Photoelectric effect

It was actually Becquerel who first did the obversations, then, after the discovery of electrons by J.J. Thompson, Einstein had successfully explained the photoelectric effect in one of his 3 papers that he published in 1905 (If you are interested, the 3 papers are on Photoelectric effect, Brownian motion and the special theory of relativity.)
The photoelectric effect is simply when you shine different electromagnetic radiation on a metal plate, electrons will be emitted. Electrons are released because as individual photons (a fancier word is "quanta", which we now known as photons) crash into the electron, giving it enough energy to jump from the ground state and everntually escape from the nuclei's positive drag (for more information, see "Bohr's Atom"). Wavelengths and Frequencies certainly do affect the effect that came out.
The photons of the light beam have a characteristic energy given by the wavelength of the light. In the photoemission process, if an electron absorbs the energy of one photon and has more energy than the work function, it is ejected from the material. If the photon energy is too low, however, the electron is unable to escape the surface of the material (As you know, noted in the wave-particle duality, the wavelength of an atom, in this case, photons, do affect the number of electron released according to the intensity of the electromagnetic radiation.
This can be explained by mathematics. Using this equation as our starting point,

Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron.

Algebraically speaking, it will be:

hf=hf0+1/2mvm^2

Quantum Mechanically speaking, it would be:

hf=Ek+work function

where h is planck's constant (6.626*10^-27), Ek is the kinetic energy, and the work function, or minimum energy required to remove an electron from atomic binding. If the photon energy is lower than the work function, no elecrons would possibly be released. Lastly, f0 is the frequency that must be reached in order to let the photoemission to occur.