Dual Nature of Radiation and Matter
What this domain tests
Dual Nature of Radiation and Matter tests photoelectric effect, photon energy, work function, stopping potential, de Broglie wavelength and matter waves. Numerical questions use electron-volt conversions.
Core rules
- Photon energy E = hf = hc/λ. Useful shortcut: E(eV) ≈ 1240/λ(nm).
- Einstein photoelectric equation: hf = W + K_max, where W is work function. K_max = eV_s, with V_s the stopping potential.
- Threshold frequency f0 = W/h; threshold wavelength λ0 = hc/W. No emission below threshold, regardless of intensity.
- de Broglie wavelength λ = h/p = h/(mv). For an electron accelerated through V volts, λ ≈ 12.27/√V Å.
- Intensity controls number of photoelectrons; frequency controls maximum kinetic energy.
Worked example
Light of wavelength 400 nm falls on a metal of work function 2.0 eV. Find K_max and stopping potential. Photon energy = 1240/400 = 3.1 eV. K_max = 3.1 - 2.0 = 1.1 eV. Since K_max = eV_s, V_s = 1.1 V. The reasoning uses the eV shortcut and keeps energy in electron-volts; converting to joules is unnecessary unless the answer requires it.
Traps
Do not say brighter light gives faster photoelectrons. Do not use λ = h/p for a photon with p = mv; for a photon p = h/λ. The stopping potential is positive in magnitude but stops the most energetic electrons. Work function is a property of the metal surface.