Fermi's Paper on Ideal Gases
From "Atomi in Famiglia" di Laura Fermi:
Fermi was teaching mechanics and mathematics in Florence, as incaricato,
a position carrying no tenure or pension privileges.
There were no other vacant chairs in mathematical physics, and Fermi
stayed in Florence. In 1926, when Corbino thought of calling him to Rome,
Fermi was still available for a permanent position. He had also better
claims to one, for in the year gone by his reputation had grown. He had
published a statistical theory "On the Quantization
of a Perfect Monoatomic Gas," a work that found its place among
the most representative in the evolution of theoretical physics.
For a few years Fermi had been interested in statistical questions,
the behavior of molecules, atoms, and electrons; the energy distribution
in radiation emission. He had given much thought to the behavior of a perfect,
hypothetical gas. The precise law which such a gas obeys had baffled him
for some time. Some factor that would bring full comprehension was missing,
and he could not figure out what it was.
Scientific problems seldom stand alone, but their solutions often interlock
with one another. For over ten years theoretical studies had been directed
to a full description of the atom and of the atomic laws that would bring
order and understanding to the confused stockpile of experimental data.
It was a boom period for atomic physics; and new theories, new principles,
and viewpoints shedding new lights on old concepts were worked out and
published in rapid succession.
In 1925 the Austrian-born physicist, Wolfgang Pauli, while studying
the energies of the atomic electrons rotating around the nucleus, discovered
his principle of exclusion, which, without the accuracy of scientific language,
reads: On each of the orbits around a nucleus there can be only one electron.
At once Fermi this principle to a perfect gas.
In those days Fermi had much time for speculation. The physics
laboratories of the University of Florence were in Arcetri, on the famous
hill where Galileo had made his home during his last years and where he
had died. While teaching at the University of Florence Fermi Iived in
Arcetri. Led by his friend Rasetti, he spent long hours chasing
geckos, small lizards, perfectly harmless despite popular belief that
they house evil spirits in their bodies. Fermi and Rasetti were going to
let their captured geckos loose in the dining hall for the simple pleasure
of scaring the peasant girls who waited on tables.
The two friends lay for hours stretched on their stomachs in the grass,
in perfect stillness, each holding a long glass rod with a brief silk lasso
at its end. During the patient vigil Rasetti observed the small world under
his eyes: a tender blade of growing grass, a busy ant scurrying by with
a bit of straw in its mouth, the play of a ray of light on his grass rod.
Fermi, who is no naturalist was not interested in that small world. While
he watched the ground, ready to pull his lasso should a gecko appear, he
let his mind wander. His subconscious worked on Pauli's principle
and on the theory of a perfect gas. From subconscious depths came the missing
factor Fermi had long sought: no two atoms of a gas can move with exactly
the same velocity or, as physicists say, there can be only on atom in each
of the quantum states possible for the atoms of a perfect monoatomic gas.
This principle permitted Fermi to work out a complete calculation of the
gas behavior, known as "Fermi's statistics."
This, in its turn, was later used both by Fermi and by other physicists
to explain a number of phenomena, including the thermal and electric conductivity
of metals.
Fermi's Paper on Ideal Gases