Constants & Atomic Data
The birth of atomic physics
and quantum mechanics
Honors Physics
Don Rhine
Energy Calculations
• Kinetic Energy: KE = ½mv2
• Speed of light: c = λν = λf
– λ (lamda) = wavelength [m]
– ν (nu) = f = frequency [Hz] = [s-1]
• Energy of a light quantum: E = hf
• New energy unit...for very small energy values
– 1 eV = 1.60 x 10-19 [C-V] or [J]
• Photoelectric Effect & Compton Scattering
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Look inside back cover of book!
Speed of Light (vacuum): c = 3.00 x 108 m/s
Elementary Charge: |e-| = |p+| = 1.60 x 10-19 C
Planck’s Constant: 6.63 x 10-34 J-s
Atomic masses...
– Electron: 9.109 x 10-31 kg
– Proton: 1.673 x 10-27 kg
– Neutron: 1.675 x 10-27 kg
deBroglie’s Wave Equations
• By the way, momentum = mass * velocity
• p = mv
λ=
h
mv
f =
E
h
– Ein = Eout (conservation of energy)
– Eincoming photon = Eenergy e- needs to break away from atom +
Are these 3
Escattered electron + Eenergy scattered photon
equations
– KEmax = hf – hfth
identical?
Max Planck Develops First
Quantum Model
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E-M Spectrum
Can describe photon by its λ, ν, or E!
Blackbody radiation did
not increase in energy as
predicted by classical
physics theory (ultraviolet
catastrophe)
In 1900 developed
resonator model with
quantized energy level
– resonator = vibrating
molecule
– required standing waves
a discrete energy levels
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E = hν
Planck’s Constant, h ≈
6.63 x 10-34 J-s
Nobel Prize in 1918
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E-M Spectrum
Can describe photon by its λ, ν, or E!
Photoelectric Effect
• Heinrich Hertz – shined
light on metal surface to
prove Maxwell’s E-M
wave equations worked
• Expected energy in E-M
waves to “hit” and eject
electrons from surface of
metal
• Strange result did not
match classical physics—
no e- ejected below until
certain color of light
shined on surface
Photoelectric Effect
Classical physics: low intensity of low-energy light should
be enough to do the job over a long enough period of
time...like heating water to boil over low flame
light from
source
sample
metal
Photoelectric Effect
Classical physics: high intensity of low-energy light should
be enough to do the job over a shorter time...like heating
water to boil faster over more low flames
light from
source
sample
metal
vacuum
tube
voltage
Result: No electrons
ejected! What happened??
vacuum
tube
expected ejected
electrons
voltage
Result: No electrons
ejected! What happened??
Photoelectric Effect
Photoelectric Effect
Classical physics: low intensity of high-energy light should
be enough to do the job...like heating water to boil faster
over more low flames
Classical physics: low intensity of high-energy light should
be enough to do the job...like heating water to boil faster
over higher energy gas burner (MAPP gas vs. LP)
light from
source
sample
metal
light from
source
sample
metal
vacuum
tube
expected ejected
electrons
voltage
Result: Electrons ejected!
Why not before?
vacuum
tube
expected ejected
electrons
voltage
Result: Electrons ejected!
Even faster now!
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Photoelectric Effect
Photoelectric Effect
• Quantum Mechanics:
• Quantum Mechanics:
– must meet threshold energy level (hft) before
electrons emitted
– The further you are above the threshold, the faster the
e- travels (higher kinetic energy, KE = ½ mv2)
– Different metals have different thresholds. Why?
– Different metals have different thresholds. Why?
a. slope of
these
lines =
what?
b. equations
for these
lines =
what?
Sample photoelectric effect
calculation
Solution process
• Suppose electrons are being emitted from
a sample metal with νth = 5000 Angstroms.
If the max observed electron speed is
10.8M kmh, what is the minimum
wavelength of the incident photons?
• Why use the word “minimum”?
• What is the deBroglie wavelength of the
emitted electron?
Solution process
10.8Mkmh =
hr
×
1km
×
3600 s
Diagram
Data (& convert to appropriate units)
Relevant equations
Find relationship
Solve
Solution process
= 1% of c
• Data
– νth = 5000 Angstroms = 500 nm = 500 x 10-9m
– v=
10.8 × 106 km 1000m 1hr
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= 3.00 × 106 m / s
Set up relationship & solve
Ein = Eout (conservation of energy)
Eincoming photon = Eenergy e- needs to break away from atom +
Escattered electron + Eenergy scattered photon
• Equations
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KE = ½mv2
c = λν = λf
E = hf
1 eV = 1.60 x 10-19 [C-V] or [J]
KEmax = hf – hfth
Eincoming photon = Eenergy needed to break away from atom +
Escattered electron + Eenergy scattered photon
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Einstein’s Next New Idea
Compton Effect
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• Photoelectric effect implies light is also
quantized into packets of energy called
photons
• Each photon has energy E = hf
• Awarded Nobel Prize in 1921 for this
quantum mechanics breakthrough
• What other key ideas did Einstein propose
(before and after this breakthrough)?
