Physical Chemistry 20130429 week 5 Monday April 29, 2013 page 1
Consider a two dimensional graph with R(ν) on the vertical axis and ν on the horizontal axis. One curve
starts at the bottom left and curves up and right, peaking at around (4*1014s-1,3) then coming back down
asymptotically to 0. That’s the curve for 1500K. A second curve starts at the bottom left and goes up
and right not as fast, but ends up peaking higher at around (8*1014s-1,4) then coming back down
asymptotically to 0. That’s the curve for 2000K. R(ν) is emitted radiation per surface area.
Consider any hollow opaque object with just one tiny hole for an entrance. This is called a cavity. As
light enters the hole, it will bounce around inside until it’s completely absorbed. Since a cavity is a
perfect absorber, it’s a perfect emitter.
equipartition of energy
2πkT
Derived from classical physics: R(ν)= ( 2 ) ν2
c
k is Boltzmann constant
This formula leads to the UV catastrophe. By that formula, there should be no darkness. Even at room
temperature, everything should emit visible and ultraviolet light.
Now we’re starting quantum mechanics:
Plank did this derivation by hand (trial and error).
≈1900
R(ν)=
R(ν)=
aν2
bν
(e ⁄T -1)
2πh ν2
c 2 ehν⁄kT -1
a=
2πh
c2
b=
h
e
k is Boltzmann constant
This is where Plank ' s constant comes from.
The derivation depends on an important assumption.
Heat makes atoms vibrate. Plank called them oscillators. He said energy wouldn’t concentrate in high
energy oscillators. This means we hardly get high frequencies of light. Energy doesn’t concentrate in
just one atom.
Wien’s Law: λmaxT=constant=2.898*10-3 K-m
Stefan-Boltzmann Law: P=σT4
Kelvins
P is power
K is Kelvins
m is meters λmax=wavelength at peak
σ=56.4nWm-2K4
P is power
nW is nanowatt K is
By classical mechanics, energy levels can be any value. By quantum mechanics (Plank’s model), energy
levels can only be certain values: E0, E1, E2, E3….
red flag: photoelectric effect
Einstein got the Nobel Prize for the photoelectric effect, not relativity.
Lenard (1900)
Consider a metal with a layer of potassium on it. Say electromagnetic radiation hits this from an angle.
The EM radiation is symbolized hν. Where the EM radiation hits the surface, electrons come off at the
opposite angle. The electrons are symbolized e.
Energy comes in packages. ∆E=nhν
n=0,1,2,3…
ν is frequency
h=6.63*10-34 Js
Consider a graph with KE (kinetic energy) on the vertical axis and ν (frequency)of the incoming light on
the horizontal axis. From a nonzero horizontal position on the x axis (ν0) a diagonal line goes up and
right. The x intercept ν0 is the threshold frequency.
Consider a graph with number of electrons ejected on the vertical axis and light intensity on the
horizontal axis. Assuming ν is constant and ν > ν0, the graph is a straight diagonal line up and right from
the origin.
Consider a graph of KE (kinetic energy) of the ejected electrons on the vertical axis and light intensity on
the horizontal axis. The result is a horizontal line above y=0. This violates classical physics. By classical
physics: Iαε2 where ε is amplitude.
Einstein (1905): Electromagnetic radiation (light) comes in elementary units (quanta) and it is the
energy of the elementary unit (NOT the total energy) that determines whether an electron is liberated
or not. G. N. Lewis called these units “photons.”
analogy: 2000 machine gun bullets to a target = no damage but 1 15” shell = destroyed target
Consider a graph of voltage (V) on the vertical axis and ν (frequency) on the horizontal axis. From a
point (ν0,0) a diagonal line goes up and right. The formula for this line is hν=hν0+KE where KE is kinetic
energy. The slope of this line is h/e where e is the charge of an electron.
KE=.5mv2=eV
v is speed
V is voltage
Charge * voltage = energy
hν – hν0 = eV
h
(ν-ν0 )=V
e
V is voltage
We know e so we can find h.
1
hνphoton =ϕ+ mv 2
2
ɸ is work function. It’s the minimum energy to remove an electron.
1. If hνphoton < ɸ then there is no photoelectric effect. The light gets scattered.
2. Since ν0 = constant for a given metal:
ɸ=hν0
ɸ is constant
3. If hνphoton > ɸ then as ν↑ so does the KE of the ejected electron.
red flags: 1. heat capacity
2. blackbody radiation
3. photoelectric effect
Light is very complex.
Light has wave properties: 1. diffraction
2. interference
Electrons can undergo diffraction, so electrons can behave like waves.
Suppose there is a wall with a small hole. Light hits the wall from the left side, so light can go through
the hole. Right of the whole the light spreads out into cocentric circles, centered on the whole. To the
right is a screen. See the handout. On the screen there are cocentric circles, with a bright dot at their
center. Each larger circle is not as bright as the one inside it.