Transcript Waves and Modern Physics

Towards a Quantum Theory of Light
Recap of the theory of light
 Historically, physicists have grappled with the nature
of light as either a stream of particles or a wave
phenomenon.
 The ray(particle) model of light (i.e light travels in
straight lines) was supported by evidence such as
shadows cast by the sun and flashlights shining
straight beams of light. Furthermore, this theory was
supported by Newton and others. It successfully
described the properties of reflection and refraction .
Recap of the theory of light
 Christiaan Huygens, a Dutch physicist , and a
contemporary of Newton proposed a different theory. He
believed that light travelled as waves and that the wave
theory could successfully explain the phenomenon of
diffraction, the property of waves such as water waves
where the waves bend in behind obstacles. Francesco
Grimaldi demonstrated that light exhibited the property of
diffraction.
 If you hold your finger up to a light source and bring it
closer to your eye, you will notice that the border of your
finger is not clear, but blurry. This suggests that the light
waves are bending to get around your finger.
Recap of the theory of light
 In 1801, Thomas Young, a British physicist conducted
his now famous double-slit experiment
Recap of the theory of light
 Young observed the property of light wave
interference. The particle model could not explain
these results and the wave theory of light was adopted.
 The universal wave equation was given by v = fλ where
v = wave speed in m/s , f was frequency in Hz, and λ
was wavelength in m
Recap of the theory of light
 Electromagnetic waves travelled at the speed of light
i.e. c= 3.00 x 108 m/s and c = fλ
 James Clerk Maxwell showed that an accelerating
charge generated electromagnetic (EM) radiation i.e.
light. Accelerating charges generate an oscillating
magnetic field, which in turn generates an oscillating
electric field and these travel simultaneously as an EM
wave.
Recap of the theory of light
 All forms of electromagnetic radiation have been
arranged in a spectrum called the Electromagnetic
Spectrum
Recap of the theory of light
 Only a small part of the EM spectrum is visible
 IR  R O Y G B I V  UV X-rays  Gamma Rays
 λred = 670 nanometres ( 1 nm = 1 x 10-9 m)
 λviolet = 400 nanometres
 Using c = fλ, find the frequency for red and violet light.
Blackbody Radiation
 At the end of the 19th century, the spectrum of light emitted by
hot objects remained unexplained.
 All objects emit radiation and the total intensity α T4 where T is
in Kelvins.
 At lower temperatures we are unaware of this radiation as its
intensity is so low, however, at higher temperatures, we can first
feel the heat (infrared radiation) if we are close enough. As the
temperature continues to rise e.g. 1000K, objects glow like a stove
or electric toaster element. At temperatures above 2000 K the
glow is yellow or white such as a light bulb filament. This
behaviour is similar for all incandescent solids.
 The relative brightness of the glow given off i.e. the EM radiation
emitted ,depends primarily on the temperature. The spectrum of
emitted EM radiation shifts to higher frequencies
Heated objects give off light
feps.as.arizona.edu/outreach/bbwein.html
www.freefoto.com
Blackbody Radiation
 From Huygens in the late 1600’s to Maxwell in the late
1800’s physicists had been studying light and EM
radiation.
 Maxwell’s Equations summarized the knowledge on
electromagnetism and EM radiation
 http://en.wikipedia.org/wiki/Maxwell's_equations
 They represented the equivalent of Newton’s laws for
EM radiation
 The problem of blackbody radiation would upset the
established order in physics.
Blackbody Radiation
 While studying emission and absorption spectra of
gases, Gustav Kirchhoff and Robert Bunsen observed
that when gases were heated to a high enough
temperature, light of different frequencies was given
off.
 When white light was shone through the gases, they
absorbed the same frequencies they emitted, so
Kirchhoff reasoned that all objects absorb the same
frequencies of radiation they emitted and further that
since black objects absorb all frequencies of light, they
should emit all frequencies when heated sufficiently
Blackbody Radiation
 So a “blackbody” is a perfect radiator as it emits the full
spectrum of EM radiation .
 Blackbodies can be easily simulated in the lab


