■ Quantum Physics – Detailed Short Notes
1. Wave–Particle Duality
Light and matter exhibit both wave and particle properties, known as wave-particle duality.
de Broglie hypothesized that all matter has wave properties, especially microscopic particles like electrons, protons,
and neutrons.
de Broglie wavelength formula: λ = h/p = h/mv
Electron diffraction experiments confirm that matter exhibits wave nature.
Important: Wave behavior is prominent only for very small particles.
2. Photoelectric Effect
Emission of electrons from a metal surface when light of frequency f ≥ threshold frequency f■ strikes it.
Einstein's Photoelectric Equation: hf = φ + ½ mv²_max
Where φ = work function, hf = photon energy, ½ mv² = kinetic energy of emitted electron.
Key Points:
• Threshold frequency f■ = φ/h
• Increasing light intensity increases number of electrons but not their energy
• Explained why classical wave theory of light failed to describe photoelectric effect
Applications: Photodiodes, Solar cells, Light sensors
3. Bohr’s Atomic Model
Electrons move in quantized circular orbits around the nucleus without radiating energy.
Quantization of angular momentum: mvr = n(h/2π), n=1,2,3...
Energy levels: E_n = -13.6/n² eV
Bohr model explains hydrogen atomic spectrum (Lyman, Balmer, Paschen series).
Limitations: Works accurately only for hydrogen-like atoms.
Important: Introduced concept of quantization preventing electron collapse into nucleus.
4. Schrödinger Wave Equation
Time-independent Schrödinger equation: -h²/2m d²ψ/dx² + Vψ = Eψ
ψ²(x) gives probability density of finding the particle at position x.
Quantum numbers: n (principal), l (azimuthal), m_l (magnetic), m_s (spin)
Wavefunction describes probabilistic nature of particles at microscopic scale.
Applications: Atomic orbitals, Hydrogen atom solutions, Quantum wells
5. Heisenberg’s Uncertainty Principle
Position (x) and momentum (p) cannot be measured simultaneously with arbitrary precision.
∆x · ∆p ≥ h / 4π
Applies to all microscopic particles (electrons, protons).
Significance: Shows the limitation of classical physics at atomic scale.
1. Wave–Particle Duality
Light and matter exhibit both wave and particle properties, known as wave-particle duality.
de Broglie hypothesized that all matter has wave properties, especially microscopic particles like electrons, protons,
and neutrons.
de Broglie wavelength formula: λ = h/p = h/mv
Electron diffraction experiments confirm that matter exhibits wave nature.
Important: Wave behavior is prominent only for very small particles.
2. Photoelectric Effect
Emission of electrons from a metal surface when light of frequency f ≥ threshold frequency f■ strikes it.
Einstein's Photoelectric Equation: hf = φ + ½ mv²_max
Where φ = work function, hf = photon energy, ½ mv² = kinetic energy of emitted electron.
Key Points:
• Threshold frequency f■ = φ/h
• Increasing light intensity increases number of electrons but not their energy
• Explained why classical wave theory of light failed to describe photoelectric effect
Applications: Photodiodes, Solar cells, Light sensors
3. Bohr’s Atomic Model
Electrons move in quantized circular orbits around the nucleus without radiating energy.
Quantization of angular momentum: mvr = n(h/2π), n=1,2,3...
Energy levels: E_n = -13.6/n² eV
Bohr model explains hydrogen atomic spectrum (Lyman, Balmer, Paschen series).
Limitations: Works accurately only for hydrogen-like atoms.
Important: Introduced concept of quantization preventing electron collapse into nucleus.
4. Schrödinger Wave Equation
Time-independent Schrödinger equation: -h²/2m d²ψ/dx² + Vψ = Eψ
ψ²(x) gives probability density of finding the particle at position x.
Quantum numbers: n (principal), l (azimuthal), m_l (magnetic), m_s (spin)
Wavefunction describes probabilistic nature of particles at microscopic scale.
Applications: Atomic orbitals, Hydrogen atom solutions, Quantum wells
5. Heisenberg’s Uncertainty Principle
Position (x) and momentum (p) cannot be measured simultaneously with arbitrary precision.
∆x · ∆p ≥ h / 4π
Applies to all microscopic particles (electrons, protons).
Significance: Shows the limitation of classical physics at atomic scale.
