| Scientist | Year | Model / Contribution |
|---|
| Newton | 1670 | Corpuscular model — light is a particle. Explained reflection and refraction. |
| Huygens | 1690 | Wave model — light is a mechanical wave. Explained interference, diffraction, polarization. Needed ether medium. |
| Maxwell | 1865 | EM wave — light is a non-mechanical transverse wave. No medium required. EM wave nature. |
| Max Planck | 1901 | Quantum model — light is a particle, E = hf. Explained black body radiation, photoelectric effect, Compton effect. |
| De-Broglie | 1923 | Dual nature — light behaves as ray AND as wave AND as particle. |
| Davisson & Germer | 1927 | Proved electron is a wave (diffraction experiment). |
| G.P. Thomson | — | Nobel prize for experimental verification of e⁻ as a wave. |
2
Photon and its Properties
Properties of Photon
- Charge = 0 (neutral); cannot be deflected by electric or magnetic field
- Rest mass = 0 (massless particle)
- Speed in vacuum: c = 1/√(μ₀ε₀) = 3×10⁸ m/s
- Speed in medium: v = c/μ = c/√(μrεr) = 1/√(με)
- Photon cannot be charged; X-ray is a collection of photons
- Frequency does NOT depend on medium or distance from source; only depends on nature of source
Energy of photon: E = hν = hc/λ = 2×10⁻²⁵/λ(m) J = 12400/λ(Å) eV
h = Planck's constant = 6.63×10⁻³⁴ J·s; 1 eV = 1.6×10⁻¹⁹ J
Momentum of photon: p = mc = E/c = hν/c = h/λ
Power of light beam: P = E/t = nhν/t = nhc/(tλ)
No. of photons per sec: n/t = Pλ/(hc)
Intensity (total energy per sec per unit area): I = nE/(At) = nhν/(At) = nhc/(λAt) = Power/Area
⚡ Key Relationships
- Source remains same (ν = same): I ∝ no. of photons, I ∝ n
- Source is variable (ν changing): I ∝ nν
3
Radiation Pressure and Force
Complete absorptive (σ = 0): P = I/c; Force = IA/c = Power/c
Complete reflective (σ = 1): P = 2I/c; Force = 2IA/c = 2Power/c
Partial (reflection coefficient σ): P = I(1+σ)/c; Force = IA(1+σ)/c
General: P = I[2−σ]/c ; Force = 2IA/c (for σ=1) or IA/c (σ=0)
σ = 0 → no reflection; σ = 1 → complete reflection; σ = 1/2 → 50% reflection
Definition
- Ejection of electrons from metal surface by falling of light of sufficient energy
- Photon (light energy) → Electron (electric energy)
- Instantaneous process: time lag ≈ 10⁻⁹ sec (between falling of photon and ejection of e⁻)
- One photon → one electron (one-to-one interaction)
- Efficiency of photoelectric = no. of electrons / no. of photons = 10⁻³ to 10⁻⁴
- If 1e⁻ is ejected → 1/need photon = 10⁻³ → need 10³ photons per electron
Work Function (φ)
- Minimum energy required to pull an electron from a material
- φ = hν₀ = hc/λ₀ (ν₀ = threshold frequency; λ₀ = threshold wavelength)
- Only depends on nature of metal; unit = eV
- Methods to provide work function energy: Thermionic emission (heat), Field emission (electric field), Secondary emission (collision of e⁻), Photoelectric effect (light)
Einstein's Photoelectric Equation: Ephoton = φ + (KE)max
hν = hν₀ + eV₀ | hc/λ = hc/λ₀ + ½mev²max
KEmax = E − φ = hν − hν₀ = h(ν − ν₀)
Stopping potential V₀: eV₀ = KEmax → V₀ = KEmax/e
Condition for PEE: νlight ≥ ν₀ OR λlight ≤ λ₀
Key Notes on Photoelectric Effect
- Intensity ∝ no. of photons ∝ no. of electrons ejected ∝ photocurrent
- Frequency ∝ energy of photon ∝ KEmax ∝ stopping potential V₀
- Photocurrent depends on INTENSITY (not frequency)
- Stopping potential depends on FREQUENCY (not intensity)
- From V₀ vs ν graph: slope = h/e (gives Planck's constant); y-intercept = −φ/e
- Saturation current = maximum photocurrent (all ejected electrons collected)
| When Intensity ↑ (same ν) | When Frequency ↑ (same I) |
|---|
| More photons → more e⁻ → photocurrent ↑ | Energy of photon ↑ → KEmax ↑ → V₀ ↑ |
| KEmax unchanged (same energy photon) | No. of photons same → photocurrent unchanged |
| Stopping potential unchanged | Saturation current unchanged |
5
Matter Waves — De-Broglie Hypothesis
De-Broglie's Hypothesis
- Every matter has dual nature (both particle and wave)
- De-Broglie wavelength: λ = h/p = h/(mv) = h/√(2mKE) = h/√(2mqV)
- Valid for e⁻, proton, neutron — NOT for photon (formula is derived differently)
- λ ∝ 1/√m (lighter particle → larger wavelength)
- λ ∝ 1/√V (higher accelerating voltage → smaller wavelength)
De-Broglie wavelength: λ = h/p = h/(mv) = h/√(2mKE) = h/√(2mqV)
For electron: λe = 12.27/√V Å (V in volts)
For proton: λp = 0.286/√V Å
For deuteron: λd = 0.202/√V Å
For α-particle: λα = 0.101/√V Å
For gas molecule: λ = h/√(3mkBT)
Relativistic: λ = h√(1−v²/c²)/(m₀v)
For charged particle (charge q, voltage V): λ = h/√(2mqV)
6
Heisenberg's Uncertainty Principle
Δx·Δp ≥ h/(4π) (position-momentum uncertainty)
ΔL·Δθ ≥ h/(4π) (angular momentum-angle uncertainty)
h/(4π) = ℏ/2 where ℏ = h/(2π) = reduced Planck's constant
More precisely we know position → less precisely we know momentum (and vice versa)
Q: Light of λ = 500 nm falls on metal with φ = 1.9 eV. Find KEmax and stopping potential.
E = hc/λ = 12400/500 = 24.8 eV → E = 2.48 eV; KEmax = E − φ = 2.48 − 1.9 = 0.58 eV; V₀ = 0.58 V
Ans: KEmax = 0.58 eV; V₀ = 0.58 V ✓
Q: An electron is accelerated through V = 100 V. Find de-Broglie wavelength.
λe = 12.27/√100 = 12.27/10 = 1.227 Å
Ans: λ = 1.227 Å ✓