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Quantum Theory of Light
A TimeLine
Light as an EM Wave
Light as an EM Wave (Maxwell 1865-1873)
Quantum theory did not begin with an attempt to explain the behaviour of light.
Light as an EM Wave (Maxwell 1865-1873)
Quantum theory did not begin with an attempt to explain the behaviour of light.
Scientists had already accepted Maxwell’s description of light!
Light as an EM Wave (Maxwell 1865-1873)
Maxwell had proposed that light was an electromagnetic disturbance created by extremely high frequency oscillators.
Light as an EM Wave (Maxwell 1865-1873)
Maxwell had proposed that light was an electromagnetic disturbance created by extremely high frequency oscillators.
Light as an EM Wave (Maxwell 1865-1873)
It was assumed from this theory that these oscillators (resonators) were able to emit light of frequency equal to their own.
Light as an EM Wave (Maxwell 1865-1873)
Hertz was successful in indirectly proving (was no way frequencies higher than 109 Hz) the theory by showing that it described the properties of light.
Light as an EM Wave (Maxwell 1865-1873)
Hertz was successful in indirectly proving (was no way frequencies higher than 109 Hz) the theory by showing that it described the properties of light.
I.e. Reflection, interference etc.
Light as an EM Wave (Maxwell 1865-1873)
Hertz was successful in indirectly proving (was no way frequencies higher than 109 Hz) the theory by showing that it described the properties of light.
I.e. Reflection, interference etc. (Hertz unknowingly discovered the
photoelectric effect during his experimental verifications)
Light as an EM Wave (Maxwell 1865-1873)
The success of the theory lead to its application to the blackbody radiation problem.
Light as an EM Wave (Maxwell 1865-1873)
The success of the theory lead to its application to the blackbody radiation problem.
However all attempts failed. (see Wien, Rayleigh-Jeans Law)
Planck (1900)
The discovery by Planck was the beginning of quantum theory.
Interpolating Wein’s law and the relationship at low frequency he showed that
1
18),(
3
3
kThfec
hfTfu
Planck (1900)
From his work he concluded that the energy was quantised, where the frequency f can only be an integral multiple of hf.
Planck (1900)
That is the energy which an resonator can lose is nhf, where n = 1,2,3… .
Planck (1900)
That is the energy which an resonator can lose is nhf, where n = 1,2,3… .
The idea of quantised energy levels (states) was the significant development.
Planck (1900)
That is the energy which an resonator can lose is nhf, where n = 1,2,3… .
The idea of quantised energy levels (states) was the significant development.
This assumption contradicted what was accepted classically.
Planck (1900)
Using this assumption he was able to correctly produce a theory which agreed with experimental results.
Planck (Summary)
In deriving his formula he made two assumptions:
The energy of an oscillator of frequency f can only be nhf.
During an emission or absorption the change in energy is hf.
Planck (Summary)
Despite the significance, it was left to Einstein to develop these ideas to the next step.
Photoelectric Effect(1905)
Photoelectric Effect (1905)
When a metallic surface is illuminated by light can cause electrons to be emitted from the surface.
Photoelectric Effect (1905)
The number of electrons ejected from the metal surface per second depends on the intensity of the light.
Photoelectric Effect (1905)
The number of electrons ejected from the metal surface per second depends on the intensity of the light. -expected
Photoelectric Effect (1905)
The number of electrons ejected from the metal surface per second depends on the intensity of the light.
The kinetic energy of the electrons did not depend on intensity.
Photoelectric Effect (1905)
The number of electrons ejected from the metal surface per second depends on the intensity of the light.
The kinetic energy of the electrons did not depend on intensity.
Kinetic energy of the electrons depends on the wavelength of the light.
Photoelectric Effect (1905)
The number of electrons ejected from the metal surface per second depends on the intensity of the light.
The kinetic energy of the electrons did not depend on intensity.
Kinetic energy of the electrons depends on the wavelength of the light. And there was a cut of wavelength where no electrons are emitted.
