Dual Nature of Matter
What this domain tests
Dual nature tests the photoelectric effect, Einstein's photoelectric equation, stopping potential and the de Broglie wavelength - the evidence that light and matter each show both wave and particle behaviour.
Core rules
- Photon energy E = hν = hc/λ; the shortcut hc ≈ 1240 eV nm saves time. Momentum p = E/c = h/λ; rest mass is zero.
- Einstein's equation: hν = φ₀ + K_max, where φ₀ = hν₀ is the work function and ν₀ the threshold frequency.
- Stopping potential: eV₀ = K_max, so K_max depends on frequency only, never on intensity.
- Intensity controls the number of photoelectrons, hence the saturation current; there is no emission below ν₀ however intense the beam.
- de Broglie: λ = h/p = h/√(2mK); for an electron accelerated through V, λ = h/√(2meV).
Worked example
Light of 400 nm strikes a metal of work function 2.0 eV. Find K_max and the stopping potential. E = hc/λ = 1240/400 = 3.1 eV. Then K_max = 3.1 − 2.0 = 1.1 eV, so the stopping potential is 1.1 V. The 1240 eV nm shortcut avoids dividing by 1.6×10⁻¹⁹; if you work in SI, keep joules throughout and convert only at the end.
Traps that cost marks
- Claiming brighter light gives faster photoelectrons - it gives more of them.
- Forgetting the cutoff: no emission below the threshold frequency.
- Using λ = h/p with momentum expressed in eV.
- Confusing photon momentum p = h/λ with energy hν.