# This Quantum World/Serious illnesses#Planck

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## 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, aka the UV
catastrophe.) 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 $~\hbar=h/2\pi~$, we then
have

$$E = \hbar\omega$$. This theory is valid at all temperatures and
helpful in explaining radiation by black bodies.

## 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 than 0.01% of the diameter of the
entire atom. He suggested that the atom is spherical in shape and the
atomic electrons orbit the nucleus much like planets orbit a star. He
calculated mass of electron as 1/7000th part of the mass of an alpha
particle. Rutherford\'s atomic model is also called the Nuclear model.

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 0.5×10^-10^ seconds. 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.)

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