Einstein - Photoelectric Effect (1905)
Noted that although Maxwell’s classical theory described the interaction of light over a long period, a new description was needed for the individual interactions of light and matter.
Photoelectric Effect (1905)
He extended Planck’s ideas to include that light was also quantized.
Photoelectric Effect (1905)
He extended Planck’s ideas to include that light was also quantized.
Light and matter interactions occur in discrete packets called photons.
The energy of a photon is
hc
hf
Compton Effect (1922)
Compton Effect (1922)
The Compton effect shows that photons behave like particles with momentum
c
hf
Compton Effect (1922)
The Compton effect shows that photons behave like particles with momentum
Classical theory predicted that incident radiation of frequency f0 would cause electrons to be acceleration in the direction of the radiation
c
hf
Compton Effect (1922)
The Compton effect shows that photons behave like particles with momentum
Classical theory predicted that incident radiation of frequency f0 would cause electrons to be acceleration in the direction of the radiation and that the freq of the scattered radiation depend on the intensity and time of exposure.
c
hf
Compton Effect (1922)
Instead Compton showed that only on the scattering angle.
Compton Effect (1922)
Instead Compton showed that only on the scattering angle.
This result disagrees with classical theory
Compton Effect (1922)
Instead Compton showed that only on the scattering angle.
This result disagrees with classical theory and is only explained if the photons act as particles.
Wave-Particle Duality
Wave-Particle Duality
Various experiments have been shown which highlight either the wave nature or particle nature of light.
Wave-Particle Duality
Various experiments have been shown which highlight either the wave nature or particle nature of light.
Is light simultaneous a wave and a particle?
Wave-Particle Duality
Various experiments have been shown which highlight either the wave nature or particle nature of light.
Is light simultaneous a wave and a particle?
Many questions on the nature of light arise from issues in classical mechanics.
Wave-Particle Duality
Classically the two have mutually properties.
Both views are required to describe the behaviour of light.
Wave-Particle Duality
Classically the two have mutually properties.
Both views are required to describe the behaviour of light.
Neither model can exclusively describe radiation adequately.
Wave-Particle Duality
Classically the two have mutually properties.
Both views are required to describe the behaviour of light.
Neither model can exclusively describe radiation adequately.
Therefore for now both must be used.
Bohr Atom
Particle Nature (1913)
Bohr Atom
The Bohr model was developed from the work of Rutherford to describe a stable atomic model.
Bohr Atom
The Bohr model was developed from the work of Rutherford to describe a stable atomic model.
He provided to first successful theory of atomic line spectra.
Bohr Atom
For his model he postulated that classical radiation theory did not hold at the atomic level.
Bohr Atom
For his model he postulated that classical radiation theory did not hold at the atomic level.
He also used the work Planck and Einstein for the idea of quantised energy levels and quantisation of light.
Bohr Atom
From these ideas he proposed that electrons generally remained in stable, stationary states.
However when an electron moves between states specific frequency radiation is emitted.
Matter Waves
De Broglie (1923)
Matter Waves
By the early 1920s it was recognised that the Bohr theory had many inadequacies:
Matter Waves
By the early 1920s it was recognised that the Bohr theory had many inadequacies:
It could not predict the observed intensities of spectral lines.
Matter Waves
By the early 1920s it was recognised that the Bohr theory had many inadequacies:
It could not predict the observed intensities of spectral lines.
Limited success in predicting emission, absorption wavelengths of multi-electron atoms.
Matter Waves
Overemphasized the particle nature but couldn’t explain the wave-particle duality.
Matter Waves
Overemphasized the particle nature but couldn’t explain the wave-particle duality.
Didn’t supply a general scheme for quantising other systems.
Matter Waves
Overemphasized the particle nature but couldn’t explain the wave-particle duality.
Didn’t supply a general scheme for quantising other systems.
Just a few of the problems.
Enter Louis deBroglie
Matter Waves
He proposed that all forms of matter have wave
Matter Waves
He proposed that all forms of matter have wave and particle properties.
