Dual Nature of Radiation and Matter
Dual Nature of Radiation and Matter tests the photon picture, the photoelectric effect and matter waves. Numericals are short, but conceptual questions on intensity versus frequency decide many marks.
Core rules
- Photon energy E = hν = hc/λ, with h = 6.63×10⁻³⁴ J s and c = 3×10⁸ m s⁻¹. A convenient form is E(eV) = 1240/λ(nm).
- 1 eV = 1.6×10⁻¹⁹ J; photon momentum p = h/λ = E/c.
- Einstein's photoelectric equation: hν = φ₀ + K_max, where φ₀ = hν₀ is the work function and ν₀ the threshold frequency.
- Stopping potential: eV₀ = K_max, so V₀ depends on frequency and not on intensity.
- Laws: saturation photocurrent is proportional to intensity; K_max rises linearly with frequency and is independent of intensity; emission is immediate above threshold.
- de Broglie wavelength λ = h/p = h/√(2mK) = h/√(2meV) for an electron accelerated through V volts; numerically λ ≈ 12.27/√V Å.
Worked example
Light of 400 nm falls on a metal of work function 2.0 eV. Find K_max and the stopping potential. Photon energy = 1240/400 = 3.1 eV. Then K_max = 3.1 − 2.0 = 1.1 eV, so the stopping potential is 1.1 V. The reasoning is energy conservation for a single photon, not per unit intensity.
Traps
Saying brighter light gives faster electrons; mixing joules and electron volts; using hc = 1240 eV nm with λ in metres; forgetting that below threshold no emission occurs however intense the light; and assuming the de Broglie wavelength depends on the charge.