MP Board Class 12 Physics Chapter 11: Dual Nature of Radiation and Matter — Notes & Formulas for 2026 Exam

Chapter 11: Dual Nature of Radiation and Matter is one of the most important chapters in the MP Board Class 12 Physics syllabus for the 2026 BOARD YEAR exam. This chapter bridges classical and quantum physics, introducing revolutionary concepts like the photoelectric effect, de Broglie wavelength, and wave-particle duality. Below are comprehensive revision notes, key formulas, and tables for quick reference.

Key Concepts at a Glance

This chapter deals with the dual nature of light — it behaves both as a wave (interference, diffraction) and as a particle (photoelectric effect, Compton effect). The same dual nature applies to matter particles like electrons (de Broglie hypothesis).

1. Photoelectric Effect

When light of sufficient frequency falls on a metal surface, electrons are emitted. Key experimental observations:

  • No electrons are emitted if the incident frequency is below a threshold frequency (f0), regardless of intensity.
  • Kinetic energy of emitted electrons increases linearly with frequency, not intensity.
  • Emission is instantaneous — no time lag.
  • Number of emitted electrons is proportional to intensity of incident light.

Einstein’s Photoelectric Equation

E = hf = phi + K.E.max

Symbol Quantity Unit
E = hf Energy of incident photon eV or J
phi = hf0 Work function of the metal eV or J
K.E.max = eV0 Maximum kinetic energy of photoelectron eV or J
f0 Threshold frequency Hz
lambda0 = c/f0 Threshold wavelength m
V0 Stopping potential V (volt)

Also: K.E.max = eV0 = hf – phi = h(f – f0)

2. Important Formulas

Formula Description
E = hf = hc/lambda Energy of a photon (Planck’s relation)
p = h/lambda Momentum of a photon
K.E.max = hf – phi Einstein’s photoelectric equation
V0 = (h/e)f – phi/e Stopping potential vs frequency (linear)
lambda = h/p = h/mv de Broglie wavelength of a particle
lambda = h / sqrt(2mqV) de Broglie wavelength of accelerated electron
lambda = h / sqrt(2m(K.E.)) de Broglie wavelength from kinetic energy
d = lambda / (2 sin-theta) Davisson-Germer: crystal spacing from diffraction
hf = hf’ + K.E. Compton effect (photon scattering)
delta-lambda = h/(m0c) (1 – cos-phi) Compton shift (lambda’ – lambda)

3. Important Constants

Constant Symbol Value
Planck’s constant h 6.63 x 10^-34 J.s
h 4.14 x 10^-15 eV.s
Speed of light c 3 x 10^8 m/s
Electron charge e 1.6 x 10^-19 C
Electron mass me 9.1 x 10^-31 kg
Compton wavelength h/(m0c) 2.43 x 10^-12 m
1 eV — 1.6 x 10^-19 J

4. Experimental Devices and Discoveries

Experiment Scientist(s) Key Finding
Photoelectric effect Hertz, Hallwachs, Lenard Light ejects electrons from metal
Photoelectric equation Einstein (1905) Light consists of photons; E = hf – phi
Davisson-Germer experiment Davisson and Germer (1927) Electrons show diffraction — proof of wave nature of matter
de Broglie hypothesis Louis de Broglie (1924) Every moving particle has a wavelength lambda = h/p
Compton effect Compton (1923) X-ray photon wavelength increases after scattering

5. Wave-Particle Duality Summary

Phenomenon Nature of Light Explanation
Interference, Diffraction Wave Requires superposition and phase
Photoelectric effect Particle (photon) Energy transfer in discrete quanta
Compton scattering Particle Momentum transfer like billiard balls
Polarisation Wave (transverse) Electric field oscillation direction
Reflection, Refraction Both Explained by both models

6. Quick Revision One-Liners

  • Stopping potential (V0) depends only on frequency, not intensity.
  • Saturation current increases with intensity of incident light.
  • Work function (phi) is the minimum energy needed to eject an electron.
  • Threshold frequency (f0) = phi/h. Below this, no photoelectric emission.
  • Photoelectric effect can NOT be explained by wave theory — validates particle nature.
  • Davisson-Germer experiment confirmed de Broglie’s hypothesis experimentally.
  • de Broglie wavelength of a macroscopic object is negligible.
  • Photon rest mass = 0. Photon always travels at speed c.
  • Momentum of photon p = h/lambda = E/c.
  • Slope of V0 vs f graph = h/e (Planck’s constant / electron charge).

7. Solved Example

Q: The work function of cesium metal is 2.14 eV. Find (a) threshold wavelength, (b) maximum kinetic energy of photoelectrons when light of wavelength 4000 Angstrom is incident, (c) stopping potential.

Solution:

(a) phi = 2.14 eV = 2.14 x 1.6 x 10^-19 = 3.424 x 10^-19 J
lambda0 = hc/phi = (6.63×10^-34 x 3×10^8) / 3.424×10^-19 = 5.81 x 10^-7 m = 5810 Angstrom

(b) E = hc/lambda = (6.63×10^-34 x 3×10^8) / (4000×10^-10) = 4.97 x 10^-19 J = 3.10 eV
K.E.max = E – phi = 3.10 – 2.14 = 0.96 eV

(c) eV0 = K.E.max implies V0 = 0.96 / 1 = 0.96 V

Key Exam Tips for BOARD YEAR 2026

  • Einstein’s photoelectric equation is the MOST frequently asked derivation.
  • Numerical problems from photoelectric effect and de Broglie wavelength are common.
  • Know the definitions of threshold frequency, work function, and stopping potential.
  • Davisson-Germer experiment — diagram + explanation is a popular 5-mark question.
  • de Broglie hypothesis and its experimental verification — must know.
  • Compton effect derivation is usually asked for 2-3 marks.

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