Modern Physics-1
A Brief History of Modern Physics
and the development of the Schrödinger Equation
"Modern" physics means physics discovered after 1900; i.e. twentieth-century physics.
1900:
Max Planck
(German) tried to explain blackbody radiation using Maxwell's equations and
statistical mechanics and found that he could not.
He could only reproduce the experimentally-known
BB spectrum by assuming that the energy in an electromagnetic wave of frequency f is
quantized
according to
EM wave
En
=
h
f
,
where
n = 1, 2, 3, …
and
h = Planck's constant = 6.6
×
10
−
34
(SI units)
Planck regarding this as a math trick; he was baffled by its physical significance.
1905: Albert Einstein
, motivated in part by Planck's work, invents the concept of a
photon
to explain
the photoelectric effect. A photon is a quantum (packet) of electromagnetic radiation, with energy
Eh
f
γ
=
=ω
=
.
1911: Ernest Rutherford
(New Zealand/Britain) shows that an atom
consists of a small, heavy, positively-charged nucleus, surrounded by
small light electrons.
But there is a problem with the classical theory of
this nuclear atom: An electron in orbit about a nucleus is accelerating
and, according to Maxwell's equations, an accelerating charge must
radiate (give off EM radiation). As the electron radiates, giving energy, it
should spiral into the nucleus.
1913: Niels Bohr
(Danish), a theorist working in Rutherford's lab,
invents the Bohr model.
This is essentially a classical model, treating
the electron as a particle with a definite position and momentum, but
the model has two non-classical,
ad hoc
assumptions:
Classically, an electron in an
atom should radiate and spiral
inward as it loses energy.
1) The angular momentum of the electron is quantized:
Ln
=
=
.
2) The electron orbits, determined by (1), are stable ("stationary"), do
not radiate, unless there is a transition between two orbits, and then the
atom emits or absorbs a single photon of energy
fi
hf
E
E
=−
The predictions of Bohr model match the experimental spectrum of
hydrogen perfectly.
It is important to remember that the Bohr model is simple, useful, and
wrong
. For instance, it predicts
that the ground state of the H-atom has angular momentum
L
=
=
, when in fact, the ground state of the
H atom (s-state) has L = 0.
The Bohr model is a
semi-classical model
, meaning it combines aspects of
classical and quantum mechanics.
Semi-classical models are frequently used by physicists because they
are heuristically useful (easy to understand and often give correct results). But they must always be used
Last update: 1/28/2008
Dubson Phys3220 Notes,
©
University of Colorado