Unit 8

Modern Physics

Class 11 Physics

Chapter 24

Nuclear Physics

Class 11 Physics – Nuclear Physics Notes PDF

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Chapter Overview

Nuclear physics studies the atomic nucleus, its mass, size, binding, stability and the energy released when nuclei are transformed. This chapter begins with Rutherford’s discovery of the nucleus and proceeds through nuclear density, isotopes, Einstein’s mass–energy relation, mass defect, binding energy, creation and annihilation, and nuclear fission and fusion.

Microscopic Scale

The nucleus is extremely small compared with the atom but contains nearly all of its mass.

Energy Scale

Nuclear energy changes are commonly expressed in electron-volts, especially MeV, because tiny mass changes correspond to large energies.

24.1 Discovery of the Nucleus

Rutherford’s Alpha-Particle Scattering Experiment

Rutherford, Geiger and Marsden directed alpha particles at a very thin gold foil and observed where the particles struck a fluorescent screen.

Most alpha particles passed almost straight through.
Some were deflected through small angles.
A very small fraction suffered large-angle deflection or were scattered backward.

Rutherford concluded that the atom is mostly empty space and that almost all positive charge and mass are concentrated in a tiny central nucleus.

Diagram 1 — Rutherford Scattering Experiment

Large-angle scattering is possible only if positive charge and most atomic mass are concentrated in a tiny nucleus.

24.2 Nuclear Size, Atomic Number, Mass Number and Nuclear Density

Atomic Number and Mass Number

The atomic number Z is the number of protons in the nucleus. The mass number A is the total number of nucleons:

A = Z + N

where N is the neutron number. A nuclide is written as:

^A_ZX

Nuclear Radius

An empirical relation for nuclear radius is:

R = R₀A^1/3, where R₀ ≈ 1.2 × 10⁻¹⁵ m

Nuclear Density

Approximating the nucleus as a sphere:

ρ = nuclear mass / nuclear volume ≈ (Am_n)/[(4/3)πR³]

Since R³ = R₀³A, the factor A cancels:

ρ ≈ 3m_n / (4πR₀³)

Thus nuclear density is approximately independent of mass number and is of order 10¹⁷ kg m⁻³.

Diagram 2 — Nuclide Notation and Nuclear Radius

Mass number counts all nucleons; nuclear radius grows approximately as the cube root of A.

24.3 Atomic Mass and Isotopes

Isotopes are nuclei of the same element with the same atomic number Z but different neutron numbers and therefore different mass numbers A.

Example: hydrogen has protium ¹H, deuterium ²H and tritium ³H.

Nuclide	Protons	Neutrons	Mass number
¹H	1	0	1
²H	1	1	2
³H	1	2	3

Diagram 3 — Isotopes of Hydrogen

Isotopes have the same proton number but different neutron numbers.

24.4 Einstein’s Mass–Energy Relation

Einstein showed that mass is a form of energy. A mass change Δm corresponds to an energy change:

E = mc² and ΔE = Δm c²

Because c² is extremely large, a small mass difference can correspond to a large nuclear energy.

1 u × c² ≈ 931.5 MeV

Exam tip: For nuclear calculations, converting atomic mass units directly with 1 u c² = 931.5 MeV is often faster than converting through kilograms and joules.

24.5 Mass Defect, Packing Fraction and Binding Energy

Mass Defect

The measured mass of a bound nucleus is less than the sum of the masses of its separated nucleons. The difference is called mass defect.

Δm = Zm_p + Nm_n − M_nucleus

If atomic masses are used consistently, an equivalent expression can be written using hydrogen-atom mass and the atomic mass of the nuclide.

Binding Energy

The energy required to separate a nucleus completely into free nucleons is its binding energy:

B = Δm c²

Binding energy per nucleon is:

B/A

A larger binding energy per nucleon generally means a more tightly bound nucleus.

Packing Fraction

One traditional measure of mass deviation from an integer mass number is the packing fraction:

Packing fraction = [(M − A)/A] × 10⁴

where M is the isotopic mass in atomic mass units and A is the mass number.

Diagram 4 — Binding Energy per Nucleon Curve

The curve rises sharply for light nuclei, peaks around medium-mass nuclei, then decreases slowly for very heavy nuclei.

24.6 Creation and Annihilation

In high-energy processes, energy can be converted into particle mass and particle mass can be converted into other forms of energy, subject to conservation laws.

Pair Creation

A sufficiently energetic photon can produce a particle–antiparticle pair in the presence of another body that can conserve momentum:

γ → e⁻ + e⁺ (in the field of a nucleus)

The minimum photon energy for electron–positron pair creation is slightly above 2m_ec², with momentum conservation also required.

Annihilation

e⁻ + e⁺ → γ + γ

Diagram 5 — Pair Creation and Annihilation

Creation converts radiation energy into particle rest mass; annihilation converts particle–antiparticle energy into other particles such as photons.

24.7 Nuclear Fission and Fusion

Nuclear Fission

Fission is the splitting of a heavy nucleus into two medium-mass fragments, usually with neutrons and energy released. A typical schematic reaction is:

²³⁵U + n → fission fragments + neutrons + energy

The emitted neutrons can trigger further fissions, producing a chain reaction.

