Dual Nature of Matter
What this domain tests
Dual Nature of Matter tests the photoelectric effect, Einstein's photoelectric equation, stopping potential, de Broglie waves and evidence for wave-particle duality.
Core rules
- Photon energy E = hν = hc/λ; hc = 1240 eV nm is a convenient constant.
- Einstein: hν = φ + K_max, where φ is the work function; K_max = eV_stopping.
- Threshold frequency ν0 = φ/h; below it there is no emission, whatever the intensity.
- Photoelectric emission is instantaneous; intensity controls current, not the maximum energy.
- de Broglie: λ = h/p = h/mv; for electrons accelerated by V, λ ≈ 1.227/√V nm.
Worked example
Light of wavelength 400 nm falls on a metal with work function 2.0 eV. Photon energy = 1240/400 = 3.10 eV. K_max = 3.10 − 2.0 = 1.10 eV, so the stopping potential is 1.10 V. Increasing intensity increases the number of photoelectrons but leaves this stopping potential unchanged.
Traps
- Saying brighter light gives faster photoelectrons; it gives more electrons.
- Forgetting to convert eV to joules, or mixing nm with m.
- Using λ = h/mv with the wrong mass or outside the non-relativistic range.
- Confusing work function with stopping potential.