Modern Physics: Atoms, Nuclei, Photoelectric Effect & Semiconductors
Study dual nature of light, photoelectric effect, Bohr model, nuclear physics, radioactivity, semiconductors and logic gates for JEE Main Physics.
The central idea of this chapter
Matter and energy show both particle and wave nature. This chapter connects quantum concepts with atomic structure, nuclear phenomena and semiconductor devices.
What should you understand first?
Modern Physics is highly scoring in JEE Main. Master photoelectric equation, Bohr model formulas and nuclear decay laws. Semiconductors and logic gates are direct formula-based questions.
Core concepts
- Photoelectric effect Kmax = hν − φ
- Bohr model Eₙ = −13.6Z²/n² eV
- De Broglie λ = h/p
- Radioactivity N = N₀e^−λt
- Semiconductors Logic gates
Useful building blocks
- Photon energy E = hν = hc/λ
- Stopping potential eV₀ = Kmax
- Angular momentum mvr = nh/2π
- Half life T₁/₂ = 0.693/λ
- Mass-energy E = mc²
Modern Physics formula sheet
Use consistent units. Apply photoelectric and Bohr formulas with proper constants (h = 6.63×10⁻³⁴ J·s, c = 3×10⁸ m/s).
| Topic | Formula / Relation | Meaning or use |
|---|---|---|
| Photon energy | E = hν = hc/λ | Energy of electromagnetic radiation |
| Photoelectric equation | Kmax = hν − φ = eV₀ | Einstein's photoelectric equation |
| Threshold frequency | ν₀ = φ/h | Minimum frequency for emission |
| De Broglie wavelength | λ = h/p = h/mv | Wave nature of matter |
| Bohr radius | rₙ = 0.529 n²/Z Å | Radius of nth orbit for a hydrogen-like species |
| Bohr energy | Eₙ = −13.6Z²/n² eV | Energy of electron in nth orbit |
| Angular momentum | mvr = nh/2π | Quantization condition |
| Rydberg formula | 1/λ = R(1/n₁² − 1/n₂²), n₂ > n₁ | Wavelength of spectral lines |
| Radioactive decay | N = N₀e^−λt | Number of nuclei at time t |
| Half life | T₁/₂ = 0.693/λ | Time for half nuclei to decay |
| Mean life | τ = 1/λ = T₁/₂/0.693 | Average lifetime of nucleus |
| Mass defect | Δm = Zmp + (A−Z)mn − M | Difference in nuclear mass |
| Binding energy | BE = Δm × 931.5 MeV | Energy equivalent of mass defect |
| Logic gates | AND, OR, NOT, NAND, NOR | Basic digital logic operations |
How to approach Modern Physics problems
First identify topic (photoelectric, Bohr, nuclear, semiconductor), then apply appropriate formula. Use energy conservation and quantization conditions carefully.
Dual nature & atoms
- Photoelectric? Kmax = hν − φ
- De Broglie? λ = h/mv
- Bohr orbit? Eₙ = −13.6Z²/n² eV
- Spectral line? 1/λ = R(1/n₁² − 1/n₂²)
- Transition energy? ΔE = Ef − Ei
Nuclear & semiconductors
- Decay law? N = N₀e^−λt
- Half life? T₁/₂ = 0.693/λ
- Binding energy? BE = Δm × 931.5
- Logic gates? Truth tables
- Diode bias? Forward/Reverse
How to prepare Modern Physics
Start with photoelectric effect and de Broglie hypothesis, then master Bohr model and spectral series. Finish with nuclear physics, radioactivity and basic semiconductor devices.
What to do
- Learn photoelectric equation and stopping potential
- Master Bohr model formulas for hydrogen-like species
- Practise de Broglie wavelength problems
- Understand radioactive decay and half life calculations
- Revise logic gates and semiconductor basics
Common mistakes
- Wrong sign in photoelectric equation (Kmax = hν − φ)
- Confusing n values in Rydberg formula
- Using wrong half life formula (T₁/₂ = 0.693/λ)
- Mixing forward and reverse bias conditions
- Forgetting units conversion (eV to J, Å to m)
Ready to test Modern Physics?
Revise the formula sheet, then solve mixed JEE Main problems on photoelectric effect, Bohr model, nuclear physics and semiconductors.
Modern Physics FAQ
Short answers to frequently tested ideas in this chapter.
Photoelectric effect is the emission of electrons when light falls on a metal surface. Einstein's equation is Kmax = hν − φ where φ is work function.
Bohr model describes electrons in quantized orbits around nucleus. Energy Eₙ = −13.6Z²/n² eV for hydrogen-like species. Angular momentum is quantized as mvr = nh/2π.
De Broglie wavelength relates particle momentum to wavelength as λ = h/p. It shows wave-particle duality of matter.