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05-2 Atomic Structure
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201-Avatar1-QM-Atoms
CHAUCER: Now, let’s see how Quantum Mechanics helps us to understand
atomic structure.
KEVIN: Ahh – Bohr and de Broglie are two of my heroes.
DIANA: Boron who?
CHAUCER: Cute, Diana, cute. Jeeves?
205-AtomicStructure
It was during the early decades of the 19th century that the structure of atoms
was coming into focus. It was known for example that a hydrogen atom
contained one proton and one electron. But the scientists of the time could think
of no stable arrangement of the two particles.
It was known that protons in any atom were grouped in a small central region
called the nucleus and that the electrons were somehow arranged at
comparatively large distances outside the nucleus.
But, in hydrogen, if the electron were stationary, it would fall into the nucleus
since the charges on the particles would cause them to attract one another.
Yet the electron couldn’t be in an orbit circling the nucleus either. Circular motion
requires constant acceleration of the circling body to keep it from flying away.
But the electron has charge and charged particles radiate light when they are
accelerating. So an electron in a circular orbit would radiate light and would
spiral into the nucleus.
210-BohrAtom
Neils Bohr proposed the first working model of the hydrogen atom. In the Bohr
model, the electron circles the nucleus as if it were a planet going around the
sun.
And with a nod to the energy quantization that Max Planck dreamed up for
solving the Ultraviolet Catastrophe, Bohr said that inside the hydrogen atom, the
electron was allowed to have only discrete values of angular momentum in its
orbits around the nucleus. Translated, this means the electron can occupy
orbits only at a certain distances from the nucleus.
And Bohr simply dismissed the problem of the electron radiating away its energy
by stating that “it just didn’t happen” (even great scientists cheat sometimes!)
He postulated that inside an atom, electrons only radiate energy when they jump
from one allowable orbit to another, and the energy of this radiation, reveals the
allowable orbits.
The wavelengths of light absorbed by hydrogen when white light is shined upon
it, as well as the wavelengths of light when it is subsequently re-radiated had
been precisely studied at the time but never explained. Here is a sample of an
absorption spectrum and an emission spectrum.
By predicting the values of orbits that an electron could have, Bohr’s model also
predicted the wavelengths of the lines in the hydrogen spectrum.
And his model was tremendously successful. It explained in exquisite detail the
atomic spectra of hydrogen.
When the energy of the wavelengths of the spectral lines are compared to the
energy differences in orbits allowed in the Bohr Atom – they agree exactly.
So the quantum approach worked well in explaining the allowable orbits, but no
one was certain why only those orbits were allowed.
215-ParticleWaves
In his doctoral dissertation in 1924, Louis de Broglie put forward a simple idea
that significantly advanced the understanding of the extremely tiny (a quantum
leap forward you might say). Since Einstein and Planck and Compton had firmly
established that light could have characteristics of both a wave and a particle, de
Broglie suggested that matter particles…protons, electrons, atoms, billiard balls,
etc could sometimes act like waves.
And when this idea was applied to the Bohr atom, it answered many questions.
First, the allowed orbits had to be exact multiples of the wavelengths calculated
for the electrons. Other orbits produced destructive interference of the waves
and so the electron couldn’t exist there.
So the circumference of the orbit must equal the wavelength…
Or twice the wavelength…
Or 3 times the wavelength…
Or, for that matter, any multiple of the wavelength.
Second, these orbits weren’t really orbits in the traditional sense. These
electrons didn’t travel around the nucleus in a circle. Rather they took the form of
a standing wave that surrounded the nucleus entirely. The exact position and
momentum of the electron particle could not be specified at any given instant