Modern Physics is an important part of JEE Main Physics. It includes the dual nature of matter and radiation, atoms, nuclei, radioactivity, and semiconductor-related concepts. Most questions are based on fundamental concepts, formulas, graphs and numerical applications.
1. Dual Nature of Radiation
Light shows both wave nature and particle nature.
The particle nature of light was explained through the photoelectric effect.
Photon
A photon is a packet of electromagnetic energy.
Energy of a photon:
E = hν
Since:
ν = c/λ
Therefore:
E = hc/λ
Where:
E = energy of photon
h = Planck's constant
ν = frequency
c = speed of light
λ = wavelength
Useful relation:
hc ≈ 1240 eV·nm
Therefore:
E(eV) = 1240 / λ(nm)
2. Photoelectric Effect
The emission of electrons from a metal surface when electromagnetic radiation of suitable frequency falls on it is called the photoelectric effect.
The emitted electrons are called photoelectrons.
Important Terms
Work Function (φ):
Minimum energy required to remove an electron from the metal surface.
Threshold Frequency (ν₀):
Minimum frequency required to produce photoelectric emission.
The relation is:
φ = hν₀
Einstein's Photoelectric Equation
The energy of an incident photon is used partly to overcome the work function and the remaining energy appears as the kinetic energy of the emitted electron.
hν = φ + Kmax
Therefore:
Kmax = hν − φ
Also:
Kmax = eV₀
Hence:
eV₀ = hν − φ
Where V₀ is the stopping potential.
Important Observations
Photoelectric emission occurs only when the frequency is greater than the threshold frequency.
Photoelectric current depends mainly on the intensity of incident radiation.
Maximum kinetic energy depends on the frequency of radiation, not its intensity.
Photoelectric emission is practically instantaneous.
Increasing intensity increases the number of emitted photoelectrons.
JEE Main Concept
If the frequency of incident radiation is increased, maximum kinetic energy increases.
If intensity is increased while frequency remains unchanged, photoelectric current increases, but maximum kinetic energy remains unchanged.
3. Matter Waves – de Broglie Hypothesis
According to de Broglie, every moving particle has an associated wave.
The wavelength associated with a particle is called the de Broglie wavelength.
λ = h/p
Since:
p = mv
Therefore:
λ = h/mv
For a particle having kinetic energy K:
λ = h/√(2mK)
For an electron accelerated through potential difference V:
λ = h/√(2meV)
For electrons, a useful relation is:
λ(Å) ≈ 12.27/√V
where V is in volts.
Important Concept
A particle with greater momentum has a smaller de Broglie wavelength.
4. Davisson-Germer Experiment
The Davisson-Germer experiment provided experimental evidence for the wave nature of electrons.
Electrons were scattered from a nickel crystal and diffraction was observed.
This confirmed the de Broglie hypothesis.
5. Atomic Models
Thomson's Atomic Model
According to Thomson:
Atom is a positively charged sphere.
Electrons are embedded inside it.
Total positive and negative charges are equal.
This model could not explain the results of Rutherford's scattering experiment.
6. Rutherford's Nuclear Model
Rutherford's alpha-particle scattering experiment showed that:
Most of the atom is empty space.
Almost all positive charge is concentrated in a tiny central region.
Nearly the entire mass of the atom is concentrated in the nucleus.
Electrons revolve around the nucleus.
Limitation
According to classical electromagnetic theory, an accelerating electron should continuously radiate energy and lose energy. Therefore, it should eventually fall into the nucleus.
This could not explain atomic stability.
7. Bohr's Atomic Model
Bohr proposed the following postulates:
First Postulate
Electrons revolve around the nucleus only in certain permitted orbits called stationary orbits.
Second Postulate
Electrons in stationary orbits do not radiate energy.
Third Postulate
Angular momentum of the electron is quantized:
mvr = nh/2π
where:
n = 1, 2, 3, ...
These are called principal quantum numbers.
8. Radius of Bohr Orbit
For a hydrogen-like atom:
rₙ = a₀ n²/Z
where:
a₀ = 0.529 Å
For hydrogen:
rₙ = 0.529 n² Å
Thus, the radius increases as n².
