The Ultraviolet Catastrophe
Classical physics predicted that an object at any temperature should emit an infinite amount of energy at short wavelengths (ultraviolet light). This was obviously wrong. Max Planck fixed it by assuming that energy is not continuous, but comes in small packets called Quanta.
\[E = hf\]
Worked Examples
Example 1: The Energy of a Photon
Calculate the energy of a photon of blue light (\(f = 7.5 \times 10^{14}\) Hz). Using \(h = 6.626 \times 10^{-34}\) J·s, we find \(E \approx 5 \times 10^{-19}\) Joules. This tiny amount of energy is the fundamental "pixel" of light.
The Bridge to Quantum Mechanics
This was the birth of Quantum Mechanics. Planck didn't want to believe energy was quantized; he thought it was a mathematical trick. But this "trick" is the only way to explain why you don't get a sunburn from a toaster. The fact that energy is discrete (\(E=hf\)) is the first pillar of the quantum world.