By the early 20th century experiments were conducted in which light knocked electrons out of metal surfaces. Classical EM theory should have expected as much. After all, an electric fields (one part of light) exert forces on charges (electrons) just as gravity exerts a force on mass. [br][br]Recall that the intensity of light is proportional to the electric field amplitude squared, or [math]I\propto E^2[/math]. The logical expectation, therefore, was that bright light with a large enough intensity has a large enough electric field to produce large enough forces on the charged electrons (q) via [math]\vec{F}=q\vec{E}[/math] to eject them. In short: Bright light = big electric field = big force on electrons = they get knocked out.[br][br]According to this line of reasoning, success of ejecting an electron should not depend on the frequency of the light used, and we should expect the process to take a measurable time to build - like the amplitude of a child on a swing at the park as you begin pushing them. This time delay should be rather pronounced for dim light.[br][br]The problem with the expectations is that they didn't match experiments! Instead, what was found was that light above a certain wavelength had no ability to eject electrons, and when ejection did occur below a threshold wavelength value, the process was nearly instantaneous and independent of intensity of the light source![br][br]This meant that, for instance, light of 400 nm wavelength could constantly and easily eject electrons from some metal - even if it was very dim (low intensity, small E field) - and yet at 500 nm, light sources thousands of times more intense (huge E field) would not eject a single electron no matter how long they waited. Imagine the confusion!

What was found experimentally was that the kinetic energy of the ejected electrons rose with the frequency of the light illuminating the metal. A simple relationship emerged to describe that kinetic energy:[br] [center][math]K_{max}=hf-\phi,[/math][/center]where the equation gives the maximum measured kinetic energy of electrons in terms of two constants h and [math]\phi.[/math] It was clear from experiments that [math]\phi[/math] was dependent on the type of metal (aluminum, magnesium, etc) and that [i]h[/i] was constant regardless of the metal used. The name given to [math]\phi[/math] was the work function.[br][br]This expression is simple. All it implies is that there is incoming energy hf from light. Take away the work that needs to be done to strip an electron out of the material [math]\phi[/math], and what's left over is carried away as the electron's kinetic energy. [br][br]While it was nice to understand how those variables fit the experimental data, what was most troubling was the interpretation. What did 'hf' represent, and why is only the frequency of the light relevant?

In the next section we will see the resolution to both of the problem of the blackbody radiation and the photoelectric effect... and it was one and the same.

[table][tr][td]Metal[/td][td]Work Function (eV)[/td][/tr][tr][td]Aluminum[/td][td]4.2[/td][/tr][tr][td]Calcium[/td][td]2.87[/td][/tr][tr][td]Iron[/td][td]4.7[/td][/tr][tr][td]Lithium[/td][td]2.9[/td][/tr][tr][td]Magnesium[/td][td]3.66[/td][/tr][tr][td]Nickel[/td][td]5.2[/td][/tr][tr][td]Platinum[/td][td]5.5[/td][/tr][tr][td]Tin[/td][td]4.42[/td][/tr][tr][td]Titanium[/td][td]4.33[/td][/tr][/table]