What is de Broglie's hypothesis?

de Broglie proposed that matter (like electrons) also has wave properties. The de Broglie wavelength is λ = h/mv = h/p, where h is Planck's constant, m is mass, and v is velocity.

Tamil Nadu Class 12 Physics — Dual Nature of Radiation and Matter (Samacheer Kalvi)

Q: State Einstein's photoelectric equation.

Einstein's equation: KE_max = hf − φ, where h is Planck's constant, f is the frequency of incident light, φ (= hf₀) is the work function (minimum energy needed to eject an electron), and KE_max is the maximum kinetic energy of emitted electrons.

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Quick Summary

This chapter explores the quantum nature of light (photons) and the wave nature of matter (de Broglie). Weightage: 5–7 marks in TN HSE. The photoelectric effect is a guaranteed 1–2 mark question in NEET; de Broglie wavelength appears in JEE.

Key Concepts and Definitions

Photon: Quantum of electromagnetic radiation with energy E = hf
Work function (φ): Minimum energy needed to eject an electron from a metal surface
Threshold frequency (f₀): Minimum frequency for photoelectric emission; φ = hf₀
Stopping potential (V₀): Minimum retarding potential to stop photoelectrons; eV₀ = KE_max
de Broglie wavelength: Wave associated with a moving particle; λ = h/p

Formulae

Concept	Formula
Photon energy	E = hf = hc/λ
Photon momentum	p = h/λ = E/c
Work function	φ = hf₀
Einstein's equation	KE_max = hf − φ
Stopping potential	eV₀ = KE_max
de Broglie wavelength	λ = h/mv = h/p
For electron accelerated by V	λ = h/√(2meV)

Constants: h = 6.626 × 10⁻³⁴ J·s, e = 1.6 × 10⁻¹⁹ C, m_e = 9.1 × 10⁻³¹ kg

Photoelectric Effect

Experimental Observations

1. Emission starts only above threshold frequency f₀ (depends on metal, not intensity) 2. Kinetic energy of photoelectrons increases with frequency, not intensity 3. Emission is instantaneous 4. Increasing intensity increases number of photoelectrons (not their energy)

Failures of Classical Wave Theory

Wave theory predicted: higher intensity → more KE. Experiment: KE depends on f, not intensity.
Wave theory predicted: time delay for emission. Experiment: instantaneous emission.

Einstein's Explanation (Photon Theory)

Light consists of packets of energy called photons, each with energy E = hf.

Einstein's equation: KE_max = hf − φ

Stopping potential: eV₀ = hf − φ → V₀ = (h/e)f − (φ/e)

This gives a straight line of V₀ vs f with slope h/e — verified by Millikan.

Wave Nature of Matter

de Broglie hypothesis (1924): If light (waves) can behave like particles (photons), then particles can behave like waves.

de Broglie wavelength: λ = h/mv = h/p

For an electron accelerated through potential V: KE = eV = p²/2m → p = √(2meV)

λ = h / √(2meV)

Davisson-Germer Experiment

Confirmed de Broglie hypothesis by observing diffraction of electrons from a nickel crystal — electrons behaved as waves.

Wave-Particle Duality

Light shows wave nature: interference, diffraction, polarisation
Light shows particle nature: photoelectric effect, Compton scattering
Electrons show wave nature: Davisson-Germer experiment
Electrons show particle nature: definite mass, charge, deflection in fields

Heisenberg's Uncertainty Principle: Δx · Δp ≥ h/4π — cannot simultaneously know exact position and momentum.

Important Questions

One Mark

1. What is the work function of a metal? 2. Define stopping potential. 3. Write de Broglie's equation. 4. What is the energy of a photon of wavelength 6000 Å? 5. Why does the photoelectric effect not occur below threshold frequency?

Short Answer (3 marks)

1. Explain the photoelectric effect. State the experimental observations that classical wave theory failed to explain. 2. State Einstein's photoelectric equation and explain each term. 3. Describe the Davisson-Germer experiment and its significance.

Long Answer (5 marks)

1. Explain the photoelectric effect. Discuss Einstein's photon theory and derive the expression for stopping potential as a function of frequency.

Board Exam Tips

"Intensity increased, frequency same — what happens?" → more photoelectrons ejected, KE same
"Frequency increased, intensity same — what happens?" → more KE, same number of photoelectrons
de Broglie wavelength numerical — accelerating potential given, use λ = h/√(2meV)
Units: 1 eV = 1.6 × 10⁻¹⁹ J — always convert to Joules for calculations

Revision Checklist

[ ] State and explain photoelectric effect observations
[ ] Derive/apply Einstein's photoelectric equation
[ ] Find stopping potential from given frequency and work function
[ ] Apply de Broglie wavelength formula
[ ] Describe Davisson-Germer experiment
[ ] Explain wave-particle duality

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Frequently Asked Questions

The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency falls on it. It was explained by Einstein using the concept of photons — light quanta of energy hf.