Dual Nature of Radiation and Matter
What is examined
Dual Nature of Radiation and Matter tests the photon picture, the photoelectric effect, Einstein's equation, stopping potential and de Broglie wavelength.
Core rules
- Photon energy E = hν = hc/λ; momentum p = h/λ. Useful value: hc = 1240 eV nm.
- Work function φ = hν₀ = hc/λ₀, the minimum energy needed to eject an electron; below the threshold frequency there is no emission at any intensity.
- Einstein: K_max = hν − φ = eV₀, where V₀ is the stopping potential.
- Photoelectric laws: K_max depends on frequency, not intensity; saturation current is proportional to intensity; emission is instantaneous.
- The stopping potential is independent of intensity but rises linearly with frequency; a graph of V₀ against ν has slope h/e and intercept −φ/e.
- de Broglie: λ = h/p = h/(mv) = h/√(2mK) for a particle of kinetic energy K.
- Davisson–Germer electron diffraction confirmed matter waves.
Worked example
Light of 400 nm falls on a metal with φ = 2.0 eV. Find K_max and V₀. E = 1240/400 = 3.1 eV. K_max = 3.1 − 2.0 = 1.1 eV. V₀ = 1.1 V. Reasoning: compute the photon energy first; subtract the work function only once; K_max in eV equals V₀ in volts.
Traps
Increasing intensity to increase K_max; using λ in nm without converting in hc/λ; mixing eV and J; and using the proton mass for an electron in de Broglie calculations.