Matter Waves
He proposed that all forms of matter have wave and particle properties.
But couldn’t be confirmed at the time.
Matter Waves
He proposed that all forms of matter have wave and particle properties.
But couldn’t be confirmed at the time. According to de Broglie, electrons also
had a particle and wave nature.
Matter Waves
He proposed that each electron was accompanied by a wave
Matter Waves
He proposed that each electron was accompanied by a wave (not an EM wave)
Matter Waves
He proposed that each electron was accompanied by a wave (not an EM wave) which piloted the electrons through space.
Matter Waves
He proposed that each electron was accompanied by a wave (not an EM wave) which piloted the electrons through space.
The proposed relationship frequency and wavelength of a matter associated with a particle is:
p
h
h
Ef and
Matter Waves
He proposed that each electron was accompanied by a wave (not an EM wave) which piloted the electrons through space.
The proposed relationship frequency and wavelength of a matter associated with a particle is:
p
h
h
Ef and
Matter Waves
Recall that the relativistic momentum is
22420
222 cmcmcpE
mvvmp 0
and
Matter Waves
Recall that the relativistic momentum is
22420
222 cmcmcpE
mvvmp 0
andwhere pcEphoton (these equations were
originally applied to photons )0 om
Matter Waves
Recall that the relativistic momentum is
Solving for the velocity gives
22420
222 cmcmcpE
v
c
mv
mc
p
h
h
Efvp
22
mvvmp 0
andwhere pcEphoton (these equations were
originally applied to photons )0 om
Matter Waves
Recall that the relativistic momentum is
Solving for the velocity gives
22420
222 cmcmcpE
v
c
mv
mc
p
h
h
Efvp
22
mvvmp 0
andwhere pcEphoton (these equations were
originally applied to photons )0 om
Where is the ‘velocity’ of the matter wave and is the velocity of material particle
vpv
Matter Waves
Where this velocity is the phase velocity or velocity of a wave crest.
Matter Waves
Where this velocity is the phase velocity or velocity of a wave crest.
However from the expression, this gives a phase velocity greater than c.
Matter Waves
Where this velocity is the phase velocity or velocity of a wave crest.
However from the expression, this gives a phase velocity greater than c.
The problem arises because a single matter wave can not properly represent the localized particle.
Matter Waves
Instead a superposition of many waves is needed. These waves interfere to form a wave group.
This wave group has a group velocity.
Wave Packets
Representing particles by finite wave groups
Wave Packets
We determined that properly define a particle by a wave a superposition of waves (wave group) is needed.
Wave Packets
We determined that properly define a particle by a wave a superposition of waves (wave group) is needed.
The velocity of the wave group now is equal to the velocity of the particle.
Wave Packets
A wave packet is set of waves with different wavelengths
Wave Packets
A wave packet is set of waves with different wavelengths, amplitudes and phases
Wave Packets
A wave packet is set of waves with different wavelengths, amplitudes and phases which interfere constructively over a small region of space.
Wave Packets
A wave packet is set of waves with different wavelengths, amplitudes and phases which interfere constructively over a small region of space.
Outside the region they interfere destructively so that they have zero amplitude.
Wave Packets
The wave may be described by the formula: y = A cos(kx-ωt) where
k is the wave numberk
vp
Wave Packets
The wave equation for the wave packet can be constructed from the superposition of each wave.
Wave Packets
In general the velocity is given by
kvp
Wave Packets
The main property of the wave packet is that it has time duration and space .xt
Wave Packets
The main property of the wave packet is that it has time duration and space .
In general the larger the spatial width, the larger the wave numbers required.
xt
Wave Packets
The main property of the wave packet is that it has time duration and space .
In general the larger the spatial width, the larger the wave numbers required.
This relationship is represented mathematically as
xt
1 kx
Wave Packets
Similarly to produce a small duration the range of frequencies must be increased. ie. 1 t
Wave Packets
This preceding analysis is used to show that a wave group can represent an electron.
