Franck-Hertz Experiment
lasers
“We thought it [the laser] might have some uses, but we had no
application in mind. If we had, it might have hampered us…”—A.
Schawlow, one of the inventors of the laser
The Franck-Hertz* Experiment (1914)
This famous experiment confirmed the existence of Bohr’s
atomic energy levels.
Accelerated electrons colliding
with atoms give up energy to
atomic electrons, provided their
energy is sufficient to promote
an atomic electron from one
energy level to a higher one.
*1925 Nobel Prize for Franck and Hertz. And no, not the Hertz of Hz fame.
Gustav Hertz, not Heinrich Hertz.
Hyperphysics shows the
experimental setup (previous
slide) and this actual data.
(Note: I purchased a
hyperphysics “license” to use
this material in my teaching.)
Here is an interactive Franck-Hertz experiment.
Things I might ask on a test: what did this experiment
demonstrate? Interpret the dips in the current versus voltage
curve.
4.9 Lasers
Background information and terms.
Absorption and emission
(induced) absorption -- we have talked
about this already; a photon raises an atom to
an excited state
(spontaneous) emission -- we have talked about this
already; an atom in an excited state drops back to the ground
state via emission of a photon
(induced) emission -- a photon of the energy required to
produce induced absorption can induce an atom to drop from
the excited state back to the ground state -- the probability of
this occurring is same as the probability of absorption
occurring
huh?
“Induced emission” is also called stimulated emission. For
atoms in a radiation field, quantum theory (Einstein, 1916)
shows that the probability of a ground state atom absorbing a
photon is equal to the probability of an excited state atom
emitting the same photon.
Those of you who have pushed children (or
brothers, sisters, etc.) on a swing have
experienced this.
You can give the swinger energy by pushing in
phase with the swings.
Or you can remove energy from the swinger by pushing out of
phase with the swings.
Those of you who have sunk your fleet of toy ships
in the bathtub by sloshing back and forth to make
ever-increasing waves have done the same.
When mom hollers, you absorb the wave energy by sloshing
out of phase.
More terms:
lifetime
Here’s a schematic energy-level
diagram of an excited state.
Most excited states have very short
lifetimes.
E1 > E0
excited
state
E0
ground
state
electron
metastable state -- a relatively long-lifetime excited state
population inversion -- a majority of the atoms in a system
are in excited states
If a majority of atoms are in excited states, then emission
rather than absorption is more probable.
optical pumping -- using photons to create a population
inversion
Laser: light amplification by stimulated emission of radiation.
Required for a laser:
metastable states in the lasing material
an optical cavity
method of pumping metastable states to achieve a
population inversion
We’ll see the significance of all these fine-sounding
requirements in a bit.
Any Nobel Prizes? Townes, Basov, and Prokhorov, 1964. Also Bloembergen
and Schawlow, 1981; Chu, Tannoudji, and Phillips, 1997; and Cornell,
Ketterle, and Wieman, 2001. Maybe if you want a Nobel prize, do
something with lasers! On the other hand, Gordon Gould invented the “laser”
and built the first one; it took 20 years for him to win any recognition for it.
Properties of lasers
Laser light is:
 coherent; i.e. all waves are exactly in phase
 (nearly) monochromatic
 controlled by the size of the aperture through which
it leaves; the divergence can be made extremely small
 very intense (1030 K, whatever a temperature that
high really means)
More toys! (Illustrating some of the above properties.)
Let’s make a laser. Begin by finding an atom with a
metastable state. Atomic spectroscopists have measured
zillions of atomic states, so we can surely find one.
Start to make a population inversion, by exciting an electron to
the metastable state. Remember,
this state lives a long time.
Now excite another electron to
the metastable state.
E1 > E0
E0
metastable
state
ground
state
Oh dang! I forgot that the incoming photon is just as likely to
induce emission as it is to induce absorption.* (Another toy
here.)
This won’t work! What to do?
*This picture does not reflect reality. I really should draw many different atoms,
showing an electron in each. Also, the 2nd photon could excite a 2nd electron.