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Models of the Hydrogen Atom
• Theoretical models evolved as experimental
observations provided more insight, especially
the strange quantum phenomena...
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Ancient Atom
Billiard Ball (John Dalton 1803)
“Plum Pudding” – J.J. Thomson
Solar System – Ernest Rutherford
Quantized Energy Level – Niels Bohr
Particle Wave Model - deBroglie
Electron Cloud Model - Schrödinger
Arthur Compton (1923),
Nobel Prize 1927
Photon = wave or particle?
If particle, can use photons
to collide with electrons, and
should have billiard ball-like
collisions
Some energy should transfer
to e-, and photon should lose
some as it bounces off
Use x-rays on block of
carbon atoms in crystal
lattice structure
It worked – scattered photon
had lower energy
By product: x-ray
crystallography – common
technique still used today!
Ancient Idea of Atom – 400 BC
• Leucippus &
Democritus
• Atom = Smallest
Indivisible Quantity
• PhET Simulation & Virtual Lab Exercise
Discovery of Electrons
& “Plum Pudding” Model
Billiard Ball Model
• John Dalton (17661844)
• Early chemist explored
structure of molecules
• Around 1800 Dalton
proposed all chemical
compounds comprised
of atoms that cannot be
altered or destroyed
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J.J. Thomson (1856 – 1940)
Electric field could bend “beam” from
cathode ray tube
Correctly assumed beam was composed of
negatively charged particles that must be
part of an atom, “corpuscles” (e-)
First to propose atom comprised of smaller
parts
Atoms neutrally charges, so assumed there
must be a sea of + charges around
“corpuscles”
Thomson also predicted charge:mass ratio
of eNobel Prize in 1906
Millikan’s famous 1909 oil drop experiment
measured charge (and therefore mass) of e(1923 Nobel Prize)
Crooke’s Tube
“Cathode Ray Tube”
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Rutherford’s Scattering Experiment
Mostly empty space w/ + core – solar system model
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Ernest Rutherford, 1871 – 1937
1911: Directed + charged alpha
particles He2+ at thin gold leaf foil
(couple hundred atoms in thickness)
J.J. Thomson’s model predicted α
particles pass through
Particles were scattered!
Rutherford assumed that positively
charges grouped together in a nucleus
caused scattering
Proposed “planetary model” – but not
stable in classical physics—electron
orbits would lose energy and decay
Proposed existence of neutron as well
(proven in 1932 by Chadwick)
Nobel Prize in 1913
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Quantized Model of the Hydrogen Atom
• Niels Bohr (1885 –
1962)
• Incorporated Planck’s
& Einstein’s ideas
• Developed quantized
energy model
• Explained (some)
spectral emissions
• Nobel Prize 1922
Matter Waves
Heisenberg Uncertainty Principle
deBroglie model uses wave-particle duality
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Louis deBroglie (1892 - 1987)
1924: All moving particles behave
like matter and waves simultaneously
1927 experimental evidence:
electrons (particles) moving through
slits formed diffraction patterns (like
waves)
deBroglie Wavelength & frequency:
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λ =
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h
mv
f =
E
h
Matter waves explained Bohr model
– standing waves “fit” electron “orbits”
Nobel Prize 1929
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Electron Cloud Model
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Erwin Schrödinger (1887 – 1961)
Built on deBroglie and Heisenberg’s
ideas...developed more complex
wavefunction equation (ψ) model
Predicted behavior of e- in space
and time – think of it as predicting
where and when an e- based on
probability*
If you map out these likely locations
over time, you would see a “cloud”
of possible locations around the
nucleus*
|ψ|2 is proportional to the probability
of finding the e- at a particular
location at a particular time*
The most likely location (highest
probability) corresponds to the
Bohr/deBroglie orbits
Nobel Prize 1933
Werner Heisenberg (1901 - 1976)
1927: it is fundamentally
impossible to make simultaneous
measurements of a particle’s
position and momentum (mass x
velocity) with infinite accuracy
Result: can’t pin down location of
electron as assumed in Bohr &
deBroglie atomic models
Look at deBroglie’s equation:
λ =
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h
mv
deBroglie: If you know wavelength,
then you know the exact
momentum (p = mv) – Heisenberg
said that is impossible!
Nobel Prize 1932
The birth of quantum mechanics
• These were just a few of the scientists
who help develop an initial understanding
of a new field of physics...quantum
mechanics
• Our understanding of the sub-atomic
structure of the atom continues to evolve
through both theory and experimentation
• Many practical applications followed (e.g.,
modern electronics, lasers, nuclear power)
• *Another scientist, Max Born (1882 – 1970), is credited with developing the
statistical interpretation of Schrödinger’s equations. He won a Nobel Prize in 1954.
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