Threshold Frequency

Threshold frequency f₀ is the minimum frequency of light below which no photoemission occurs, regardless of intensity.

Defined by the work function: hf₀ = φ ⇒ f₀ = φ/h.

Equivalently, threshold wavelength λ₀ = hc/φ. Below f₀ (or above λ₀): no photoelectrons.

Threshold is metal-specific. Cesium (φ ≈ 2.14 eV) responds to visible red. Copper (φ ≈ 4.7 eV) needs UV.

Above f₀: any non-zero intensity produces photoelectrons instantaneously (no measurable delay even at extremely low intensities — classical theory predicted ~minutes of delay).

Threshold is sharp — there is no 'gradual onset'. It's a step function in classical experiments.

Threshold frequency was a primary mystery for classical physics — solved by Einstein's photon model.