Modern Physics

Planck constant, h, = 6.636 x 10-34 Js

Equation

E = hf

7.2

Equation

Ε = hf = hc/λ

7.3

The Ultraviolet Catastrophe

Max PlanckUseful as the blackbody curve is, there was a serious problem that the energy distribution from a blackbody did not match scientists’ predictions, which were based on the electromagnetic (EM) wave properties of light. The predictions suggested that an ideal black body at thermal equilibrium would emit energy proportional to the frequency squared. So the amount of energy radiated simply gets greater and greater at higher and higher frequencies. The name Ultraviolet Catastrophe was used to describe this failure of theory because UV light has a higher frequency than visible light. Obviously, the total energy output at any frequency is not infinite, a point made by Einstein and others. This would conflict with the law of conservation of energy.

The solution to the contradiction came in 1900. Max Planck, the German physicist we met above, proposed that the electromagnetic energy emitted by a black body could only exist in discrete packets he called quanta, and were later called photons. That would reduce the amount of energy in each EM oscillation and bring the observations in line with theory.  These quantum intervals are whole number multiples of the Planck constant, h, which is equal to 6.636 x 10-34 Js (Joule seconds). Planck stated that the energy of an electromagnetic wave is:

Energy = Planck constant X frequency
E = hf

Where E is the energy of the wave, h is the Planck constant, and f is the frequency. Notice that the energy of a wave is directly proportional to its frequency. Therefore, low frequency radio waves have very low energies, while high frequency gamma rays have very high energies. We can further define the energy as a function of wavelength by combining the Eqn 7.2 with Eqn 6.1:  f = c/λ:

Energy = Planck constant X the speed of light / wavelength
Ε = hf = hc/λ

Planck’s constant value of 6.6 x 10-34 Js is a terribly small number, but that would be expected when referring to energy associated with a single photon. Also, look back to the equation. It is saying that radiation such as a photon has both a frequency and a discrete energy. Waves have frequencies, and particles have discrete energy levels (based on how fast they are moving and how massive they are), so photons have characteristics of both waves and particles. Talk about a split personality!