Download Lecture 14: Electromagnetic Radiation • Reading: Zumdahl 12.1

Lecture 14: 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
–  Classical and Quantum Mechanics
–  The nature of electromagnetic radiation.
–  Light has energy (Photons vs. Waves)
–  The work-function of metals. (Photoelectric Effect)
•  Problems: 12.21, 12.23, 12.25, 12.27
Classical & Quantum Mechanics
•  Mechanics: branch of the physical sciences
that deals with the motion of objects. It is
divided into two major sub-disciplines:
–  Classical Mechanics: A mathematical theory of
motion developed by Galileo, Kepler, Newton.
It describes the motions of macroscopic objects
subjected to a system of forces (F=Ma).
Velocities must be much less than the speed of
light (3x108 ms-1). Classical & Quantum Mechanics
•  In Newtonian Mechanics, the laws of
motion (i.e. Second Law of Motion: F=Ma)
are used to predict the trajectories of objects
under the influence of forces.
The velocity and position
of a mass can be predicted
for all time to arbitrary
accuracy.
Classical & Quantum Mechanics
•  Newton and Leibniz invented a branch of
mathematics called calculus to treat
mechanical problems. Position is described
as a function of time x(t), velocity v(t) is the
change of x(t) with time …called a
derivative with respect to time:
Acceleration is the derivative with respect
to time of velocity Classical & Quantum Mechanics
•  In the early 20th century, classical mechanics
failed to explain correctly a number of
experimental results and measured quantities:
–  The heat capacities Cv of atomic solids and diatomic
gases (3R and 7R/2, vs. 0 and 5R/2 at low
temperatures).
–  The frequencies of radiation emitted by a metallic
object when heated to incandescence (black body
radiation)
–  Photoelectric Effect
–  Atomic Spectrum of Hydrogen
Classical & Quantum Mechanics
•  These problems were initially explained by ad
hoc corrections to classical mechanics: –  Motions of small particles (e.g. atoms, electrons) were
confined to particular pathways (spatial quantization).
–  Energy was assumed to be absorbed in discrete
quantities called photons. Energy changes had to be in
discrete amounts: ΔE=hν.
–  Planck’s constant h=6.62x10-34 J s.
–  Small particles seemed to behave like waves and
electromagnetic radiation (i.e. waves) seemed to
display somes properties of particles.
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
Light (E&M Radiation)
•  Wavelength (λ): The distance between two
consecutive peaks in the wave.
Increasing Wavelength
λ1 > λ2 > λ3
Unit: length (m)
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.
Speed of light
Decreasing Frequency
ν1 < ν2 < ν3
Dimension: 1/time; units (1/sec)
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.
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.
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?
“The Ultraviolet Catastrophe”
•  Comparison of experiment to the “classical”
prediction which is Intensity=8πkT/λ4:
Classical prediction is
for significantly higher
intensity as smaller wavelengths than what is observed.
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.
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 oscillators
(loosing energy) to light (gaining energy).
Light as Energy
•  In general the relationship between frequency and
“photon” energy is
• Example: What is the energy of a 500 nm photon (i.e. green
light? The smaller the wavelength the higher the energy.
Consider car paint.
“No Ultraviolet Catastrophe”
•  With Planks theory of quantized energy E=hν the new
intensity is Intensity=8πhν [exp(hν/kT-1]-1 /λ4:
Planck’s theory correctly predicts that the
intensity of radiation is lower at shorter wavelengths
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.
The Photoelectric Effect
• Shine light on a metal and observe
electrons that are released.
•  Can measure the kinetic energy of
individual electrons
• 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
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
The Photoelectric Effect Explained
The slope of the
experimental line is
Planck’s Constant
Finally, notice that as the frequency
of the incident light is increased, the kinetic energy of emitted e-
increases linearly.
Φ = 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.
The Photoelectric Effect (cont.)
• For Na with Φ = 4.4 x 10-19 J, what wavelength corresponds to νo?
0
hc/λ = 4.4 x 10-19 J λ = 4.52 x 10-7 m = 452 nm
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.
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!