Physics 0081
Fall 1999 (00-1)
Handout #6
Spectroscopy, Electrons and a Primer on Oscillations
Experiments showed that Maxwell's prediction of travelling electromagnetic waves was
correct in all details. Oscillating charges are the source (p-s) of electromagnetic waves.
All electromagnetic waves (e.g., (human) visible light, X-rays, etc.) are really the same
phenomenon; they all travel in vacuum at the same speed, and they di®er from one another
only in their frequency of oscillation. The general features of oscillations and waves will be
discussed in class. For now:
Frequency is the number of times per second that a periodic motion repeats.
Periodic motions simply repeat exactly in a certain time { the period, e.g., one
says that the period of the moon's motion is about one (Earth) month. The
frequency of the pendulum on my clock is close to 1 s.
Visible light is identical in features to all other types of electromagnetic radiation as
noted above. Human chauvinism being what it is, the extremely narrow band of frequencies
is especially important and when we usually speak of \light" we mean that part of the
spectrum visible to humans. Examining the spectrum of electromagnetic radiation emitted
by objects (both in the laboratory and in the heavens) allow one to determine what atoms are
actually doing the emitting. It was determined that each atomic species (i.e., element) emits
and absorbs light at special frequencies unique to itself. Spectroscopy revealed that the same
chemical elements exist both on the Sun and on the Earth (and as we now experimentally
determine) in the rest of the universe. Quantum physics was built on the experiments of
early precise spectroscopy of the hydrogen and other elements. But what was doing the
oscillating in an atom?
Faraday's and others' experiments strongly suggested a basic unit of electric charge, and
it was given the name \electron" (without yet knowing what it was). J. J. Thomson did
experiments around the turn of the century in which he isolated \electrons" from a variety
of gases and accelerated them using electric and magnetic ¯elds. An electron of charge e
in an electric ¯eld E feels an electric force Fe = eE. An electron moving with speed v
in a suitably oriented magnetic ¯eld B feels a magnetic force Fm = evB. By measuring
the de°ection (acceleration) of the electron beam due to both electric and magnetic ¯elds,
Thomson determined a profound result: the experimental charge to mass ratio of an electron: e=m = 1:8 £ 10¡11 Coul=kg. This is a profound result, since Thomson got the same
result for \electrons" produced from all the di®erent materials. Notice that his experiments
stood on the shoulders of the experiments of the "electricians" Coulomb, Oersted and others.
This ratio was larger than could be accounted for with a whole atom. Eventually Thomson measured the mass of the electron separately and it was about 1/2000 the mass of a
hydrogen atom. It is these electrons in atoms which (somehow) generate the oscillations to
produce characteristic electromagnetic radiation from each atom type. Solving the \somehow" problem required quantum theory. The periodic table was being ¯lled out but without
explanation of the regularities. But quantum theory was not far o®.
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Primer on oscillations: (see, e.g., Hewitt Ch. 18) A gently displaced pendulum has a to
and fro oscillatory motion which is an example of \simple harmonic motion". Think of a
mass on a spring, with the mass slightly displaced from the equilibrium position. When you
release the mass, the spring tension brings it toward the equilibrium, but the inertia causes
the mass to overshoot. Eventually it stops and starts back, overshooting again. Same for a
pendulum; they will oscillate forever (ideally, neglecting frictional losses). Simple harmonic
motion is characterized by a restoring force on the mass (i.e., a force trying to accelerate the
mass back to the equilibrium position) that is proportional to the displacement: F / ¢x, or
putting in a proportionality constant k, F = k¢x directed toward the equilibrium position.
Notice that the acceleration of the mass driven by that restoring force is NOT constant, so
you cannot use the earlier equations to describe the motion. Obviously a falling body and a
periodically moving mass are completely di®erent.
As noted above the frequency is the number of (complete) oscillations per second. The
voltage in your wall socket is varying 60 times per second, so we say the frequency is 60 Hz
or Hertz after the experimenter who ¯rst generated radio waves in the laboratory. Clearly
if the frequency of an oscillator is 10 Hz, it makes 10 oscillations per second. This means
that the time per oscillation is 0.1 second. The time per oscillation is the period, so knowing
the period is equivalent to knowing the frequency { there is no new information. We have
generally
1
; or equivalently,
period
1
period =
frequency
frequency =
One more issue will be discussed more later: periodic waves. The wavelength, ¸ of a
wave is the distance over which the wave pattern repeats, i.e., it measures the periodicity of
the pattern in space. There is a relation for all traveling waves: if V is the speed of the wave
(like the speed of light for electromagnetic waves) and º is the frequency of the wave, then
V = º¸. Using this with the speed of light allows you to calculate the wavelength for any
frequency and vice versa. This explains the ¯gure on p.26 of the text. The speed of light in
vacuum (p-s also called \free space") is denoted c = 3 £ 108 m=s.
Some Exercises:
1. Imagine starting o® a pendulum by displacing it from its equilibrium position and
releasing it from rest. The frequency of the pendulum is 10 Hz. How many times per
second does the pendulum bob cross the equilibrium position?
2. The wall sockets produce a periodic \voltage" with frequency 60 Hz. Compute the
time for the voltage to execute one complete cycle.
3. Certain atoms in an electric discharge emit electromagnetic waves with frequency about
1015 Hz. Compute the period of the oscillations. By counting the number of complete
oscillations we can devise extremely accurate \atomic" clocks.
4. Suppose the frequency of the microwaves in your oven is 1012 Hz. Compute the wavelength of the waves.
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