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Chapter 27
LECTURE NOTES
The period from 1890-1930 saw many discoveries about the atomic realm. The electron was
discovered first.




Thompson measured the charge to mass ratio (e/m) of cathode rays and theorized they
were tiny, charged pieces of the atom.
Millikan did "oil drop" experiments that determined e = 1.6 x 10-19C and that all charges
were integral multiples of this smaller charge.
Planck explained black body radiation by quantifying the energy of molecular vibrations
(E = nhf for n = 1,2, . . . ). In particular there is a minimum energy E = hf where f is the
frequency of the radiation and h (Planck's constant) = 6.626 x 10-34Js.
Einstein explained Planck's formula by resurrecting the particle model of light. The
photon is the particle of light carrying energy hf. Einstein used this model to explain the
photoelectric effect.
When certain metals are illuminated by light, they eject "photoelectrons." In the wave model of
light, where energy was proportional to intensity squared, a brighter light should eject electrons
that travel faster (from the extra energy). Instead, a brighter light just ejected more electrons
with no increase in speed. The color or frequency of the light was important -- higher frequency
light led to the ejection of faster electrons while light below a certain cutoff frequency failed to
eject any electrons. The wave model could not explain this.
Einstein's photon model of light said brighter light had more particles and so they would eject
more electrons. Since the energy of each photon depends on frequency (or color) alone, a
brighter light would not be expected to increase the speed of ejected electrons. But, if the
frequency increased, the energy of each photon increased and would lead to faster photons. The
cut off frequency corresponded to the energy (the work function of the metal) binding electrons
to atoms.
If a photon did not have more than this minimum energy, it could not eject an electron. Einstein
thus found KEmax = hf -w where w = hfco is the work function of the metal, KEmax the maximum
kinetic energy of the ejected electrons, and f is the frequency of incident light. He was awarded
the Nobel Prize for this discovery (not for his special theory of relativity).
The Compton effect refers to the scattering of photons by electrons. The scattered photons have
longer  (less energy) than the incident photons showing they lost energy in the collision. This
E hf h
 . Though the photon is massless, it carries
used the momentum of a photon p  
c
c 
momentum.
Pair production was also first seen during this period. An energetic photon can create an e- , e+
pair. This demonstrated (E = mc2) energy could turn into mass.
Today we believe light is not simply described by analogy to a wave model or particle model.
We say light has a dual nature. When experiments involve interference and diffraction, light
shows its wave nature; in other experiments light is more easily explained with the photon
concept. Bohr's principal of complementarity states we will observe one aspect or the other but
not both at one time.
Louis de Broglie found matter also has a dual nature. He theorized matter waves would have
h
wavelength λ 
for a mass m moving with velocity v. This was seen by Davisson and
mv
Germer when they produced diffraction patterns with electrons. This set the stage for the
electron microscope.
Thompson deflected the mysterious rays coming from the cathode using magnetic and electric
fields. The magnetic force on a charge e, mass m, velocity v particle moving through a B field
was F = evB and this was a centripetal force causing the particles to curve in part of a circle of
e v
mv 2
radius r. Thus Fmagnetic =
= evB or
. The electric field could eliminate this

r
m rB
E
deflection. Since Felectric = eE = Fmagnetic = evB, v = E/B and e/m =
. Thompson knew the
rB 2
electric and magnetic field strengths in his experiment and he measured r, the radius of
deflection. Thus although he did not know e and m separately, he knew their ratio, e/m.
Millikan sprayed a mist of very fine oil droplet from an atomizer (perfume sprayer). The
droplets became negatively charged by friction and started to fall between the parallel plates of a
capacitor. By adjusting the charge on the plates (or the electric field between the plates),
Millikan could make the oil droplets hover when mdropg = eE. Millikan found mdrop by
measuring the terminal velocity of a droplet when the electric field was off. Thus he measured e
and using Thomson's e/m ratio could find m (for the electron).
MODELS OF THE ATOM
Thompson proposed a plum pudding model where the positive charge was smeared out (the
pudding) and the negative electrons were scattered about (like plums).
Rutherford did experiments which showed this was wrong; the positive charge was concentrated
1
in a tiny nucleus only
of the volume of the atom. The electrons orbited the nucleus like
10,000
planets do the sun in Rutherford's solar system model of the atom.
In his experiments, Rutherford fired α particles (helium nuclei) at thin gold foils. Most passed
right through, with a few knocked straight back. Thus the atom must be mostly empty space,
with a strongly concentrated positive core.
Others were looking at spectra near the end of the 19th century. Rydberg and others found
formulas that would describe the location of series of lines for various elements given off when
glowing discharges of these elements were analyzed. For hydrogen,
1
1 
1
 R  2  2  ; n = 2, 3, . . . gives the Lyman series of ultraviolet lines,

n 
1
2
1
 1
 2  2
n
2
1 

 1
 the Balmer visible lines, and  2  2  the Paschen infrared series.
n 
3

All of this led to Bohr's 1912 Rutherford-like model of the atom. Bohr theorized the electrons
could move only in certain allowed circular orbits without radiating energy (classically, an
accelerating charge (such as the electron moving in a circle) would continuously radiate energy
and spiral into the nucleus in a very short time). Bohr called these allowed orbits stationary
states. A photon is emitted, Bohr saw, when an electron drops from a higher to a lower level
with the energy difference between levels going to the photon Eupper - Elower = hf.
nh
by allowing only
2
certain radii rn for circular orbits was explained by de Broglie as arising from the matter wave of
the electron needing to fit a whole number of times around the orbits circumference.
The quantum condition Bohr imposed on angular momentum L = mvrn =

h
nh
nh
for an electron; the circumference 2rn 
or mvrn =
as Bohr proposed.
mv
mv
2
Bohr further offered his correspondence principle that stated quantum physics with very large n
should be the same as classical physics.
For atoms with atomic number Z, Bohr's model gave
n 2 r1
h2
rn 
, where r1  2
= Bohr radius = 0.529 x 10-10m.
z
4 mke 2
En 
Z2
 2 2 e 4 mk 2
E
,
where
E

= -13.6eV.
1
1
n2
h2
We can show the  of a photon emitted when an electron drops from one level nupper to another
1 2 2 Z 2 e 4 mk 2  1
1 
nlower is 
.

2
 n2


h 3c
n
lower
upper


3