Revision Atoms and Nuclei Class 12
Atoms and Nuclei – Class 12 Physics: Complete Notes, Concepts & Important Formulas
Atoms and Nuclei is an important chapter in CBSE Class 12 Physics and plays a significant role in board examinations as well as competitive exams such as JEE Main. The chapter explains the structure of atoms, Bohr’s atomic model, hydrogen spectrum, nuclear composition, radioactivity, nuclear reactions and nuclear energy.
In this article, we will cover the most important concepts and formulas from Atoms and Nuclei in a simple and exam-oriented manner.
1. Rutherford’s Atomic Model
Ernest Rutherford proposed his atomic model based on the famous alpha-particle scattering experiment.
According to Rutherford:
- An atom contains a very small, positively charged nucleus at its centre.
- Almost the entire mass of the atom is concentrated in the nucleus.
- Electrons revolve around the nucleus.
- Most of the atom is empty space.
However, Rutherford’s model had an important limitation.
According to classical electromagnetic theory, an accelerating charged particle should continuously lose energy in the form of electromagnetic radiation. Therefore, an electron revolving around the nucleus should lose energy and eventually fall into the nucleus.
This meant that Rutherford’s model could not explain the stability of atoms.
It also could not explain the line spectrum of hydrogen.
2. Bohr’s Model of the Hydrogen Atom
Niels Bohr proposed a model that successfully explained the stability of the hydrogen atom and its line spectrum.
Bohr gave three important postulates.
First Postulate – Stationary Orbits
Electrons can revolve around the nucleus only in certain permitted orbits called stationary or stable orbits.
While moving in these orbits, electrons do not radiate energy.
Second Postulate – Quantisation of Angular Momentum
The angular momentum of an electron is quantised:
mvr = nh/2π
where:
- m = mass of electron
- v = velocity of electron
- r = radius of orbit
- n = principal quantum number
- h = Planck’s constant
Here, n = 1, 2, 3, …
These orbits are also called energy levels.
Third Postulate – Emission and Absorption of Energy
An electron emits or absorbs radiation only when it jumps from one energy level to another.
The energy of the emitted or absorbed photon is:
hν = E₂ − E₁
For emission, the electron moves from a higher energy level to a lower energy level.
3. Radius of Bohr Orbit
The radius of the nth orbit of a hydrogen atom is:
rₙ = n²a₀
where a₀ is the Bohr radius.
The value of Bohr radius is:
a₀ = 0.529 Å = 5.29 × 10⁻¹¹ m
For hydrogen-like atoms:
rₙ = (n²/Z)a₀
where Z is the atomic number.
Therefore, the radius increases with n² and decreases with atomic number Z.
4. Energy of Electron in Hydrogen Atom
The energy of an electron in the nth orbit of a hydrogen atom is:
Eₙ = −13.6/n² eV
For hydrogen-like atoms:
Eₙ = −13.6 Z²/n² eV
The negative sign indicates that the electron is bound to the nucleus.
For the ground state:
n = 1
Therefore:
E₁ = −13.6 eV
For n = 2:
E₂ = −3.4 eV
For n = 3:
E₃ = −1.51 eV
As n increases, the energy becomes less negative.
At:
n → ∞
the energy approaches zero. This corresponds to the electron being completely free from the atom.
5. Hydrogen Spectrum
When an electron jumps between different energy levels, electromagnetic radiation is emitted or absorbed.
The wavelength of the emitted radiation is given by the Rydberg formula:
1/λ = R(1/n₁² − 1/n₂²)
where:
- R = Rydberg constant
- n₂ > n₁
- λ = wavelength of radiation
The different spectral series of hydrogen are:
Lyman Series
The electron falls to:
n₁ = 1
It lies in the ultraviolet region.
Balmer Series
The electron falls to:
n₁ = 2
It lies mainly in the visible region.
Paschen Series
The electron falls to:
n₁ = 3
It lies in the infrared region.
Brackett Series
The electron falls to:
n₁ = 4
It lies in the infrared region.
Pfund Series
The electron falls to:
n₁ = 5
It also lies in the infrared region.
Important Exam Point
For a transition from a higher energy level n₂ to a lower energy level n₁:
Energy of photon = E₂ − E₁
and
λ = hc/ΔE
6. Limitations of Bohr’s Model
Although Bohr’s model was successful for hydrogen and hydrogen-like atoms, it had limitations.
It could not satisfactorily explain:
- Spectra of multi-electron atoms
- Fine structure of spectral lines
- Zeeman effect
- Stark effect
- Wave nature of electrons
Modern quantum mechanics provides a more complete description of atomic structure.
7. What is a Nucleus?
The nucleus is the tiny, dense central part of an atom.
It contains:
- Protons – positively charged
- Neutrons – electrically neutral
Protons and neutrons are collectively called nucleons.
The atomic number is represented by Z and represents the number of protons.
The mass number is represented by A:
A = Z + N
where N is the number of neutrons.
Therefore:
N = A − Z
8. Nuclear Size
The radius of a nucleus is approximately:
R = R₀A¹ᐟ³
where:
R₀ ≈ 1.2 × 10⁻¹⁵ m
This tells us that nuclear radius depends on the cube root of the mass number.
Since the volume is proportional to R³:
Volume ∝ A
This is one reason why nuclear density is approximately independent of the mass number.
9. Mass Defect
The mass of a nucleus is slightly less than the combined mass of its individual protons and neutrons.
This difference is called mass defect.
For a nucleus containing Z protons and N neutrons:
Δm = Zmₚ + Nmₙ − M
where M is the actual mass of the nucleus.
