⚛ CBSE · Class 12 · Physics · Chapter 11

Dual Nature of
Radiation and Matter

Complete chapter resources for CBSE Class 12 Physics — photoelectric effect, de Broglie's hypothesis, Davisson-Germer experiment, key formulas, sample questions, and board exam preparation.

3Topics
5–7Board marks
8Sample questions
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Key Formulas — Chapter 11
  • Photon energy: E = hν = hc/λ
  • Photoelectric eq: KE_max = hν − φ₀
  • Stopping potential: eV₀ = hν − φ₀
  • Threshold freq: ν₀ = φ₀ / h
  • de Broglie λ: λ = h/p = h/mv
  • λ (accelerated e⁻): λ = h/√(2meV)
Chapter Overview

What this chapter covers

Chapter 11 of NCERT Class 12 Physics introduces the revolutionary concept that radiation and matter both exhibit dual nature — behaving as waves in some experiments and as particles in others. The chapter opens with the photoelectric effect, first observed by Hertz and later explained by Einstein, who proposed that light consists of discrete energy quanta called photons. Each photon carries energy E = hν, where h is Planck's constant and ν is frequency. Einstein's photoelectric equation, KEmax = hν − φ₀, explains why photoemission depends on the frequency — not the intensity — of incident light.

The second major theme is de Broglie's matter-wave hypothesis, which proposed that every moving particle — not just light — has an associated wavelength given by λ = h/mv. This bold prediction was experimentally confirmed by the Davisson-Germer experiment, in which electrons scattered by a nickel crystal produced a diffraction pattern, directly proving the wave nature of electrons. The de Broglie wavelength of a charged particle accelerated through potential V is given by λ = h/√(2meV), a formula that appears regularly in board numericals.

Board questions on this chapter span conceptual reasoning (why does intensity not affect stopping potential?), formula-based short answers (find threshold frequency given work function), and multi-step numericals (calculate de Broglie wavelength of an electron with given kinetic energy). A clear understanding of the distinction between particle properties (momentum, kinetic energy) and wave properties (wavelength, frequency) is essential for scoring full marks.

Topics

What's inside Chapter 11

As per NCERT Class 12 Physics (CBSE syllabus)

Topic 1
Photoelectric Effect
Hertz's observation, Lenard's experiments, effect of intensity and frequency on photocurrent and stopping potential, Einstein's photon explanation, work function, threshold frequency, and photoelectric equation KE_max = hν − φ₀.
Topic 2
Wave Nature of Matter — de Broglie Hypothesis
de Broglie's proposal that matter has wave-particle duality, de Broglie wavelength λ = h/p, wavelength of a particle accelerated through potential V, and the Heisenberg uncertainty principle as a consequence.
Topic 3
Davisson-Germer Experiment
Experimental proof of de Broglie's hypothesis using electron diffraction by a nickel crystal. Setup, observation of intensity peak at 50° for 54 V accelerating potential, and calculation confirming λ = 0.167 nm for electrons.
Connections

How this chapter fits in

Useful for setting question difficulty and cross-chapter papers.

Builds on
Ch 8 · Electromagnetic Waves
Wave properties of light, speed of light, photon concept
Ch 2 · Electrostatics
Work done by electric field, kinetic energy of charged particles
Chapter 11 Dual Nature
of Radiation
Leads to
Ch 12 · Atoms
Bohr model uses quantisation derived from de Broglie waves
Ch 13 · Nuclei
Nuclear binding energy and quantum stability of matter
Board Blueprint

Marks & question-type breakdown

Typical pattern based on CBSE Class 12 Physics board papers from the last five years.

Question type Marks Typical count What's usually tested
Assertion-Reason / MCQ 1 1–2 Effect of intensity vs frequency on stopping potential; photon momentum
Very Short Answer 2 1 Define work function, threshold frequency, or de Broglie wavelength
Short Answer / Numerical 3 1 Calculate stopping potential, maximum KE, or de Broglie wavelength
Long Answer / Experiment 5 0–1 Davisson-Germer experiment OR Einstein's photoelectric equation derivation
Total (approximate) 5–7 3–4 Weightage varies across paper sets and years
Sample Questions

8 sample questions — generated by MarksZen AI

Aligned to CBSE Class 12 Physics Chapter 11. Covers all question types across Easy, Medium, and Hard difficulty.

