order of:

200 MeV

Form of Released Energy

The fission energy initially appears as:

• Kinetic energy of the fragments
• Kinetic energy of neutrons
• Gamma radiation

It is eventually converted into heat in the surrounding material.

Fission Products

Fission fragments are generally neutron-rich and unstable.

They undergo successive beta decays to form more stable nuclei.

Nuclear Chain Reaction in Physics Chapter 13 Revision Notes

A fission event may release several neutrons.

These neutrons can cause fission in other uranium nuclei.

This produces a chain of reactions called a nuclear chain reaction.

Controlled Chain Reaction

In a controlled chain reaction:

• The reaction rate is regulated.
• Only the required number of neutrons produces further fission.
• Energy is released steadily.

Controlled fission is used as an energy source in nuclear power systems.

Uncontrolled Chain Reaction

In an uncontrolled reaction:

• The number of fissions rises rapidly.
• Energy is released in a very short time.
• The process becomes explosive.

The enormous energy of an atomic bomb comes from uncontrolled nuclear fission.

Nuclear Fusion in Class 12 Physics Nuclei Notes

Nuclear fusion is the combination of two light nuclei to form a heavier nucleus.

Examples include:

²₁H + ²₁H → ³₂He + ¹₀n + 3.27 MeV

and:

²₁H + ²₁H → ³₁H + ¹₁H + 4.03 MeV

Why Fusion Releases Energy

Light nuclei have relatively low binding energy per nucleon.

When they combine:

• A more tightly bound nucleus forms.
• Binding energy per nucleon increases.
• Total mass decreases.
• Energy is released.

Fusion can release a very large amount of energy per unit mass.

Coulomb Barrier in Nuclear Fusion Revision Notes

The nuclei taking part in fusion are positively charged.

They repel each other through the Coulomb force.

For fusion to occur:

• The nuclei must come very close.
• They must overcome electrostatic repulsion.
• The short-range nuclear force must become effective.

The required energy is called the Coulomb-barrier energy.

For two protons, the barrier is of the order of:

400 keV

Very high temperatures are required to give nuclei sufficient kinetic energy.

Thermonuclear Fusion in CBSE Class 12 Nuclei Notes

Fusion produced by heating nuclear fuel to extremely high temperatures is called thermonuclear fusion.

At such temperatures:

• Atoms become fully ionised.
• Matter exists as plasma.
• Nuclei move with very high speeds.
• Some collisions overcome the Coulomb barrier.

Thermonuclear fusion is the main source of stellar energy.

The Sun’s core temperature is approximately:

1.5 × 10⁷ K

Even though this is below the simple classical estimate for overcoming the barrier, some particles have enough energy to undergo fusion.

Proton-Proton Cycle in Chapter 13 Physics Notes

The Sun converts hydrogen into helium through a series of fusion reactions called the proton-proton cycle.

The main steps include:

1. Two protons combine to produce deuterium, a positron and a neutrino.
2. The positron combines with an electron and produces gamma photons.
3. Deuterium combines with another proton to form helium-3.
4. Two helium-3 nuclei combine to form helium-4 and release two protons.

The net result is approximately:

4¹₁H → ⁴₂He + energy

The total energy released is about:

26.7 MeV

The reaction also produces positrons, neutrinos and gamma radiation.

Source of Solar Energy

Hydrogen acts as the main fuel in the Sun.

As hydrogen fuses into helium:

• A small amount of mass disappears.
• This mass is converted into energy.
• The energy eventually reaches the solar surface and is radiated into space.

Fusion of Heavier Elements in Stars

After hydrogen in a star’s core is depleted:

• The core contracts under gravity.
• Its temperature rises.
• Helium fusion may begin.
• Carbon and heavier elements can form.

Fusion can produce increasingly heavy nuclei up to nuclei near the maximum of the binding-energy curve.

Elements much heavier than iron cannot release energy through ordinary fusion because their binding energy per nucleon does not increase further.

Controlled Thermonuclear Fusion in Class 12 Physics Chapter 13 Notes

The purpose of controlled thermonuclear fusion is to produce steady and usable energy from fusion reactions.

The fuel must be heated to temperatures near:

10⁸ K

At these temperatures, the fuel exists as plasma.

Main Challenge

No ordinary material container can directly hold plasma at such a high temperature.

The main challenge is therefore to:

• Heat the plasma
• Confine it
• Maintain sufficient density
• Keep it confined long enough for fusion to occur

Magnetic and other confinement techniques are being developed in different countries, including India.

Successful controlled fusion could provide a very large long-term energy source.

Nuclear Fission and Fusion Comparison

Both processes release energy because the products have greater binding energy per nucleon.

Nuclear Reactions and Conservation Laws

A valid nuclear reaction must conserve:

• Total electric charge
• Total nucleon number
• Total mass-energy
• Total momentum

The number of atoms of each element need not remain unchanged because one element may transform into another.

In ordinary nuclear reactions, mass number and atomic number must balance on both sides.

Mass-Energy Conversion

The number of protons and neutrons may remain conserved while the measured nuclear masses change.

This happens because nuclei on the two sides can have different total binding energies.

The difference appears as:

• Released kinetic energy
• Absorbed energy
• Electromagnetic radiation

Nuclei Formula Notes

Important Terms in Class 12 Physics Chapter 13

Useful Links for Class 12 Physics