Quantum Physics (Copy)

A2 Level Physics – Section 22: Quantum Physics (Detailed Notes)

22.1 Energy and Momentum of a Photon

1. Particulate Nature of Electromagnetic Radiation

• EM radiation shows particle-like behaviour in certain phenomena (e.g. photoelectric effect).
• Photon: A quantum (discrete packet) of EM energy.

2. Photon Energy

• E = h·f
  • E = energy of a photon (J)
  • h = Planck constant = 6.63 × 10⁻³⁴ J·s
  • f = frequency of EM wave (Hz)

3. Electronvolt (eV)

• 1 eV = 1.60 × 10⁻¹⁹ J
• Energy gained by an electron when accelerated through 1 V
• Common unit for atomic and quantum processes

4. Photon Momentum

• p = E / c = h·f / c = h / λ
  • p = momentum (kg·m/s)
  • c = speed of light = 3.00 × 10⁸ m/s

22.2 Photoelectric Effect

1. Photoelectric Emission

• When light of sufficient frequency shines on a metal surface, electrons are emitted.
• Electrons emitted = photoelectrons

2. Threshold Frequency and Wavelength

• Threshold frequency (f₀): Minimum frequency needed to eject electrons
  • If f < f₀ → no emission
• Threshold wavelength (λ₀): Corresponds to f₀
  • λ₀ = c / f₀

3. Photon Energy and Work Function (Φ)

• Φ (phi) = minimum energy needed to eject an electron (work function), in joules or eV
• hf = Φ + ½·mv²_max
  • hf = photon energy
  • Φ = work function
  • ½·mv²_max = maximum kinetic energy of photoelectron

4. Effect of Intensity and Frequency

• Kinetic energy of photoelectrons depends on frequency, not intensity
• Photoelectric current is proportional to intensity (more photons = more emitted electrons)

22.3 Wave–Particle Duality

1. Dual Nature of Light

• Photoelectric effect: Evidence for particle nature
• Interference & diffraction: Evidence for wave nature

2. Electron Diffraction

• Electrons diffract and interfere when passed through thin crystal (like light waves)
• Pattern produced = evidence of wave nature of particles

3. de Broglie Wavelength

• λ = h / p = h / (mv)
  • λ = de Broglie wavelength
  • h = Planck constant
  • p = momentum = m·v
• Applies to all matter with momentum

22.4 Energy Levels and Line Spectra

1. Discrete Energy Levels

• Electrons in atoms occupy discrete energy levels
• Cannot have values between levels

2. Emission and Absorption Spectra

• Emission spectrum: Electrons fall from higher to lower levels → emit photons (bright lines on dark background)
• Absorption spectrum: Photons absorbed as electrons move to higher levels → missing lines in continuous spectrum (dark lines on bright background)

3. Transition Equation

• hf = E₁ – E₂
  • f = frequency of emitted/absorbed radiation
  • E₁ = higher energy level
  • E₂ = lower energy level
  • h = Planck constant
• Energy of photon = difference between energy levels