This missing mass is converted into energy according to Einstein’s famous equation:
E = mc²
Therefore, the energy equivalent of mass defect is called binding energy.
10. Nuclear Binding Energy
The energy required to completely separate a nucleus into its individual nucleons is called binding energy.
Binding Energy = Δmc²
If mass defect is expressed in atomic mass units (u), then:
Binding Energy = Δm × 931.5 MeV
A nucleus with greater binding energy per nucleon is generally more stable.
The binding energy per nucleon curve is one of the most important concepts in nuclear physics.
It reaches a maximum around the nuclei of iron and nearby elements.
This explains why energy can be released through both:
- Nuclear fusion of light nuclei
- Nuclear fission of heavy nuclei
11. Nuclear Force
The force that holds protons and neutrons together inside the nucleus is called nuclear force.
Important properties of nuclear force include:
- It is extremely strong.
- It is short-range.
- It is approximately charge independent.
- It shows saturation property.
- It is attractive at normal nuclear distances.
Nuclear force is much stronger than the electrostatic repulsion between protons at nuclear distances.
12. Radioactivity
Radioactivity is the spontaneous disintegration of an unstable nucleus accompanied by the emission of radiation.
There are three major types of radioactive radiation:
Alpha Radiation
An alpha particle is essentially a helium nucleus:
⁴₂He
It contains two protons and two neutrons.
Alpha radiation has:
- High ionising power
- Low penetrating power
Beta Radiation
Beta radiation consists of high-speed electrons or positrons.
For beta-minus decay:
n → p + e⁻ + ν̄
where ν̄ is an antineutrino.
Gamma Radiation
Gamma rays are high-energy electromagnetic radiation.
They have:
- Very high penetrating power
- Very low ionising power compared with alpha particles
13. Radioactive Decay Law
The rate of radioactive decay is proportional to the number of undecayed nuclei.
dN/dt = −λN
The decay equation is:
N = N₀e⁻λt
where:
- N₀ = initial number of nuclei
- N = number remaining after time t
- λ = decay constant
The activity of a radioactive sample is:
A = λN
14. Half-Life
The half-life of a radioactive substance is the time required for half of the radioactive nuclei to decay.
It is given by:
T₁/₂ = 0.693/λ
After one half-life:
N = N₀/2
After two half-lives:
N = N₀/4
After three half-lives:
N = N₀/8
Therefore:
N = N₀(1/2)ⁿ
where n is the number of half-lives.
15. Mean Life
Mean life is represented by τ and is given by:
τ = 1/λ
The relationship between mean life and half-life is:
T₁/₂ = 0.693τ
16. Nuclear Fission
Nuclear fission is the process in which a heavy nucleus splits into two or more lighter nuclei with the release of a large amount of energy.
A common example is the fission of uranium-235.
A neutron strikes the uranium nucleus, causing it to become unstable and split.
During the process, additional neutrons are released. These neutrons can cause further fission reactions.
This produces a chain reaction.
Nuclear reactors use controlled chain reactions to produce energy.
17. Nuclear Fusion
Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus, releasing a large amount of energy.
Fusion occurs naturally in stars.
For example, hydrogen nuclei ultimately combine through nuclear processes to form helium.
Fusion requires extremely high temperatures because positively charged nuclei repel each other.
The energy produced by the Sun is ultimately due to nuclear fusion.
18. Fission vs Fusion
| Nuclear Fission | Nuclear Fusion |
|---|---|
| Heavy nucleus splits | Light nuclei combine |
| Used in nuclear reactors | Occurs in stars |
| Requires heavy nuclei | Requires light nuclei |
| Produces large energy | Produces enormous energy |
| Can sustain a chain reaction | Requires extremely high temperature |
19. Important Formulas for Class 12
Students should remember these formulas for board examinations and numerical problems:
Bohr quantisation:
mvr = nh/2π
Bohr radius:
rₙ = n²a₀/Z
Energy of hydrogen-like atom:
Eₙ = −13.6Z²/n² eV
Rydberg formula:
1/λ = R(1/n₁² − 1/n₂²)
Nuclear radius:
R = R₀A¹ᐟ³
Mass number:
A = Z + N
Binding energy:
BE = Δmc²
Radioactive decay:
N = N₀e⁻λt
Activity:
A = λN
Half-life:
T₁/₂ = 0.693/λ
Mean life:
τ = 1/λ
20. Exam Preparation Tips
The chapter Atoms and Nuclei can be highly scoring if the concepts and formulas are properly understood.
Students should focus especially on:
- Bohr’s postulates
- Energy and radius of Bohr’s orbit
- Hydrogen spectral series
- Rydberg formula
- Nuclear size
- Mass defect
- Binding energy and binding energy per nucleon
- Radioactive decay law
- Half-life and mean life
- Nuclear fission and fusion
Numerical questions based on energy levels, wavelength, half-life, decay constant, mass defect and binding energy should be practised thoroughly.
Conclusion
The chapter Atoms and Nuclei connects the microscopic world of atoms with the enormous amount of energy stored inside atomic nuclei. Bohr’s model helps us understand atomic energy levels and hydrogen spectra, while nuclear physics explains radioactivity, nuclear stability, fission, fusion and the origin of nuclear energy.
For CBSE Class 12 Physics, students should not simply memorise the formulas. Understanding the relationship between energy levels, photon emission, mass defect and binding energy makes numerical problems much easier.
A strong command over this chapter can help students score well in board examinations and also provides an important foundation for JEE Main and other competitive examinations.
- For more Class 12 Physics notes, conceptual explanations, numerical practice and exam-oriented preparation, stay connected with Sanchay Coaching Centre.
