Early Quantum Theory and Models of the Atom

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Chapter 27 Early Quantum Theory and Models of the
Atom
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27.1 Discovery and Properties of the Electron
In the late 19th century, discharge tubes were
made that emitted cathode rays.
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27.1 Discovery and Properties of the Electron
It was found that these rays could be deflected
by electric or magnetic fields.
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Centripetal Electric forces
What happens to the charge particle as it enters
the B field?
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
If an electric field is turn on, the particles
direction can be straighten out.
Sometimes it is convenient to express the path of
a particle in terms of its charge to mass ratio
e is the charge on an electron
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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
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Demonstration

• Bring in CRT monitor with magnet.

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Millikans 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.
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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

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Photon Theory of Light and the Photoelectric
Effect
Einstein suggested that, given the success of
Plancks theory, light must be emitted in small
energy packets
These tiny packets, or particles, are called
photons.
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Quantum number

• Planck proposed that energy of any molecular
  vibration can only be a whole number of hf
• n is the quantum number or number of photons
• h is Plancks constant

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Photoelectric Effect
The photoelectric effect When light strikes a
metal, electrons are emitted.
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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
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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
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Photon Theory of Light and the Photoelectric
Effect
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.
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Photon Theory of Light and the Photoelectric
Effect
hf is the energy of the incoming photon ? is
the work function, the energy required to break
the electron free KE is the kinetic energy of
the released electron
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Increasing the intensity of light (100W bulb vs.
60W bulb)
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).
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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
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If the photon doesnt 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
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Hydrogen Spectrum
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27.12 The Bohr Atom
The lowest energy level is called the ground
state the others are excited states.
Z is the of Charges n is the Energy State
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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 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
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Compton Effect
This is another effect that is correctly
predicted by the photon model and not by the wave
model.
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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
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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 Emc2
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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.
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Photon Interactions Pair Production

• Photons passing through matter can undergo the
  following interactions
• Photoelectric effect photon is completely
  absorbed, electron is ejected
• Photon may be totally absorbed by electron, but
  not have enough energy to eject it the electron
  moves into an excited state
• The photon can scatter from an atom and lose
  some energy
• The photon can produce an electron-positron pair.

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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.
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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
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Early Models of the Atom
Rutherfords model of the atom is mostly empty
space
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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.
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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.
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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.
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Summary of Chapter 27

• Plancks 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

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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

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Photon absorption and Emission