How did Albert Einstein explain the photoelectric effect?

In 1905, Albert Einstein explained the photoelectric effect by proposing that light is composed of individual particles, or photons, rather than acting solely as a continuous wave. This radical hypothesis resolved inconsistencies that classical physics could not explain, such as why the kinetic energy of ejected electrons depends on the frequency of light rather than its intensity.312

Einstein’s explanation relied on two primary assumptions:
* Light consists of quanta of energy, where the energy of each photon is given by $E=h\nu$ ($h$ is Planck’s constant and $\nu$ is frequency).31
* An atom in a metal absorbs a single photon entirely, using that energy to free an electron.32

The energy required to liberate an electron from a metal surface is known as the work function ($\varphi$ or $\psi$). If the photon's energy exceeds this threshold, the excess is converted into the kinetic energy of the emitted electron, expressed by the equation:
$$E_k=h\nu -\varphi$$
This model correctly predicted that no electrons are emitted below a specific threshold frequency (${\nu }_0=\varphi /h$) and that emission occurs with no detectable time delay.312