A subject that looked finished
By the end of the 19th century physics was a triumph. Newton's mechanics ran the heavens and the workshop, Maxwell had unified electricity, magnetism and light, and thermodynamics governed every engine. It was fashionable to say the great work was done and only the next decimal place remained.
Lord Kelvin is said to have spoken of just two small clouds on the horizon. One was the failure to detect Earth's motion through the ether — that cloud burst into special relativity. The other was the light given off by hot objects. This track follows that second cloud, and it did not stay small: it opened the whole quantum world of atoms, light and the nucleus.
Everything glows — the blackbody problem
Every object warmer than absolute zero radiates light — this is thermal radiation. A stirred fireplace poker heats from dull red to orange to yellow-white as it gets hotter, shifting its glow across the electromagnetic spectrum. Even you glow, in the infrared.
To study this cleanly, physicists idealize a perfect absorber and emitter called a blackbody — think of a small hole into a hot oven. Its glow depends on temperature alone, not on what it is made of, and as it heats up the peak colour slides to shorter wavelengths (Wien's law).
Wien's law: the peak wavelength moves inversely with temperature — hotter means bluer.
Here is the crisis. Classical physics (the Rayleigh–Jeans calculation, using the equipartition of energy) predicted that the intensity should keep rising without limit at short wavelengths. A warm oven should therefore blast out infinite ultraviolet and X-rays. This obvious nonsense was named the ultraviolet catastrophe — a plain sign that the classical rules were broken.
Planck's lump of energy
In 1900 Max Planck found the fix, almost against his will. Suppose the tiny oscillators in the walls of the blackbody cannot hold just any energy, but only whole-number multiples of a basic packet whose size is set by the frequency f. Energy comes in lumps, not as a smooth stream.
Allowed energies of an oscillator: whole multiples of the quantum hf.
The proportionality constant h is Planck's constant, about 6.63\times10^{-34} J·s — a fantastically small number. That smallness is exactly why the lumpiness is invisible in everyday life, yet it fits the blackbody radiation curve perfectly at every temperature. Planck later called it an act of desperation; it was the first crack of the quantum.
The ladder of matter — a roadmap
From here the track descends into the very small. We will meet light behaving as particles (photons and the photoelectric effect), then matter behaving as waves (de Broglie waves and uncertainty), then the inside of the atom (energy levels and spectra), and finally the nucleus with its radioactivity, fission and fusion.
Keep one theme in mind throughout: on this ladder, energy, light and even matter turn out to be grainy and probabilistic rather than smooth and certain. Everything that follows is the working-out of that single, world-changing idea.