Dual Nature of Radiation and Matter — Physics Class 12 Notes (CBSE & HBSE)
Free NCERT Physics notes for Dual Nature of Radiation and Matter (Class 12) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Dual Nature of Radiation and Matter (CBSE & HBSE)
CBSE emphasizes Einstein's photoelectric equation derivation, stopping potential, de Broglie hypothesis, and Davisson-Germer experimental evidence. HBSE focuses on photoelectric effect observations, Einstein's equation, work function, and de Broglie wavelength numericals.
Photoelectric Effect and Einstein's Equation
Photoelectric Effect
When light of sufficient frequency falls on a metal surface, electrons are emitted from the surface. These emitted electrons are called photoelectrons.
Discoverers: Hertz (1887) observed; Hallwachs and Lenard studied; Einstein explained (1905).
Experimental Observations
| Observation | Classical Wave Theory Prediction | Actual Result |
|---|---|---|
| Effect of intensity | Should increase electron energy | Only increases number of electrons |
| Threshold frequency | Should not exist | Exists: below ν₀, no emission |
| Time lag | Should be delay for energy buildup | Instantaneous emission |
| Stopping potential | Should depend on intensity | Depends only on frequency |
Key Terms
| Term | Definition |
|---|---|
| Work function (φ₀) | Minimum energy needed to eject an electron from metal surface |
| Threshold frequency (ν₀) | Minimum frequency of light for photoelectric effect: φ₀ = hν₀ |
| Threshold wavelength (λ₀) | Maximum wavelength: λ₀ = c/ν₀ = hc/φ₀ |
| Stopping potential (V₀) | Minimum retarding potential to stop all photoelectrons |
| Maximum KE | KE_max = eV₀ (where e = electron charge) |
Einstein's Photoelectric Equation
Light consists of photons (quanta of energy):
Energy of photon E = hν = hc/λ
When photon is absorbed by electron:
hν = φ₀ + KE_max = φ₀ + ½mv²_max
hν = hν₀ + eV₀
eV₀ = h(ν − ν₀) → Stopping potential increases linearly with frequency
Slope of V₀ vs ν graph = h/e (gives Planck's constant!)
Effect of Intensity and Frequency
| Parameter | Increase Intensity | Increase Frequency |
|---|---|---|
| Number of photoelectrons | Increases | No change |
| Maximum KE | No change | Increases |
| Stopping potential V₀ | No change | Increases |
| Photoelectric current | Increases | Slight change |
Millikan's Experimental Verification
Millikan (1914-15) measured the V₀ vs ν graph for different metals:
- Confirmed linear relationship
- Measured h = 6.63×10⁻³⁴ J·s (within 0.5% of theoretical value)
- Confirmed Einstein's equation
Diagram Indicator: [Photoelectric setup with light hitting metal cathode, electrons collected at anode; circuit showing stopping potential; graph of stopping potential V₀ vs frequency ν showing straight line with slope h/e and x-intercept at ν₀.]
de Broglie Hypothesis and Matter Waves
Wave-Particle Duality of Light
Light shows:
- Wave nature: Interference, diffraction, polarization
- Particle nature: Photoelectric effect, Compton effect
de Broglie Hypothesis (1924)
Louis de Broglie proposed that matter also has wave nature. Every moving particle has an associated wave called a matter wave or de Broglie wave.
de Broglie wavelength: λ = h/p = h/(mv)
where p = mv = momentum, h = 6.63×10⁻³⁴ J·s (Planck's constant)
de Broglie Wavelength in Various Forms
For particle of KE: λ = h/√(2mKE)
For particle accelerated through voltage V: KE = eV → λ = h/√(2meV)
For electron: λ = 1.226/√V nm (V in volts)
de Broglie Wavelength Table
| Object | Mass/Speed | λ |
|---|---|---|
| Bullet (0.01kg, 300m/s) | — | ~10⁻³⁴ m (negligible) |
| Electron (100V) | — | 0.123 nm |
| Electron (54V) | — | 0.167 nm |
| Proton at same energy | — | ~1836 times smaller than electron |
For macroscopic objects, λ is negligibly small — wave nature undetectable.
Bohr's Angular Momentum Condition
de Broglie's hypothesis provides the physical basis for Bohr's quantization:
Standing wave condition: nλ = 2πr (n complete wavelengths fit in circular orbit)
Substituting λ = h/mv: mvr = nh/(2π) = nℏ ← Bohr's quantization condition!
Heisenberg's Uncertainty Principle
Δx·Δp ≥ ℏ/2 (ℏ = h/2π)
Or: ΔE·Δt ≥ ℏ/2
The more precisely we know position, the less precisely we know momentum, and vice versa.
Diagram Indicator: [Electron in circular Bohr orbit with de Broglie wave shown as standing wave fitting exactly n wavelengths in circumference; also wavelength vs momentum graph showing λ=h/p hyperbola.]
Davisson-Germer Experiment
Davisson-Germer Experiment (1927)
Clinton Davisson and Lester Germer provided experimental confirmation of de Broglie's hypothesis by demonstrating electron diffraction.
Experimental Setup
- Electron gun: Electrons accelerated through voltage V (54V used)
- Nickel crystal target: Acts as diffraction grating (lattice spacing d ≈ 0.091 nm)
- Detector: Faraday cup that can rotate to measure intensity at various angles
Key Observation
At accelerating voltage V = 54V, a strong intensity peak was observed at θ = 50° from the incident beam (φ = 50°).
Verification of de Broglie Hypothesis
de Broglie wavelength at 54V: λ = 1.226/√54 = 1.226/7.35 = 0.167 nm
Bragg's law for diffraction peak: 2d sinφ = nλ
Using d = 0.091 nm, φ = 65° (glancing angle = 90° − 50°/2 = 65°):
2 × 0.091 × sin65° = 2 × 0.091 × 0.906 = 0.165 nm ≈ 0.167 nm ✓
Both values match! — de Broglie wavelength experimentally confirmed.
Significance of Davisson-Germer Experiment
- First direct evidence of electron wave nature
- Confirmed de Broglie's hypothesis quantitatively
- Led to development of electron microscopy (resolution ~0.1 nm)
- Nobel Prize: de Broglie (1929), Davisson (1937)
Electron Microscope
Based on wave nature of electrons:
- Electrons have much shorter λ than visible light
- Resolution ∝ λ → electron microscope has ~1000× better resolution than optical microscope
- Used in materials science, biology, nanotechnology
Wave Nature: Comparison
| Radiation | Wavelength | Best Use |
|---|---|---|
| Visible light | 400-700 nm | Optical microscope |
| X-rays | 0.01-10 nm | Crystal structure |
| Electrons (100 keV) | ~0.004 nm | Electron microscope |
Diagram Indicator: [Davisson-Germer experimental setup: electron gun, nickel crystal, rotating detector, showing diffraction peak at 50°; also comparison of optical vs electron microscope resolution.]
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