Science · Class 12
Dual Nature of Radiation
Learn Dual Nature of Radiation with notes, examples, and practice questions.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Light and matter show wave-particle duality. Photoelectric effect and de Broglie wavelength connect quantum ideas to Class 12 physics.
Photoelectric Effect
Einstein
K_max = hν − φ = eV₀
Photon energy
E = hν = hc/λ
Momentum
p = h/λ = E/c
de Broglie
Matter wave
λ = h/p = h/(mv)
Electron
λ = 1.22/√V nm (V in volts)
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Photon energy
λ=500nm.
- 1E=hc/λ=1240eV·nm/500nm≈2.48eV
Answer
≈ 2.48 eV
de Broglie
Electron accelerated through 100V.
- 1λ≈1.22/√100=0.122nm
Answer
≈ 0.12 nm
Key Points to Remember
- ✓ Threshold frequency ν₀=φ/h
- ✓ Intensity ∝ photon number
- ✓ Wave-particle complementarity
Exam Tips
- • Use eV·nm shortcut hc≈1240
- • Stopping potential V₀=K_max/e
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Formula Cheat Sheet
Quick reference — NCERT board exam formulas
Photoelectric Effect
- Einstein:K_max = hν − φ = eV₀
- Photon energy:E = hν = hc/λ
- Photon momentum:p = h/λ = E/c
- Threshold:ν₀ = φ/h
de Broglie Waves
- Matter wave:λ = h/p = h/(mv)
- Electron:λ = 1.22/√V nm (V in volts)
- Shortcut:hc ≈ 1240 eV·nm
Practice MCQs — Dual Nature of Radiation
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Photoelectric effect supports: