Announcements
• HWK 7 due Wed. 10AM.
• Week 7 online participation available at
the website.
• Reading for Mon.: TZ&D Chap. 5.1-5.4
on atomic spectra.
Einstein’s Explanation of the Photoelectric Effect
Photon…
Puts in kick of energy
KE = photon energy – work function
energy needed to kick
highest electron out of metal.
“WORK FUNCTION” (φ)
Each photon has: E = h f = Plancks constant * Frequency
(Energy in Joules)
E=hf=(6.626*10-34 J-s)*(f s-1)
E=hc/λ = (1.99*10-25 J-m)/(λ m)
(Energy in eV)
E=hf= (4.14*10-15 eV-s)*(f s-1)
E= hc/λ = (1240 eV-nm)/(λ nm)
KEELECTRON = hf − φ
Depends on type
of metal.
KE300
V
A photon of 300 nm will kick out an electron with an
amount of kinetic energy, KE300. Consider a photon of
half the wavelength hitting the same electron in the
same metal. KE150 of the electron coming out is:
A)less than ½ KE300.
B) ½ KE300.
D) 2 x KE300.
E) more than 2 x KE300
C) = KE300
KE300
V
A photon of 300 nm will kick out an electron with an
amount of kinetic energy, KE300. Consider a photon of
half the wavelength hitting the same electron in the
same metal. KE150 of the electron coming out is:
more than 2 x KE300
hf150
hf300
KE300
KE = photon energy-work function
= hf - Φ
if λ is ½ then, f twice as big, Ephot =2hf300
so have new KEnew= 2hf300- Φ
compared with KE300 =hf300- Φ
so KEnew is more than twice as big.
Student question:
Why do the electrons in the simulation come out
with different energies if all the incoming
photons come in with the same energy?
e’s
I
Photoelectric effect experiment: Photons still conserve Energy
Energy in = Energy out
Energy of photon = Work function + Initial KE of electron
gets electron out
left-over energy
Electron Potential
Energy
Loosely stuck electron, takes least energy to kick out
work function (Φ) = energy needed to kick
Outside
metal
Inside
metal
highest electron out of metal
Tightly stuck, needs more energy
to escape
Apply Conservation of Energy with Photons.
Energy in = Energy out
Energy of photon = Work function + Initial KE of electron
gets electron out
left-over energy
Electron Potential
Energy
What happens if send in bunch of blue photons?
Ephoton
work function (Φ)
Outside
metal
Photon gives electron
“kick of energy”.
Inside
metal
Electrons have equal chance of absorbing photon:
Æ Max KE of electrons = photon energy - Φ
Æ Min KE = 0
Æ Some electrons, not enough energy to pop-out, energy into heat.
Typical energies for photoelectric problems
Photon Energies:
Each photon has: E = hf = Planck’s constant * Frequency
(Energy in Joules)
(Energy in eV)
E=hf=(6.626*10-34 J-s)*(f s-1)
E=hc/λ = (1.99*10-25 J-m)/(λ m)
Red Photon: 650 nm
E=hf= (4.14*10-15 eV-s)*(f s-1)
E= hc/λ = (1240 eV-nm)/(λ nm)
Ephoton = 1240 eV-nm = 1.91 eV
650 nm
Work functions of some metals (in eV):
Aluminum
4.08 eV
Cesium
2.1
Lead
4.14
Potassium
2.3
Beryllium
5.0 eV
Cobalt
5.0
Magnesium
3.68
Platinum
6.35
Cadmium
4.07 eV
Copper
4.7
Mercury
4.5
Selenium
5.11
Calcium
Carbon
2.9
4.81
Gold
Iron
5.1
4.5
Nickel
Niobium
5.01
4.3
Silver
Sodium
4.73
2.28
Uranium
3.6
Zinc
4.3
KE300
V
Shine in light of 300 nm on some metal. The most energetic
electrons come out with kinetic energy, KE300. A voltage
diff of 1.8 V is required to stop these electrons. What is
the work function Φ for this plate?
