Dual Nature of Radiation and Matter Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 11 notes: photoelectric effect, Einstein's photoelectric equation, stopping potential, photons and de Broglie matter waves.
Dual Nature of Radiation and Matter — Class 12 Physics Notes
Chapter Snapshot
Light behaves as a wave (Chapter 10) but also as a stream of particles (photons) — and de Broglie showed that matter has a wave nature too. This chapter covers the photoelectric effect and its laws, Einstein's photoelectric equation, stopping potential, the photon, and de Broglie matter waves.
Board relevance: part of the ~12-mark Dual Nature + Atoms/Nuclei unit. Expect a photoelectric numerical (Kmax, stopping potential, threshold) and a de Broglie wavelength question. The graphs are frequently asked.
Key Concepts & Definitions
Photoelectric effect — the emission of electrons (photoelectrons) from a metal surface when light of sufficiently high frequency falls on it.
Work function (φ₀) — the minimum energy needed to free an electron from the metal surface. Usually in electron-volts (eV); 1 eV = 1.6 × 10⁻¹⁹ J.
Threshold frequency (ν₀) — the minimum frequency that can cause emission:
ν₀ = φ₀/h
Below ν₀, no electrons are emitted no matter how intense or how long the light shines.
Stopping potential (V₀) — the negative plate potential at which the photocurrent falls to zero:
eV₀ = Kmax
Experimental laws of photoelectric emission
1. Emission occurs only if ν ν₀ (a threshold exists) and is instantaneous (~10⁻⁹ s).
2. The number of photoelectrons (photocurrent) ∝ intensity of light.
3. The maximum kinetic energy depends only on the frequency, not on intensity.
4. Stopping potential is independent of intensity but increases with frequency.
Why the wave theory failed: it predicted that any frequency should eventually eject electrons if you wait long enough, and that Kmax should rise with intensity. Both are contradicted by experiment.
Formulas — Einstein's Equation and Photons
Einstein's photoelectric equation (energy conservation for one photon–one electron):
hν = φ₀ + Kmax ⟹ Kmax = hν − φ₀ = h(ν − ν₀)
Combined with eV₀ = Kmax:
eV₀ = hν − φ₀ ⟹ V₀ = (h/e)ν − φ₀/e
Graphs to know:
- V₀ vs ν — a straight line of slope h/e, x-intercept ν₀, y-intercept −φ₀/e. The slope is the same for all metals.
- Photocurrent vs intensity — a straight line through the origin.
- Photocurrent vs collector potential — saturation current rises with intensity; the stopping potential is the same for a given frequency.
Photon properties:
Quantity Formula
Energy E = hν = hc/λ
Momentum p = h/λ = E/c
Rest mass Zero
(h = 6.63 × 10⁻³⁴ J·s; hc ≈ 1240 eV·nm — handy for quick energy calculations.)
Photons are electrically neutral (undeflected by fields), and in a photon–electron collision both energy and momentum are conserved.
de Broglie Matter Waves
Every moving particle has an associated wave:
λ = h/p = h/(mv)
For an electron accelerated through a potential difference V, p = √(2meV), so:
λ = h/√(2meV) ≈ 12.27/√V Å (V in volts)
The wavelength is significant only for very light particles — for everyday objects λ is far too small to detect. Davisson–Germer's electron-diffraction experiment confirmed the wave nature of electrons.
Worked Examples
Example 1 — Threshold: A metal has work function 2 eV. Find its threshold frequency and wavelength.
ν₀ = φ₀/h = (2 × 1.6 × 10⁻¹⁹)/(6.63 × 10⁻³⁴) ≈ 4.8 × 10¹⁴ Hz.
λ₀ = hc/φ₀ = 1240/2 = 620 nm.
Example 2 — Maximum KE: Light of 3 eV energy falls on a metal of work function 2 eV. Find Kmax and the stopping potential.
Kmax = 3 − 2 = 1 eV. Since eV₀ = Kmax, V₀ = 1 V.
Example 3 — Photon energy: Find the energy of a 500 nm photon in eV.
E = 1240/500 = 2.48 eV.
Example 4 — de Broglie: Find the wavelength of an electron accelerated through 100 V.
λ = 12.27/√100 = 12.27/10 = 1.227 Å (1.227 × 10⁻¹⁰ m).
Important Question Patterns
1. Photoelectric numerical (3 marks): Kmax = hν − φ₀; stopping potential; threshold frequency/wavelength; use hc = 1240 eV·nm.
2. Laws & failure of wave theory (2–3 marks): state the experimental laws; explain why classical wave theory cannot account for the threshold or instantaneous emission.
3. Graphs (2–3 marks): V₀ vs ν (slope h/e, same for all metals); photocurrent vs intensity; effect of changing frequency vs intensity.
4. Photon (2 marks): E = hν = hc/λ, p = h/λ; photons are neutral with zero rest mass.
5. de Broglie (2–3 marks): λ = h/mv; λ = 12.27/√V Å for electrons; why matter waves are undetectable for large objects.
⚡ Quick Revision
- Photoelectric effect: electrons ejected only if ν ν₀; emission is instantaneous.
- Work function φ₀ = minimum energy to free an electron; ν₀ = φ₀/h.
- Einstein: hν = φ₀ + Kmax, so Kmax = h(ν − ν₀) and eV₀ = Kmax.
- Intensity controls the number of electrons (photocurrent); frequency controls their maximum KE.
- V₀ vs ν graph: straight line, slope h/e (same for all metals), intercept ν₀.
- Photon: E = hν = hc/λ, p = h/λ, zero rest mass, neutral. hc ≈ 1240 eV·nm.
- de Broglie: λ = h/mv; for an electron through V volts, λ = 12.27/√V Å. Confirmed by Davisson–Germer.
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