Dual Nature of Radiation and Matter Class 12 Notes | CBSE Physics Chapter 11

Dual Nature of Radiation and Matter is Chapter 11 of CBSE Class 12 Physics. This chapter explains the photoelectric effect — the experiment that proved light behaves as particles (photons). You will learn Einstein’s photoelectric equation, the wave-particle duality of matter (de Broglie hypothesis), and the Davisson-Germer experiment.

This chapter carries 4–6 marks. Photoelectric effect numericals, Einstein’s equation, and de Broglie wavelength are most tested.

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Key Concepts

1. Photoelectric Effect

When light of sufficiently high frequency falls on a metal surface, electrons are ejected. These are called photoelectrons.

Key Observations

• Below a certain threshold frequency (ν₀), no electrons are emitted regardless of intensity
• Above ν₀, photoelectrons are emitted instantly (no time lag)
• Kinetic energy of electrons depends on frequency, not intensity
• Number of electrons (photocurrent) depends on intensity

2. Einstein’s Photoelectric Equation

KE_max = hν − φ = hν − hν₀

or: eV₀ = hν − φ

• h = Planck’s constant = 6.63 × 10⁻³⁴ J·s
• ν = frequency of incident light
• φ = hν₀ = work function (minimum energy to eject electron)
• V₀ = stopping potential

3. de Broglie Hypothesis

Every moving particle has a wave associated with it:

λ = h/p = h/(mv)

For an electron accelerated through V volts:

λ = 1.227/√V nm

The Davisson-Germer experiment confirmed matter waves by showing electron diffraction.

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Solved Examples

Example 1

Light of wavelength 400 nm falls on a metal with work function 2 eV. Find the maximum KE and stopping potential.

Answer: E = hc/λ = (6.63 × 10⁻³⁴ × 3 × 10⁸)/(400 × 10⁻⁹) = 4.97 × 10⁻¹⁹ J = 3.1 eV

KE_max = 3.1 − 2 = 1.1 eV. Stopping potential V₀ = 1.1 V.

Example 2

Find the de Broglie wavelength of an electron accelerated through 100 V.

Answer: λ = 1.227/√100 = 1.227/10 = 0.1227 nm

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Important Questions for Board Exams

3-Mark

1. State Einstein’s photoelectric equation and explain each term.
2. What is de Broglie hypothesis? Derive the expression for de Broglie wavelength.

5-Mark

1. Describe the photoelectric effect. State the laws. How does Einstein’s equation explain all observations?

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Quick Revision Points

• Photoelectric effect: light → ejects electrons from metal; needs ν ≥ ν₀
• Einstein: KE_max = hν − φ; V₀ = (hν − φ)/e
• Intensity ↑ → more electrons (photocurrent ↑), NOT more KE
• Frequency ↑ → more KE of electrons
• de Broglie: λ = h/mv = h/p; electron: λ = 1.227/√V nm
• Davisson-Germer: confirmed electron waves by diffraction

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Previous: Ch 10 — Wave Optics
Next: Ch 12 — Atoms