Problems leading up to discovery
1.) "Ultraviolet catastrophe" - Classical theory of radiation predicted that the intensity of light emitted by a black body would increase to infinity as wavelength increased
2.) Wien's law disproved by experiments - maximum intensity of the light of a hot, glowing body disagreed from the prediction of the classical model.
Planck solved both of these problems by proposing that exchanging of light is done in quantized amounts.
E = hν
h is a major building block of Quantum Mechanics and Quantum Field Theory.
Photoelectric effect and Einstein
Process - light strikes a metal and electrons come out. The measured maximum kinetic energy is obtained when a electric field is strong enough to stop all of the electrons.
1.) The kinetic energy of electrons depended only on the color of the light and not on it's intensity. The effect is linear.
2.) The current or number of electrons emitted depends on the intensity of light.
When a photon of energy is absorbed by electrons in a material they are bound by energy Wo. The electron uses the energy to escape an atom and any remaining energy is kinetic.
hν = Ekin + Wo
a retarding potential V can be used to stop electrons in this case Ekin = eV. If you solve for this voltage you get
V = (h/e)ν - (Wo/e)
plotting V as a function of ν gives a line with slope h/e. (goal of experiment).