Threshold Frequency
KE_max vs f plot — zero below f₀ = φ/h, linear slope h above. Compare 4 metals.
Key Notes
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.
Formulas
Threshold frequency
Set entirely by the material's work function.
Threshold wavelength
Useful shortcut: λ₀[nm] = 1240/φ[eV].
Einstein equation at f₀
Photoelectrons emerge with zero KE.
Important Points
Threshold is INDEPENDENT of intensity. A very dim source above f₀ still emits; a very bright source below f₀ does not.
Different metals have different f₀. The same light may emit from one metal but not from another.
Long-wavelength (red, IR) light has lower energy per photon — explains why most metals need UV.
The existence of a sharp threshold was experimental evidence that classical wave physics could not be the full story.
Useful threshold wavelengths: Cs ≈ 580 nm (yellow), K ≈ 540 nm (green), Na ≈ 540 nm. All alkali metals work with visible light.
λ₀ = 1240/φ is the most efficient calculation shortcut.
Threshold Frequency notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.