The Physics Hypertextbook™© 1998-2008 by Glenn Elert -- A Work in Progress
feps.as.arizona.edu/outreach/bbwein.html
Blackbody Radiation
 The graphs showed that as the temperature of an
incandescent body increased, the frequency of light
emitted with he highest intensity becomes higher
 Kirchhoff couldn’t explain the relationship
 Josef Stefan showed that the power emitted by a
blackbody radiator
 Pα Temp4
 This did not fit the experimental data completely.
Ultraviolet catastrophe
 Classical physics was able to explain the observed
behaviour at low frequencies, but fell apart at higher
frequencies, in particular in the UV (ultraviolet) part
of the spectrum.
 http://www.vectorsite.net/tpqm_01_01.png
Enter Quantum Theory
 Max Planck, a student of Kirchhoff, was able to explain the




graph of frequencies of a blackbody radiator.
He assumed that the energies of the oscillators in the walls
of the radiator were, in fact, discrete and that the energy
levels were “quantized”
E = hf where h is a constant and f is the frequency of the
radiation.
An oscillator could only have an energy level which was an
integral multiple of hf
When the blackbody emitted radiation, it had to drop one
or more levels and emit a unit or quantum of energy equal
to the difference between allowed levels.
Quantum Theory
 Despite the agreement of the data with Planck’s
theory, many physicists including Planck himself
remained sceptical feeling that more evidence was
required before accepting energy quantization.
The Photoelectric Effect
 Discovered by accident when Hertz was investigating EM (1887)
 Hertz apparatus
 Sparks set up in transmitter circuit generated EM radiation i.e.
energy in receiver circuit
 When UV light was shone on metal electrodes, sparks were
enhanced- he didn’t know why
 In 1897, JJ Thomson discovered the electron and physicists then
suggested that UV light caused electrons to be elected from
electrodes creating the conducting path.
 Ejection of electrons by UV light became known as the
photoelectric effect
Early Photoelectric Effect
Experiments
 Lenard (1902) set up apparatus as shown in your text p. 845 and
experimented with different frequencies of light and varying the
polarity of the power supply.
 He discovered the stopping potential i.e. the voltage which
would oppose the flow of the photoelectrons.
 He concluded that when the intensity of the light striking the
emitted increases, the number of ejected electrons increases and
that the max KE of the ejected electrons is determined only by
the frequency of the light not the intensity.
 The latter conclusion could not be explained by classical wave
theory.
Einstein and the Photoelectric
Effect
 Lenard’s work raised even more questions from an already sceptical
physics community
 Einstein (1905) proposed that light must be both absorbed and emitted
as packets (bundles) of energy called quanta or photons.
 He said that E =hf is the energy of a photon and when a photon hits a
metal surface, all its energy is absorbed by one electron. This meant
that higher frequency light (photons) would be able to give more KE to
the photoelectrons. Furthermore, increasing the intensity of the light
would only change the number of photons not the energy of each
photon.
 Einstein further indicated that some of the photon’s energy must go
into freeing the electron from the surface. The more tightly bound the
electron, the more energy is required to liberate it from the surface.
This is the work function of the metal.
Einstein and the Photoelectric
Effect
 E = W + KE (max)
 hf = W + KE (max)
 KE (max) = hf – W this looks like y = mx + b with a
negative intercept
 Robert Millikan (1916) set out to prove Einstein wrong,
but his data confirmed Einstein’s proposals
 The x-intercepts on the graphs of Kinetic energy vs
frequency for different metals showed the threshold
frequencies (minimum) for the different metals to
reach the surface but not to exit the surface since they
have no KE; they are drawn back into the metal.
The Electron Volt
 Because the energies of photoelectrons are fractions of
a Joule (a large unit for the sub-atomic world), we use
another unit called the electron volt (or eV)
 Since E = qV, 1eV = (1e)(1V) = (1.602 x 10-19 C)(1V)
 1eV = 1.602 x 10-19 J
 The photoelectric effect was used in light meters to
measure the intensity of light.