Lecture 16: Electromagnetic Radiation
Light and the Quantum Mechanical Nature of Molecules.
The energy in molecules that drives chemical reactions.
• Reading: Zumdahl 12.1, 12.2
• Outline
– The nature of electromagnetic radiation.
– Light has energy (Photons vs. Waves)
– The work-function of metals. (Photoelectric Effect)
• Problems (Zumdahl 5th Ed., Ch 12)
– 1, 22, 23, 24, 26, 27, 29
1
Electromagnetic Radiation
• Electromagnetic radiation or “light” is a form of energy.
• Has both electric (E) and magnetic (H) components.
• Light is the only way we communicate with molecules.
• Characterized by:
–Wavelength (λ)
–Amplitude (A)
Show spectrum of light
2
Light (E&M Radiation)
• Wavelength (λ): The distance between two
consecutive peaks in the wave.
Increasing Wavelength
λ1 > λ2 > λ3
Unit: length (m)
3
Light
• Frequency (ν): The number of waves (or cycles) that pass
a given point in space per second.
• The product of wavelength (λ) and frequency (ν) is a
constant.
8
λν = c = 3 ⋅10 m sec
Speed of light
Decreasing Frequency
ν1 < ν2 < ν3
Dimension: 1/time; units (1/sec)
4
Spectrum
Electromagnetic radiation by wavelength, (or frequency)
•
Visible radiation takes up only a small part of the electromagnetic
spectrum. Two fold change from red to blue.
5
Light as Energy
• For times before 1900, it was assumed that energy
and matter were not the same.
• The interaction of light with matter was one of the
first examples where the separation of energy and
matter fell apart.
• Einstein’s theory of relativity (1905) related
energy of light and momentum, even though light
has no mass, it does have momentum (p):
Elight = cp
6
Light from a Glowing Object (“Black Body”)
• The experiment on light is to measure the intensity of the
light as a function of the wavelength (or frequency) of the
light that is emitted from a solid object heated to
“incandescence” (i.e. until it glows, “red hot”).
As a body is heated, intensity
increases, and peak
wavelength shifts to smaller
wavelengths.
Can “classical” physics
understand this observation?
7
“The Ultraviolet Catastrophe”
Comparison of experiment to the “classical” prediction:
Classical prediction is
for significantly higher
intensity as smaller
wavelengths than what
is observed.
8
Energy of Light
• Planck found that in order to model this behavior,
one has to envision that energy (in the form of light)
is proportional to the frequency of the light.
• The light came from the molecules in the walls
vibrating or oscillating, and that the energy of the
light was due to the change in the energy of the
molecules in the material.
Δ E = h ⋅ν
Energy Change in
molecules as they
oscillate
Frequency of light
h = Planck’s constant = 6.626 x 10-34 J.s.
Energy is conserved: Energy is transferred from the oscillators9
(loosing energy) to light (gaining energy).
Light as Energy (Prob: Z12.22-26)
• In general the relationship between frequency and
“photon” energy is
Relativity
Classical E&M
E photon = cp
λν = c
ΔE = EPhoton = h ⋅ν = hc ⇐ Planck
λ
• Example: What is the energy of a 500 nm photon of (green)
light? The smaller the wavelength the higher the energy.
3 ⋅10
+14
+14
ν= =
=
6
⋅
10
=
6
⋅
10
Hz
−7
s
λ 5 ⋅10
E = hν = 6.6 ⋅10−34 ⋅ 6 ⋅10+14 = 4 ⋅10−19 Joules photon
E = 240kJ / mole(of photons )
c
8
Consider car paint.
10
Waves vs. Particles
• We began our discussion by defining light in terms of
wave-like properties.
• But Planck’s relationships suggest that light can be
thought of as a series of energy “packets” or photons.
11
The Photoelectric Effect
• Shine light on a metal and observe
electrons that are released.
• Can measure the kinetic energy of
individual electrons
metal
• Find that one needs a minimum frequency (“νo”) to eject
any electrons at all is the minimum amount of photon
energy.
• Also find that for ν ≥ νo, the number of electrons
increases linearly with light intensity, but not the kinetic
energy of the individual electrons.
Show photoelectric effect
12
Classical Thought and the Photoelectric Effect
What Classical Theory Predicted (assumed energy of light is
proportional to intensity).
A more intense light
source would make the
ejected electrons leave
with greater velocity
The velocity of the
electrons would be
independent of the
frequency of the light
What actually happened experimentally
The velocity of
the electrons
depends on the
frequency of light
The intensity of the light did not
affect the velocity of the
individual electrons, but the
number ejected is proportional to
the intensity
Explanation: Energy of light is proportional to frequency
13
The Photoelectric Effect Explained
As the frequency of the incident
light is increased, the kinetic
energy of emitted e- increases
linearly.
The slope of the
experimental line is
Planck’s Constant
E photon −in = ΔEelect
hν phot = ΔEelect
0
ν0
Frequency (ν)
1
2
= me v + Φ
2
Φ = hν o : Potential Energy
needed to release e-
• Light behaves as a particle. When an electron is ejected, it happens
because one electron interacts with one photon and takes its energy
from that photon. Energy is conserved.
14
The Photoelectric Effect (Prob Z12.27,29)
• For Na with Φ = 4.4 x 10-19 J,
what wavelength corresponds to νo?
0
1
2
me v = hν photon − Φ
2
hν o = Φ = 4.4 ⋅ 10-19 J
0
ν0
Frequency (ν)
hc/λ = 4.4 x 10-19 J
6.626x10−34 J.s)(3x10 8 m /s)
(
hc
λ=
=
−19
4.4 x10 J
(4.4 x10−19 J )
λ = 4.52 x 10-7 m = 452 nm15
Interference of Light
• Shine light through a crystal and look at pattern
of scattering.
• Diffraction can only be explained by treating light
as a wave instead of a particle.
16
Summary
• We have seen experimental examples where
light behaves both as a particle and as a wave.
• This is referred to as “wave-particle” duality.
• Wave-particle duality is not limited to light!
All matter demonstrates this behavior.
• Need something more than classical physics to
describe such behavior….quantum mechanics!
17