Transcript 4.1-4.3 - BYU Physics and Astronomy

Physics 222
D.S. Durfee
The Physics Revolution of the 20th
Century
Relativity – physics of the fast
 Quantum Mechanics – law of the small

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Atoms: clocks, discharge lamps, lasers
Molecules: chemistry
Nuclei: fission, fusion
Solid State: semiconductors
Degenerate Matter: superconductors
Coherence & Superposition: quantum computing
Puzzles at the Beginning of the
Twentieth Century
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
Null result of the Michelson-Morley Experiment
Ultraviolet Catastrophe
 Photoelectric Effect
 Maxwell’s Equations Spell the Demise of Atoms!
 Discrete atomic emission lines

Quantum Uncertainty Relations
Position – Momentum
Energy – Time
Other Dimensions
Angular Momentum
Thought Question
Imagine that I measure the location and momentum of an
electron. I measure the location with a precision of 1nm. If I
make a second measurement one second later, about how well
will I be able to predict where I will find the electron with the
second measurement? (me ~ 1e-30 kg, h/4¼ ~ 0.5e-34 Js)
A : To better than 1 nm
C : To within 1 μm
E : Not even to within 1 mm
B : To within around 1nm
D : To within 1 mm
Wave-Particle Duality
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Things act as wave when propagating
– or, in other words, we use waves to make predictions
as to what we will find when we make our
measurement.

Things act as waves when we measure wavelike properties.
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Things act as particles when we measure
particle-like properties
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Example: BEC interference --- theorists confused
about “undefined phase”
Postulates of Quantum Mechanics
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Every physically-realizable system is described by a
state function ψ that contains all accessible physical
information about the system in that state
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The probability of finding a system within the volume
dv at time t is equal to |ψ|2dv

Every observable is represented by an operator which
is used to obtain information about the observable
from the state function

The time evolution of a state function is determined
by Schrödinger’s Equation
4.1 The Nuclear Atom
120
An atom is largely empty space (NOT!)
4.2 Electron Orbits
124
The planetary model of the atom and why
it fails
4.3 Atomic Spectra
127
Each element has a characteristic line
spectrum
4.4 - 4.5
4.4 The Bohr Atom 130
Electron waves in the atom
4.5 Energy Levels and Spectra
A photon is emitted when an electron
jumps from one energy level to a lower
level
4.6 Correspondence Principle
138
The greater the quantum number, the closer
quantum physics approaches classical
physics
4.7 Nuclear motion 140
The nuclear mass affects the wavelengths of
spectral lines
4.8 Atomic Excitation
142
How atoms absorb and emit energy
4.9 The Laser
145
How to produce light waves all in step
Reading Quiz Question
Which spectral series resulted from
a study of the visible part of the
hydrogen spectrum?
A: The Lyman series
B:
C:
D:
E:
The Balmer series
The Paschen series
The Brackett series
The Wurald series
The Hydrogen Spectrum
The Balmer Series
1 1 
 R  2 

4 n 
1
Rutherford’s Experiment
θ
What would happen if I shot a
bullets through a piece of jello?
Thought Question
A: All of them would come nearly straight
through, but with a slightly smaller
velocity
B: Some of them would be deflected
slightly, some would lose a little velocity
C: Some would go nearly straight through,
some would deflect at large angles, some
would ricochet almost straight back
D: They would all reflect straight back
Thought Question
What would happen if I shot a bullets through
a piece of jello containing shredded carrots?
A: All of them would come nearly straight
through, but with a slightly smaller velocity
B: Some of them would be deflected slightly,
some would lose a little velocity
C: Some would go nearly straight through,
some would deflect at large angles, some
would ricochet almost straight back
D: They would all reflect straight back
What would happen if I shot a
bullets through a piece of jello
containing iron anvils?
Thought Question
A: All of them would come nearly straight
through, but with a slightly smaller velocity
B: Some of them would be deflected slightly,
some would lose a little velocity
C: Some would go nearly straight through,
some would deflect at large angles, some
would ricochet almost straight back
D: They would all reflect straight back
Johann Jakob Balmer (May 1, 1825 –
March 12, 1898) was a Swiss
mathematician and an honorary physicist.
The Hydrogen Spectrum
The Balmer Series
1 1 
 R  2 