9. Energy of Electron in Hydrogen Atom
For a hydrogen-like atom:
Eₙ = −13.6 Z²/n² eV
For hydrogen:
Eₙ = −13.6/n² eV
For the ground state:
E₁ = −13.6 eV
For n = 2:
E₂ = −3.4 eV
The negative sign indicates that the electron is bound to the nucleus.
10. Energy Levels and Transitions
When an electron moves from a higher energy level to a lower energy level, energy is emitted as radiation.
The photon energy is:
hν = E₂ − E₁
More generally:
hν = Eᵢ − E_f
where Eᵢ > E_f.
The wavelength is given by:
1/λ = RZ²(1/n₁² − 1/n₂²)
where:
R = Rydberg constant
n₂ > n₁
11. Hydrogen Spectral Series
Important hydrogen spectral series are:
| Series | Final orbit | Region |
|---|---|---|
| Lyman | n = 1 | Ultraviolet |
| Balmer | n = 2 | Visible |
| Paschen | n = 3 | Infrared |
| Brackett | n = 4 | Infrared |
| Pfund | n = 5 | Infrared |
JEE Main Tip
The Balmer series lies in the visible region.
The Lyman series lies in the ultraviolet region.
12. Ionization Energy
Ionization energy is the minimum energy required to remove an electron completely from an atom in its ground state.
For hydrogen:
Ionization energy = 13.6 eV
For a hydrogen-like atom:
Eᵢ = 13.6 Z² eV
13. Atomic Spectra
Atoms emit or absorb radiation at specific wavelengths.
Therefore, atomic spectra are discrete or line spectra.
This happens because electrons can occupy only specific quantized energy levels.
14. Nuclear Physics
The nucleus consists mainly of:
Protons
Neutrons
The number of protons is called the atomic number (Z).
The total number of protons and neutrons is called the mass number (A).
Therefore:
A = Z + N
where N is the number of neutrons.
15. Isotopes, Isobars and Isotones
Isotopes
Atoms having the same atomic number but different mass numbers.
Example:
¹H, ²H, ³H
Isobars
Atoms having the same mass number but different atomic numbers.
Example:
¹⁴C and ¹⁴N
Isotones
Atoms having the same number of neutrons but different atomic numbers.
16. Nuclear Size
The radius of a nucleus is approximately:
R = R₀A¹/³
where:
R₀ ≈ 1.2 fm
Thus, nuclear volume is approximately proportional to the mass number A.
17. Mass Defect
The mass of a nucleus is slightly less than the sum of the masses of its individual nucleons.
This difference is called mass defect.
Δm = mass of separated nucleons − mass of nucleus
The corresponding energy is:
E = Δmc²
This energy is called the binding energy.
18. Binding Energy
Binding energy is the energy required to completely separate a nucleus into its constituent protons and neutrons.
Higher binding energy per nucleon generally indicates greater nuclear stability.
The binding energy per nucleon is:
Binding energy per nucleon = Total binding energy / A
Important Concept
The binding energy per nucleon is relatively high around the iron region.
Nuclear fusion and fission can release energy because the products can have greater binding energy per nucleon.
19. Radioactivity
Radioactivity is the spontaneous disintegration of an unstable nucleus with the emission of radiation.
The major types are:
Alpha (α)
Beta (β)
Gamma (γ)
20. Alpha Decay
An alpha particle is a helium nucleus:
⁴₂He
In alpha decay:
A → A − 4
Z → Z − 2
Therefore, the daughter nucleus has mass number four less and atomic number two less.
21. Beta Decay
In beta-minus decay, a neutron changes into a proton:
n → p + e⁻ + ν̄
Therefore:
A remains unchanged
Z increases by 1
In beta-plus decay:
p → n + e⁺ + ν
Therefore:
A remains unchanged
Z decreases by 1
22. Gamma Decay
Gamma radiation consists of high-energy electromagnetic radiation.
During gamma decay:
A remains unchanged
Z remains unchanged
The nucleus simply loses excess energy.
23. Radioactive Decay Law
The rate of radioactive decay is proportional to the number of undecayed nuclei.
dN/dt = −λN
The number of nuclei remaining after time t is:
N = N₀e⁻λt
where λ is the decay constant.
24. Half-Life
Half-life is the time required for the number of radioactive nuclei to become half of the initial number.
