The photoelectric equation: $hf = φ + E_k(max)$

The Photoelectric Effect — AQA A-Level Physics

A photonA quantum (discrete packet) of electromagnetic radiation. Its energy is proportional to its frequency. above the threshold frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz).The minimum frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). of incident radiation required to cause photoelectric emission from a particular metal surface. has energyThe capacity to do work. Measured in joules (J). $hf$.
An amount $\phi$ is used to free the electron from the metal surface.
The remaining energyThe capacity to do work. Measured in joules (J). becomes kinetic energyThe capacity to do work. Measured in joules (J).The energy an object possesses due to its motion. of the photoelectron.

hf = \phi + E_{k(\max)}

$h$: Planck's constant (J s)
$f$: frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). of incident radiation (Hz)
$φ$: work functionThe minimum energy required to liberate an electron from the surface of a metal. of the metal (J)
$E_k(max)$: maximum kinetic energyThe energy an object possesses due to its motion. of emitted photoelectrons (J)

At the threshold frequencyThe minimum frequency of incident radiation required to cause photoelectric emission from a particular metal surface.: $hf_0 = \phi$ and $E_{k(\max)} = 0$. Emission only just occurs.
$E_{k(\max)}$ depends only on the frequency of the incident photons and the work functionThe minimum energy required to liberate an electron from the surface of a metal. — not on intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared..
Most photoelectrons have kinetic energyThe energy an object possesses due to its motion. less than $E_{k(\max)}$ because deeper electrons lose energy reaching the surface.

Common Mistake MEDIUM

Students often: Mixing units: using eV for work function but joules for hf in the same equation.
Instead: All terms in the photoelectric equation must be in the same units. Convert everything to joules (multiply eV by 1.60 × 10⁻¹⁹) before substituting.