This quantum world/Serious illnesses

Serious illnesses require drastic remedies

Planck

Quantum mechanics began as a desperate measure to get around some spectacular failures of what subsequently came to be known as classical physics.

In 1900 Max Planck discovered a law that perfectly describes the spectrum of a glowing hot object. Planck's radiation formula turned out to be irreconcilable with the physics of his time. (If classical physics were right, you would be blinded by ultraviolet light if you looked at the burner of a stove.) At first, it was just a fit to the data, "a fortuitous guess at an interpolation formula" as Planck himself called it. Only weeks later did it turn out to imply the quantization of energy for the emission of electromagnetic radiation: the energy $E$ of a quantum of radiation is proportional to the frequency $\nu$ of the radiation, the constant of proportionality being Planck's constant $h$:

$E=h\nu$.

We can of course use the angular frequency $\omega =2\pi \nu$ instead of $\nu$. Introducing the reduced Planck constant $\hslash =h/2\pi$, we then have

$E=\hslash \omega$.

Rutherford

In 1911 Ernest Rutherford proposed a model of the atom based on experiments by Geiger and Marsden. Geiger and Marsden had directed a beam of alpha particles at a thin gold foil. Most of the particles passed the foil more or less as expected, but about one in 8000 bounced back as if it had encountered a much heavier object. In Rutherford's own words this was as incredible as if you fired a 15 inch cannon ball at a piece of tissue paper and it came back and hit you. After analysing the data collected by Geiger and Marsden, Rutherford concluded that the diameter of the atomic nucleus (which contains over 99.9% of the atom's mass) was less that 0.01% of the diameter of the entire atom, and he suggested that atomic electrons orbit the nucleus much like planets orbit a star.

The problem of having electrons orbit the nucleus the same way that a planet orbits a star is that classical electromagnetic theory demands that an orbiting electron will radiate away its energy and spiral into the nucleus in about 0.0000000005 of a second. This was the worst quantitative failure in the history of physics, under-predicting the lifetime of hydrogen by at least forty orders of magnitude! (This figure is based on the experimentally established lower bound on the proton's lifetime.)