Dual Nature of Radiation and Matter
What the exam tests
This domain tests photoelectric effect, photon energy and momentum, Einstein photoelectric equation, stopping potential, threshold frequency, de Broglie wavelength and Davisson-Germer experiment. Numerical questions often use eV and nanometres.
Core rules
- Photon energy E = hν = hc/λ. A useful form is E(eV) = 1240/λ(nm). Photon momentum p = h/λ.
- Work function φ is the minimum energy needed to eject an electron. Threshold frequency ν0 = φ/h.
- Einstein equation: K_max = hν − φ. Stopping potential V0 satisfies eV0 = K_max.
- Intensity changes the number of photoelectrons, not their maximum kinetic energy. Frequency changes K_max.
- de Broglie wavelength λ = h/p = h/√(2mK). For an electron accelerated through V volts, λ ≈ 12.27/√V Å.
- Davisson-Germer electron diffraction confirmed matter waves.
Worked example
Light of wavelength 400 nm falls on a metal of work function 2.0 eV. Photon energy is 1240/400 = 3.1 eV. Maximum kinetic energy is 3.1 − 2.0 = 1.1 eV. The stopping potential is therefore 1.1 V. If the intensity is doubled, the saturation photocurrent doubles, but the stopping potential remains 1.1 V because the photon energy and work function are unchanged.
Traps
Do not mix joules and electron-volts. Work function is a property of the metal surface, not of the light. Maximum kinetic energy depends on frequency, not intensity. The stopping potential is numerically equal to K_max in eV, but the unit is volts. For de Broglie wavelength, use kinetic energy in joules unless using the shortcut formula carefully.