Photoelectric effect definition: Emission of electrons from a metal surface when light of frequency ≥ ν_{0} strikes it. Discovered by Hertz (1887); explained by Einstein (1905).

Einstein's equation: KE_max = hν − φ. Each photon of energy hν gives all its energy to one electron; φ is the work function (minimum escape energy).

Work function (φ): Metal-specific minimum energy for electron emission. φ = hν_{0}. Typical values: 2–5 eV for metals. Lower φ = easier emission.

Threshold frequency (ν_{0}): Minimum frequency for emission. ν_{0} = φ/h. Below ν_{0} — no emission ever, regardless of intensity.

Threshold wavelength (λ_{0}): Maximum wavelength for emission. λ_{0} = hc/φ = 1240/φ(eV) nm. Above λ_{0} — no emission.

Stopping potential ($V_{0}$): Retarding voltage that stops all photoelectrons. e$V_{0}$ = KE_max = hν − φ. In numbers: $V_{0}$ (in volts) = KE_max (in eV). Depends ONLY on frequency.

Intensity rule: Intensity controls photocurrent (number of photoelectrons per second), NOT KE_max or $V_{0}$. Doubling intensity doubles saturation current; $V_{0}$ is unchanged.

Graph 1 — KE vs ν: Straight line; slope = h (universal); x-intercept = ν_{0} (metal-specific); y-intercept = −φ.

Graph 2 — $V_{0}$ vs ν: Straight line; slope = h/e (universal); x-intercept = ν_{0}. Parallel lines for different metals (same slope, different intercepts).

Photon properties: E = hν = hc/λ; p = h/λ; m_{0} = 0; speed = c always. Practical: E(eV) = 1240/λ(nm).

de Broglie relation: λ = h/p = h/(mv). Every moving particle has associated wavelength. Heavier or faster → shorter λ.

Electron through V volts: λ = h/√(2m_e eV) = 1.227/√V nm. This shortcut ONLY works for electrons.

Mass comparison at same V: λ ∝ 1/√m (for same charge). λ_e/λ_p ≈ 43; λ_e/λ_α ≈ 121.

Davisson-Germer (1927): Electron diffraction from Ni crystal at 54 V, 50° — confirmed wave nature of matter experimentally.

hc = 1240 eV·nm: The single most useful numerical shortcut in this chapter. Memorise it.