You “can’t”* make a two-level optically-pumped laser.
Key bit of knowledge we won’t introduce until chapter 6: all
transitions have probabilities of occurring. Some transitions
have greater probabilities than others.
The intellectual leap: if I can find an atom with an excited
state and a nearby metastable state…
and if the transition from the excited state to the metastable
state is far more likely than the transition from the excited
state to the ground state…
then I can make a three-level laser.
*Not a good idea to say “can’t.” See here.
A three-level laser; the setup:
excited state
E2
E1
E0
metastable
state
ground
state
A three-level laser; how it works:
Excited
the transition to the metastable
state could be radiationless
Metastable
Ground
Put an electron in the metastable state.
(using collisions or photons)
More, more, more, more!
Notice: red photons come out not in phase. Wasted! But
population inversion has been created.
Now we have all these electrons in a metastable state. What
next?
Excited
Metastable
It’s 3:05 on a Friday. My lecture is running way over time and
shows no sign of stopping. You are all sitting here with your
packed backpacks in hand, anxious to go.
Ground
One of you can’t take it any more and walks noisily out.
Boom! You all go.
Students have been simulating
lasers for decades!
You can wait and let the final step happen naturally, or you can
stimulate it by sending in a photon having an energy equal to
the energy difference between metastable and ground state.
Excited
Metastable
Ground
The photons come virtually out all at once, and in phase!
I did “cheat” on the last slide. I made the
electrons drop to the ground state all at the
same instant, and made the photons come out
all in the same direction. They don’t. See here.
Remember the requirements for a laser?
metastable states in the lasing material--check
method of pumping metastable states to achieve
a population inversion--check
an optical cavity—missing from this presentation
Howstuffworks shows what the optical cavity does. Here’s a
toy showing the effect.
A ruby* laser is an example of a three-level laser as described
above.
excited state
2.25
eV
optical pumping
550 nm
ground state
radiationless transition
metastable
state
laser transition
694.3 nm
0 eV
Know the meaning of all the terms in the figure above!
Be able to calculate the energies and wavelengths for all
transitions!
*What’s a ruby?
1.79
eV
For a three-level laser to work, more than half the atoms must
be in the metastable state.
It would be “nice” to get lasing without having to pump so
“hard.”
A four-state laser does just that. On the next slide is a
schematic of a He-Ne laser. Sorry, no fancy animations on this
one.
He-Ne laser (energy levels not drawn to scale):
(2)
excited state
20.61 eV
(3)
(4)
metastable state 20.66 eV
excited state 18.70 eV
(1) electron impact
(2) collisions (of
what?)
(1)
(5)
(3) laser transition
632.8 nm
(4) spontaneous
emission
ground state
helium
neon
(5) radiationless
transition
Be able to explain terms and calculate energies and wavelengths!
Applications of lasers.
“It’s a solution looking for a problem!”
The National Ignition Facility
NIF is a 192-beam 1.8 MJ laser for creating conditions of
extreme temperatures and pressures in the laboratory.
The purpose: fusion!
The 192 lasers will be
focused on a target about
the size (if I remember
correctly) of the tip of a
ballpoint pen.*
Fusing about 10 targets*
per second would
produce a net energy
output comparable to a
1000 MW power plant.
Not everybody thinks this is a good idea!
*Rough figures vaguely remembered from a lecture several years ago.
Applets and other handy links, mostly already used above:
http://jersey.uoregon.edu/vlab/elements/Elements.html
http://dbhs.wvusd.k12.ca.us/Electrons/Spectrum-History.html
http://www.colorado.edu/physics/2000/quantumzone/lines2.html
http://www.colorado.edu/physics/2000/quantumzone/bohr2.html
http://www.howstuffworks.com/laser2.htm
http://www.repairfaq.org/sam/lasersam.htm
http://www.llnl.gov/nif/construction/october2001.html
http://www.colorado.edu/physics/2000/lasers/lasers2.html