Chapter 27
Early Quantum Theory and
Models of the Atom
27.1 Discovery and Properties of the
Electron
In the late 19th century, discharge tubes were
made that emitted “cathode rays.”
27.1 Discovery and Properties of the
Electron
It was found that these rays could be deflected
by electric or magnetic fields.
Centripetal & Electric forces
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
x x x x x x x x x x x x
What happens to the charge
particle as it enters the B field?
v
Fb  qv  B
v2
Fc  m
r

If an electric field is turn on, the
particles direction can be
straighten out.
FE  q  E
Sometimes it is convenient to
express the path of a particle in
terms of its charge to mass ratio
e
v

m Br
e
E
 2
m B r
e is the charge on an
electron
Properties of the Electron
By accelerating the rays through a known
potential and then measuring the radius of their
path in a known magnetic field, the charge to
mass ratio could be measured:
The result is
Demonstration
• Bring in CRT monitor with magnet.
Millikan’s Oil-drop experiment
The force due to gravity (mg) was balanced by electric
force created by an electric field.
The mass and charge of each droplet were measured
Analysis showed that the charge was always an
integral multiple of a smallest charge, e.
Quantized energy levels
• Ramp versus stair analogy. On a ramp, a box can have
continuous values of potential energy.
• On the stairs, the box can have only discrete (quantized)
values of energy
Photon Theory of Light and the
Photoelectric Effect
Einstein suggested that, given the success of
Planck’s theory, light must be emitted in small
energy packets:
E  hf
These tiny packets, or particles, are called
photons.
Quantum number
Planck proposed that energy of any molecular vibration
can only be a whole number of hf
E  nhf ,
n  1, 2,3
n is the quantum number or number of photons
h is Planck’s constant
h  6.626 x1034 Js
Photoelectric Effect
The photoelectric effect:
When light strikes a metal,
electrons are emitted.
Photon Theory of Light and the
Photoelectric Effect
Recall chapters 23 & 24 explained reflection,
diffraction, and interference using ray diagrams
and the theory that light behaves as a wave
If light is a wave, theory predicts:
Number of electrons and their energy should
increase with intensity
Frequency would not matter
Photon Theory of Light and the
Photoelectric Effect
If light is particles, theory predicts:
Increasing intensity increases number of
electrons but not energy
Above a minimum energy required to break
atomic bond, kinetic energy will increase
linearly with frequency
There is a cutoff frequency below which no
electrons will be emitted, regardless of
intensity
Photon Theory of Light and the
Photoelectric Effect
KE  hf  
A photon with a frequency of red light strikes an
electron, but only excites it to a higher energy state.
A photon with a frequency of green light strikes an
electron with enough energy to release it from the metal,
but it has no KE after being released
A photon with a frequency of blue light strikes an
electron and releases with some velocity.
Photon Theory of Light and the
Photoelectric Effect
KE  hf  
hf :
is the energy of the incoming photon
ɸ :is the work function, the energy required to break the
electron free
KE : is the kinetic energy of the released electron
Increasing the intensity of light
(100W bulb vs. 60W bulb)
KE  hf  
Increasing the intensity of light does not increase the
energy of the photon.
It does increase the number of photons, which increases
the number of ejected electrons (more current).
Photon Theory of Light and the
Photoelectric Effect
The particle theory assumes that an electron
absorbs a single photon.
Plotting the kinetic energy vs. frequency:
y = 0.4151x - 2.3575
3
KE (eV) Max
2.5
2
1.5
1
0.5
0
0
2
4
6
8
Frequency (E14 Hz)
10
12
14
If the photon doesn’t have sufficient energy to release the electron, it
can be “excited” to a higher energy state.
The electrons in free atoms can only be found in only certain
discrete energy states.
When the electrons fall back to the “ground state”, they release a
very specific spectrum of light
Hydrogen Spectrum
27.12 The Bohr Atom
The lowest energy level is called
the ground state; the others are
excited states.
2
Z
E 2
n
Z is the # of Charges
n is the Energy State
Energy, Mass, and Momentum of a Photon
When objects travel close to or at the speed of light, relativistic
equations for length, time and momentum must be observed
2
v
L  Lo 1  2
c
T
To
1
P
2
v
c2
mo v
v2
1 2
c
Photons travel at the speed of light.
If v = c, then the denominator is zero which can only happen if the
rest mass of the photon is zero.
This means a photon can never be at rest
Compton Effect
This is another effect that is correctly predicted
by the photon model and not by the wave
model.
Compton Effect
Compton found that the scattered X-rays had a
slightly longer wavelength than the incident
ones, and that the wavelength depended on the
scattering angle:
This means the exiting photon has less energy
Photon Interactions; Pair Production
In pair production, energy, electric charge, and
momentum must all be conserved.
The photon disappears and
creates an electron-positron
pair.
Rest mass is being created
from pure energy:
E=mc2
In pair production, energy, electric charge, and
momentum must all be conserved.
Energy is conserved through the mass and kinetic
energy of the electron and positron
Charge is conserve by creating both a positive and
negative charge.
The interaction must take place in the electromagnetic
field of a nucleus, which conserves momentum.
Photon Interactions; Pair Production
Photons passing through matter can undergo
the following interactions:
1. Photoelectric effect: photon is completely
absorbed, electron is ejected
2. Photon may be totally absorbed by electron,
but not have enough energy to eject it; the
electron moves into an excited state
3. The photon can scatter from an atom and lose
some energy
4. The photon can produce an electron-positron
pair.
Wave-Particle Duality;
The Principle of Complementarity
Phenomena such as diffraction and
interference show that light is a wave
Phenomena such as the photoelectric effect
and the Compton effect that show that it is a
particle.
Which is it?
This question has no answer; we must
accept the dual wave-particle nature of light.
Wave Nature of Matter
Just as light sometimes behaves as a
particle, matter sometimes behaves like a
wave.
The wavelength of a particle of matter is:
Early Models of the Atom
Rutherford’s model of the
atom is mostly empty
space:
27.11 Atomic Spectra: Key to the Structure
of the Atom
An atomic spectrum is a line spectrum – only
certain frequencies appear. If white light passes
through such a gas, it absorbs at those same
frequencies.
Atomic Spectra:
Key to the Structure of the Atom
A portion of the complete spectrum of hydrogen
is shown here. The lines cannot be explained by
the Rutherford theory.
The Bohr Atom
Bohr proposed that the possible energy states
for atomic electrons were quantized – only
certain values were possible. Then the spectrum
could be explained as transitions from one level
to another.
Summary of Chapter 27
• Planck’s hypothesis: molecular oscillation
energies are quantized
• Light can be considered to consist of
photons, each of energy
• Photoelectric effect: incident photons
knock electrons out of material
Summary of Chapter 27
• Compton effect and pair production also
support photon theory
• Wave-particle duality – both light and matter
have both wave and particle properties
• Wavelength of an object:
Photon absorption and Emission