4 n 
1
Quiz Question
In Bohr’s model of the hydrogen atom,
what determined the frequency of
emitted light?
A: The total energy of the orbiting electron
B: The energy difference between initial
and final electron states
C: The frequency of revolution of the
orbiting electron
D: The difference in revolution frequency
between initial and final electron states
E: The sum of the initial and final electron
revolution frequencies
Bohr’s Theory
He did not think in terms of waves
 He simply postulated that

– There are orbits in which the electron doesn’t
radiate.
– The light released when an electron changes
orbits is a photon with an energy equal to the
difference in energy of the two orbits

He further postulated that the orbits were
circular, with
L = n~
Results of Bohr Theory
Thought Question
How many energy levels are there
between the hydrogen ground state (13.6 eV) and the continuum (0 eV)?
A: one
B: 13
C: 14
D: 1324
E: None of the above
Wave Theory of Hydrogen
5th Solvay Conference, Brussels, 23-29 October 1927
Back row: A Piccard, E Henriot, P Ehrenfest, D Durfee, Ed Herzen, Th De Donder, E Schroedinger
E Verschaffelt, W Pauli, Waldo, W Heisenberg, R H Fowler, L Brillouin.
Middle Row: P Debye, M Knudsen, W L Bragg, H A Kramers, P A M Dirac, A H Compton,
L de Broglie, M Born, N Bohr.
Front Row: I Langmuir, M Planck, Mme Curie, H A Lorentz, A Einstein, P Langevin, Ch E Guye,
C T R Wilson, O W Richardson.
Quiz Question
“When n gets large, quantum physics
should start to look like classical
physics” is a somewhat accurate
statement of the...
A: Equivalence Principle
B: Limiting Value Principle
C: Legacy Principle
D: Completeness Principle
E: Correspondence Principle.
Thought Question
What would happen to the hydrogen
spectrum if I replace the electron with
a muon (which is like an electron but
heavier)?
A: No change
B: Almost no change
C: All of the lines will shift to significantly
longer wavelengths
D: All of the lines will shift to significantly
shorter wavelengths
E: I have no idea --- hey, its an honest
answer!
Thought Question
What would happen to the hydrogen
spectrum if I replace the nucleus (a
proton) with an alpha particle (two
protons plus two neutrons… i.e.
more charge, more mass)?
A: No change
B: Almost no change
C: All of the lines will shift to significantly
longer wavelengths
D: All of the lines will shift to significantly
shorter wavelengths
E: I have no idea
Thought Question
What would happen to the hydrogen
spectrum if I replace the nucleus (a
proton) with a deuteron (a proton
plus a neutron… i.e. same charge,
more mass)?
A: No change
B: Almost no change
C: All of the lines will shift to significantly
longer wavelengths
D: All of the lines will shift to significantly
shorter wavelengths
E: I have no idea
Frank-Hertz Experiment
The Correspondence Principle
Quick Writing Assignment

In one minute, write a short, clear, and
concise paragraph which explains the
correspondence principle.
Bohr Theory Successes/Failures
Predicts emission and absorption lines of hydrogen and
hydrogen-like ions
☺ Predicts x-ray emissions (Moseley’s law)
☺ Gives an intuitive picture of what goes on in an atom
☺ The correspondence principle is obeyed... sort of
☺
X
X
X
X
It can’t easily be extended to more complicated atoms
No prediction of rates, linewidths, or line strengths
Fine structure (and hyperfine structure) not accounted
for
How do atoms form molecules/solids?
X
Where did it come from? There must be a more
general underlying theory!
☺
It gave hints of a new, underlying theory