T₁/₂ = 0.693/λ
After n half-lives:
N = N₀/2ⁿ
Important Result
After:
1 half-life → 50% remains
2 half-lives → 25% remains
3 half-lives → 12.5% remains
4 half-lives → 6.25% remains
25. Mean Life
Mean life is:
τ = 1/λ
Relation between mean life and half-life:
T₁/₂ = 0.693τ
26. Nuclear Fission
Nuclear fission is the splitting of a heavy nucleus into two or more lighter nuclei with the release of a large amount of energy.
Example:
Uranium-235 can undergo fission after absorbing a neutron.
Fission can produce additional neutrons, which can cause a chain reaction.
Nuclear Reactor
A nuclear reactor uses a controlled nuclear fission chain reaction to produce energy.
Important components include:
Fuel
Moderator
Control rods
Coolant
27. Nuclear Fusion
Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus and release energy.
Fusion is the primary source of energy in stars.
Fusion requires extremely high temperature and pressure conditions.
28. Fission vs Fusion
| Feature | Fission | Fusion |
|---|---|---|
| Process | Heavy nucleus splits | Light nuclei combine |
| Example | U-235 | Hydrogen isotopes |
| Condition | Neutron-induced reactions possible | Extremely high temperature required |
| Energy | Very large | Very large |
| Natural example | Radioactive/nuclear processes | Stars |
29. Semiconductor Basics
Semiconductors have electrical conductivity between conductors and insulators.
Examples:
Silicon
Germanium
Intrinsic Semiconductor
A pure semiconductor is called an intrinsic semiconductor.
Extrinsic Semiconductor
A semiconductor whose conductivity is increased by adding impurities is called an extrinsic semiconductor.
There are two types:
n-type
p-type
30. n-Type Semiconductor
An n-type semiconductor is obtained by adding a pentavalent impurity such as phosphorus or arsenic to silicon.
The majority charge carriers are electrons.
31. p-Type Semiconductor
A p-type semiconductor is obtained by adding a trivalent impurity such as boron or aluminium.
The majority charge carriers are holes.
32. p-n Junction
A p-n junction is formed by joining p-type and n-type semiconductor regions.
A depletion region develops near the junction.
Forward Bias
In forward bias:
p-side is connected to positive terminal.
n-side is connected to negative terminal.
Depletion region becomes thinner.
Current increases significantly.
Reverse Bias
In reverse bias:
p-side is connected to negative terminal.
n-side is connected to positive terminal.
Depletion region becomes wider.
Only a small reverse current flows under normal conditions.
33. Important Modern Physics Formula Sheet
Photon
E = hν = hc/λ
Photoelectric Effect
hν = φ + Kmax
Kmax = eV₀
φ = hν₀
de Broglie Wavelength
λ = h/p
λ = h/mv
λ = h/√(2mK)
Bohr Model
mvr = nh/2π
rₙ = a₀n²/Z
Eₙ = −13.6Z²/n² eV
Nuclear Physics
A = Z + N
R = R₀A¹/³
E = Δmc²
Radioactivity
N = N₀e⁻λt
T₁/₂ = 0.693/λ
τ = 1/λ
34. Most Important JEE Main Concepts to Revise
Before the examination, pay special attention to:
Einstein's photoelectric equation
Work function and threshold frequency
Stopping potential
de Broglie wavelength
Davisson-Germer experiment
Bohr's postulates
Hydrogen energy levels
Hydrogen spectral series
Ionization energy
Mass defect
Binding energy per nucleon
Radioactive decay law
Half-life and mean life
Alpha, beta and gamma decay
Nuclear fission and fusion
Semiconductor basics
p-n junction
Forward and reverse bias
35. Quick Revision Strategy
For JEE Main preparation, revise Modern Physics in this order:
Photoelectric Effect → de Broglie Waves → Bohr Model → Atomic Spectra → Nuclear Physics → Radioactivity → Fission & Fusion → Semiconductors
After completing the notes, practice concept-based MCQs, numerical problems and previous-year questions from each topic.
Conclusion
Modern Physics combines conceptual understanding with direct formula-based questions. Students should focus on understanding the physical meaning of formulas rather than memorising equations alone. Regular revision of the formula sheet followed by JEE Main-level practice questions can make this section easier to handle during the examination.