Q1 Easy 1 mark MCQ
The stopping potential for photoelectric emission from a metal surface is independent of: (a) Frequency of incident radiation (b) Nature of the metal surface (c) Intensity of incident radiation (d) Work function of the metal
Q2 Easy 2 marks Short Answer
Define the work function of a metal. If the work function of sodium is 2.3 eV, find its threshold frequency. (h = 6.63 × 10⁻³⁴ J·s, 1 eV = 1.6 × 10⁻¹⁹ J)
Q3 Medium 2 marks Short Answer
Light of frequency 7.0 × 10¹⁴ Hz is incident on a metal surface with work function 2.0 eV. Calculate (i) the maximum kinetic energy of the emitted photoelectrons and (ii) the stopping potential. (h = 6.63 × 10⁻³⁴ J·s)
Q4 Medium 3 marks Short Answer
State de Broglie's hypothesis. Calculate the de Broglie wavelength of an electron accelerated through a potential difference of 100 V. (m_e = 9.1 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C, h = 6.63 × 10⁻³⁴ J·s)
Q5 Medium 3 marks Short Answer
The threshold wavelength for a metal is 400 nm. When light of wavelength 300 nm is incident on it, find the maximum kinetic energy of emitted photoelectrons and the stopping potential. (h = 6.63 × 10⁻³⁴ J·s, c = 3 × 10⁸ m/s)
Q6 Hard 4 marks Word Problem
In a photoelectric experiment, the stopping potential for two different wavelengths of light λ₁ = 200 nm and λ₂ = 300 nm are V₁ = 4.4 V and V₂ = 1.7 V respectively. (i) Find Planck's constant using this data. (ii) Find the work function of the metal. (c = 3 × 10⁸ m/s, e = 1.6 × 10⁻¹⁹ C)
Q7 Hard 5 marks Long Answer
Describe the Davisson-Germer experiment with a labelled diagram. (i) What was the significance of the intensity peak observed at 50° for 54 V accelerating potential? (ii) Verify that the wavelength calculated from de Broglie's formula agrees with the interplanar spacing obtained from the experiment. (m_e = 9.1 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J·s)
Q8 Hard 5 marks Long Answer
State and derive Einstein's photoelectric equation. Using the equation: (i) Explain why the photoelectric effect does not occur below the threshold frequency, regardless of the intensity of light. (ii) A photon of wavelength 250 nm ejects an electron from a metal with maximum velocity 6 × 10⁵ m/s. Find the work function of the metal in eV. (h = 6.63 × 10⁻³⁴ J·s, m_e = 9.1 × 10⁻³¹ kg, c = 3 × 10⁸ m/s)
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Previous Year Questions

From CBSE board examinations

Actual questions from past Class 12 Physics board papers — Dual Nature of Radiation and Matter chapter.

Board 20233 marks
The work function of caesium metal is 2.14 eV. When light of frequency 6 × 10¹⁴ Hz is incident on it, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons, (b) stopping potential, and (c) maximum speed of the emitted photoelectrons? (All India 2023)
Board 20222 marks
Draw a graph showing the variation of stopping potential with the frequency of incident radiation for two metals A and B having work functions φ_A and φ_B (φ_A > φ_B). On the graph, mark the threshold frequency for each metal. (Delhi 2022)
Board 20205 marks
Describe the experimental setup and observations of the Davisson-Germer experiment. How did the results confirm de Broglie's hypothesis of the wave nature of electrons? Show that the de Broglie wavelength of electrons accelerated through 54 V is approximately 0.167 nm. (CBSE 2020)
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FAQ

Questions teachers ask

How many marks does Dual Nature of Radiation and Matter carry in the CBSE Class 12 Physics board exam? +
Typically 5–7 marks across 2–3 questions — one 1-mark assertion-reason or MCQ on the photoelectric effect, one 2-mark short answer on threshold frequency or stopping potential, and one 3–5 mark numerical on de Broglie wavelength or Einstein's photoelectric equation. The chapter has featured in CBSE Class 12 board papers consistently over the last five years.
What is Einstein's photoelectric equation and why is it important for board exams? +
Einstein's photoelectric equation is: KE_max = hν − φ₀, where h is Planck's constant, ν is the frequency of incident light, and φ₀ is the work function of the metal. It explains why emission of photoelectrons depends on frequency rather than intensity of light. Board questions frequently ask students to use this equation to find stopping potential, threshold frequency, or maximum kinetic energy of ejected electrons — making it the single most tested formula in this chapter.
What is de Broglie's hypothesis and how is the wavelength calculated? +
de Broglie proposed that matter, like radiation, has a dual (wave-particle) nature. The de Broglie wavelength of a particle is λ = h/p = h/mv, where h is Planck's constant, p is momentum, m is mass, and v is velocity. For a particle accelerated through potential V, λ = h/√(2meV). Board questions often ask students to calculate the de Broglie wavelength of an electron, proton, or neutron given their kinetic energy or accelerating potential.
What is the difference between stopping potential and threshold frequency? +
Threshold frequency (ν₀) is the minimum frequency of incident light below which no photoelectric emission occurs, regardless of intensity. Stopping potential (V₀) is the minimum retarding potential needed to stop the most energetic photoelectrons, related by eV₀ = hν − φ₀. Board questions commonly ask students to distinguish between these two, or to find one given the other — typically as 2-mark short-answer questions.
How do I generate a custom question paper for Dual Nature of Radiation and Matter using MarksZen? +
Sign up for a free MarksZen account, choose CBSE Class 12 Physics, select Chapter 11 (Dual Nature of Radiation and Matter), set your preferred question-type mix (MCQ, short answer, numerical) and total marks — the AI generates a complete board-aligned paper with answer key in under 2 minutes, ready for PDF export.