a. 1.2 eV
b. 2.9 eV
c. 6.4 eV
d. 11.3 eV
e. none of the above
KE300
V
CQ: Shine in light of 300 nm, most energetic electrons come out with kinetic energy,
KE300. A voltage diff of 1.8 V is required to stop these electrons. What is the work
function Φ for this plate? (e.g. the minimum amount of energy needed to kick e out of
metal?)
a. 1.2 eV
b. 2.9 eV
c. 6.4 eV
d. 11.3 eV
e. none
Energy is conserved so:
the energy at the start (Ephot) = energy at end
⇒ Ephot= energy of the electron + energy to escape metal, Φ.
so
Φ= Ephot - electron energy
but electron energy = e x 1.8V = 1.8 eV, and
Ephot = 1240 eV nm/300 nm = 4.1 eV.
So Φ = 4.1eV - 1.8 eV = 2.3 eV
Photomultiplier tubes- application of photoelectric effect
most sensitive way to detect visible light, see single photons
(eye is incredibly good, can see a few photons)
glass vacuum enclosure
current
electron
big voltage
amplifier,
gives pulse of
current for each
photoelectron
B
1
2
3
4
5
Time (millisec)
What is the best material for
sensing the widest range of
photon wavelengths?
a. Platinum
Φ = 6.35 eV
b. Magnesium
= 3.68 eV
c. Nickel
= 5.01 eV
d. lead
= 4.14 eV
e. Sodium
= 2.28 eV
Photomultiplier tubes- application of photoelectric effect
most sensitive way to detect visible light, see single photons
(eye is incredibly good, can see a few photons)
glass vacuum enclosure
cq2. what would be the best
electron
big voltage
choice of these materials to
amplifier,
make this out of?
gives pulse of
a. Platinum
Φ = 6.35 eV
current for each
b. Magnesium
= 3.68 eV
photoelectron
c. Nickel
= 5.01 eV
e. sodium. 2.28 eV
d. lead
= 4.14 eV
lower work function means
= 2.28 eV
most visible light (<544 nm) will be e. Sodium
detected. Enough energy to eject electrons.
But there’s more…
Reading Quiz
Photons are particles that:
A) Have no mass and therefore no energy by E = mc2
B) Have no mass and therefore carry no momentum
C) Have no mass and therefore always have p = mc
D) Have no mass and therefore a momentum h/λ
E) None of the above.
Massless Particles!!
The photon is our first example of a relativistic
and massless particle. Always travels at the
speed of…light! Still satisfies relativity, but
without any mass:
0
E = ( pc ) + ( mc
2
2
)
2 2
So:
E hf h
p= =
=
c
c λ
Other examples: Graviton and (almost…!) the neutrino.
Big Picture Stuff so far:
Matter seems to come in chunks, or quanta. Most
obvious 19th century example is atoms of the
periodic table. Sub-atomic matter also comes in
quanta e.g., electrons, protons, neutrons. Mass,
electric charge, and spin properties are quantized.
LIGHT seems to come in quanta too. Have a good
wave theory (Maxwell), but experiment requires
photons, the quanta of light. The photon properties,
energy and momentum, are quantized:
E = hf
p=
h
λ
Big Picture Stuff Questions:
Are there other examples of physical properties
that are quantized??
If matter is quantized, is there a good wave theory
for it too??
Might that wave theory associate a frequency and a
wavelength with particle energy and momentum?
Kind-a like:
E = hf
p=
h
λ
What about photon dynamics? Why does a
photon get absorbed when it does??
?
Next week (Chapter 5)…
• Optical spectra of atoms show
quantization effects.
• The construction of the first simple wave
pictures of matter.
• Predictions of the frequency and
wavelength of material particles.
?
NO THEORY yet exists to explain why, when, and where
the photon is absorbed… NO EXPERIMENT has ever
seen that the processes can be accurately controlled.