14 Early atomic physics
briefly mention the other three great breakthroughs and their signifi-
cance for atomic physics. R ̈ontgen discovered mysterious X-rays emit-
ted from discharges, and sparks, that could pass through matter and(^31) This led to the measurement of the blacken photographic film. (^31) At about the same time, Bequerel’s dis-
atomic X-ray spectra by Moseley de-
scribed in Section 1.5.
covery of radioactivity opened up the whole field of nuclear physics.^32
(^32) The field of nuclear physics was later
developed by Rutherford, and others,
to show that atoms have a very small
dense nucleus that contains almost all
the atomic mass. For much of atomic
physics it is sufficient to think of the
nucleus as a positive charge +Zeat the
centre of the atoms. However, some un-
derstanding of the size, shape and mag-
netic moments of nuclei is necessary to
explain the hyperfine structure and iso-
tope shift (see Chapter 6).
Another great breakthrough was J. J. Thomson’s demonstration that
cathode rays in electrical discharge tubes are charged particles whose
charge-to-mass ratio does not depend on the gas in the discharge tube.
At almost the same time, the observation of the Zeeman effect of a mag-
netic field showed that there are particles with the same charge-to-mass
ratio in atoms (that we now call electrons). The idea that atoms con-
tain electrons is very obvious now but at that time it was a crucial piece
in the jigsaw of atomic structure that Bohr put together in his model.
In addition to its historical significance, the Zeeman effect provides a
very useful tool for examining the structure of atoms, as we shall see
at several places in this book. Somewhat surprisingly, it is possible to
explain this effect by a classical-mechanics line of reasoning (in certain
special cases). An atom in a magnetic field can be modelled as a simple
harmonic oscillator. The restoring force on the electron is the same for
displacements in all directions and the oscillator has the same resonant
frequencyω 0 for motion along thex-,y-andz-directions (when there is
no magnetic field). In a magnetic fieldBthe equation of motion for an
electron with charge−e, positionrand velocityv=
.
risme
dv
dt=−meω 02 r−ev×B. (1.34)In addition to the restoring force (assumed to exist without further ex-
planation), there is the Lorentz force that occurs for a charged particle(^33) This is the same force that Thomson moving through a magnetic field. (^33) Taking the direction of the field to
used to deflect free electrons in a curved
trajectory to measuree/me. Nowadays
such cathode ray tubes are commonly
used in classroom demonstrations.
be thez-axis,B=B̂ezleads to
..
r+2ΩL.
r×̂ez+ω 02 r=0. (1.35)This contains the Larmor frequencyΩL=
eB
2 me. (1.36)
We use a matrix method to solve the equation and look for a solution
in the form of a vector oscillating atω:r=Re
x
y
z
exp (−iωt)
. (1.37)
Writteninmatrixform,eqn1.35reads
ω 02 −2iωΩL 0
2iωΩL ω 02 0
00 ω^20
x
y
z
=ω^2
x
y
z