BEFORE
QUANTUM PHYSICS WAS BORN!
RADIATION FROM
INCANDESCENT OBJECTS!
Max Planck made up an equation
which would fit the experimentally observed spectrum of an
incandescent object, and then tried to derive an equation of
that form based on various assumptions. The only assumption he
found that would work is that the radiation was emitted by
charged oscillators which had an energy of oscillation
proportional to their frequency, E = hf, where h
was a universal constant of nature (like c, the speed of
light).
Total power output is P =
σεAT4.
Peak frequency is fpeak
= [1011 Hz/K]T.
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Contrary to Maxwell, the
intensity of the light does not matter, only the
frequency. |
Einstein showed that this
effect can be understood only if light consists of massless,
chargeless particles he called photons, which have kinetic
energy K = hf and momentum p = h/λ, where h
is Planck's constant. These photons can individually knock
electrons out of a piece of metal.
THE COMPTON EFFECT!
Compton discovered that
photons can elastically scatter from electrons in free space, a
beautiful confirmation of Einstein's ideas. From conservation of
relativistic energy and momentum, one finds Δλ = (h/(me
c))[1 - cos θ].
BOHR'S SEMICLASSICAL
MODEL OF HYDROGEN!
Bohr tried to blend classical
and quantum ideas by assuming that electrons could travel in
stable orbits if they had the appropriate quantum of angular
momentum, Ln = n ℏ. To his astonishment, this
seemed to give the right (experimentally observed) energy levels
for hydrogen. The idea, then, would be that only the lowest
energy level was stable, and therefore that if an electron is
placed into a higher level, it will jump to lower levels by
emitting a photon whose kinetic energy is equal to the energy
difference between levels. However, as Bohr
realized, his model is totally wrong in both concept and detail,
and he anxiously awaited what turned out to be the dawn of
quantum physics in 1920. As hydrogen was studied more
closely, it was found that the energies predicted by the Bohr
scheme were always slightly different from the actual
energies. Nor did the idea work for other atoms... nor
could it be adapted to molecules!
<
DE BROGLIE'S "MATTER
WAVES"!
br>
For ANY particle in nature,
there is a frequency f = K/h, and a wavelength λ = h/p,
but what are the waves?? They were called “matter waves” by de
Broglie, but that's no help.
HEISENBERG'S UNCERTAINTY
RELATIONS!
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Consider our old friend the
single slit. Suppose we use a laser beam with well-defined
momentum. When we send these photons through a slit of width d,
we are measuring their position to within an accuracy of Δy = d.
This creates an uncertainty in the component of momentum
parallel to the slit: Δpy is roughly equal to ℏ
divided by d! Thus the beam spreads out, its width of spread
being inversely proportional to d. Or consider a particle
which could be in one of several energy levels. If we
observe the particle for a time Δt, we find that the shorter the
time of observation, the more likely the particle is afterward
in any one of a range of different states, rather than the one
we were interested in! Measurement of a position destroys
existing momentum information, and vice versa. Similarly
measurement of a time interval destroys existing energy
information, and vice versa. This is an unavoidable
consequence of the wave nature of matter.
Beware that in homework
questions on Quest, the Uncertainty Relations are almost
always written using ≥ ℏ/2, instead of ≃ ℏ. It makes a
difference, if you are asked to compute a numerical value!
Chapter 35, 317L
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