Diagram 6 — Nuclear Fission Chain Reaction

A self-sustaining chain reaction is possible when enough released neutrons cause further fission events.

Nuclear Fusion

Fusion is the joining of light nuclei to form a heavier nucleus with energy release. Fusion powers stars. A commonly cited reaction is:

²H + ³H → ⁴He + n + 17.6 MeV

Fusion requires extremely high temperature because positively charged nuclei must approach closely enough for the strong nuclear force to bind them.

Diagram 7 — Fusion of Light Nuclei

Fusion of light nuclei moves them toward greater binding energy per nucleon, releasing energy.

Feature	Fission	Fusion
Process	Heavy nucleus splits	Light nuclei combine
Typical environment	Reactors / fission weapons	Stars / experimental fusion systems
Trigger	Often neutron absorption	Very high temperature and confinement
Energy source	Increase in binding energy per nucleon of products	Increase in binding energy per nucleon of product

Solved Numerical Examples

Example 1 — Nuclear Radius

Question: Estimate the radius of a nucleus with A = 125, using R₀ = 1.2 fm.

R = R₀A¹ᐟ³ = 1.2 × 125¹ᐟ³ fm = 1.2 × 5 = 6.0 fm

Answer: 6.0 × 10⁻¹⁵ m.

Example 2 — Mass–Energy Conversion

Question: What energy corresponds to a mass defect of 0.020 u?

E = 0.020 × 931.5 MeV ≈ 18.63 MeV

Answer: approximately 18.6 MeV.

Example 3 — Binding Energy per Nucleon

Question: A nucleus has total binding energy 224 MeV and A = 28. Find B/A.

B/A = 224/28 = 8.0 MeV per nucleon

Answer: 8.0 MeV per nucleon.

Example 4 — Nuclear Density

Question: Explain why nuclear density is approximately constant.

ρ ∝ A/R³, and R³ ∝ A ⇒ ρ ≈ constant

Answer: The mass number factor cancels because nuclear volume is proportional to A.

Important Exam Questions

Short-Answer Questions

Describe Rutherford’s observations and conclusions about the nucleus.
Define atomic number, mass number and neutron number.
State the empirical relation for nuclear radius.
Why is nuclear density approximately independent of A?
Define isotopes with examples.
State Einstein’s mass–energy relation.
Define mass defect and binding energy.
What is binding energy per nucleon and what does it indicate?
Define packing fraction.
Explain pair creation and annihilation.
Differentiate nuclear fission and fusion.
Why can both fission of heavy nuclei and fusion of light nuclei release energy?

Long-Answer / Derivation Questions

Explain Rutherford’s alpha-scattering experiment with a labelled diagram.
Using R = R₀A¹ᐟ³, show that nuclear density is approximately constant.
Explain mass defect and derive the expression for nuclear binding energy.
Sketch and explain the binding-energy-per-nucleon curve.
Explain nuclear fission and chain reaction with a diagram.
Explain nuclear fusion and the origin of the released energy.

Numerical Questions

Calculate nuclear radius for A = 64 using R₀ = 1.2 fm.
A nucleus has mass defect 0.030 u. Find its binding energy in MeV.
A nucleus of A = 16 has binding energy 127.6 MeV. Find binding energy per nucleon.
Calculate the energy equivalent of 1.0 × 10⁻³ kg using E = mc².

Diagram Questions

Rutherford scattering experiment.
Nuclide notation and nuclear radius.
Isotopes of hydrogen.
Binding-energy-per-nucleon curve.
Pair creation and annihilation.
Fission chain reaction.
Fusion of light nuclei.

One-Minute Revision

Rutherford scattering showed that atoms contain tiny dense positively charged nuclei.
A = Z + N.
Nuclear radius follows R = R₀A¹ᐟ³.
Nuclear density is approximately constant and of order 10¹⁷ kg m⁻³.
Isotopes have the same Z but different N and A.
Einstein’s relation is E = mc².
1 u c² ≈ 931.5 MeV.
Mass defect is the difference between separated-nucleon mass and bound nuclear mass.
Binding energy is B = Δmc².
B/A measures average binding per nucleon.
Medium-mass nuclei have comparatively high B/A.
Pair creation converts energy to particle–antiparticle mass.
Annihilation converts particle–antiparticle energy into other particles.
Fission splits heavy nuclei and can form a chain reaction.
Fusion combines light nuclei and powers stars.

Diagram Practice

Draw the Rutherford scattering apparatus and three representative alpha paths.
Draw nuclide notation and identify A and Z.
Draw the three hydrogen isotopes.
Sketch B/A versus A and mark the medium-mass maximum.
Draw pair creation and annihilation.
Draw a simplified fission chain reaction.
Draw deuterium–tritium fusion.

Syllabus Coverage Checklist

NEB/CDC Chapter 24 scope	Covered
24.1 Nucleus: discovery of nucleus	Yes
24.2 Nuclear density; mass number; atomic number	Yes
24.3 Atomic mass; isotopes	Yes
24.4 Einstein’s mass–energy relation	Yes
24.5 Mass defect, packing fraction, binding energy per nucleon	Yes
24.6 Creation and annihilation	Yes
24.7 Nuclear fission and fusion; energy released	Yes
Binding-energy-per-nucleon graph and numerical problems	Yes

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