Planck's Constant

Once radiation was discovered in the late 19th century, a set of prediction were made to veryify the consistancy of the laws of physics as they applied to this new phenomena. According to classical physics, energy was continuous. This meant that you could measure amounts of energy (such as light or heat) as being irrational (say 5 and 2/3 of a joule, which has the decimal 5.66666 where the 6's go on forever). In the classical model of physics, where energy is continuous, the blackbody prediction breaks down as it takes on heat energy and begins to radiate. As it gets hotter and hotter and begins emitting a higher spectrum of frequency (specifically in the ultraviolet range and beyond) classical prediction state that the energy levels in the blackbody should be infinite. This disagreed with measured experiments involving blackbody radiation, in which the result of high frequencies actually yields lower energy levels.

Max Planck, with a bit of luck and number crunching, discovered that if he applied a specific (and very small) constant to the operations of energy, that he could make more reasonable prediction. What was so special about this constant, however, was that it could only be used in whole integer multiples. This meant that energy was, in fact, not continuous, and things like light and heat are delivered in packets of energy, now known as photons. Planck's constant is 6.626 x 10^-34 m^2 kg/s.

Wave-Particle Duality

Wave-particle duality, as it was uncovered, was very hard for some people to accept. It started with light, which was originally thought to be a particle (Newton), then found to be a wave (Young), then a particle again (Einstein). Einstein, throughout the beginning of the 20th century, argued the possibility of light being both a wave and a particle. Even though it was proven in 1915 by Millikan, it wasn't accepted socially until 1923, with the support of Niels Bohr, who called the duality "the principle of complementarity."

In 1924, Einstein said, "There are therefore now two theories of light, both indispensable... without any logical connection."

The connection between these two theories formed the basis of the development of quantum mechanics in the next few hectic years. (Gribbin, 85)

There were other situation going on too, that needed wave-particle duality to explain them. It was de Broglie who suggested that perhaps matter exists as waves too. De Broglie realized two things: first, that the only thing in physics that required whole number integers is interference and normal modes of vibration (wave properties) and second, that electrons could only exist in certain orbits or levels of energy. This whole-integer property of electrons led de Broglie to discover that they too, had wave properties.

De Broglie combined Einstein's two equations for light particles:

E=hv and p=(hv)/c

E is energy, h is Planck's constant, v the frequency of the radiation, p the momentum, and c the speed of light

Since wavelength is found by L = c/v (where L is lambda or wavelength), we can write that:

pL=h

this means that smaller wavelengths have more momentum, because h is a constant, and must remain the same number no matter what values p and L are. Since electrons have a small mass, they are bound to have a small momentum, meaning that they must have an extremely huge wave affect compared to other particles at the time.