Quantum Theory & the History of Light

The Beginning of Light In the beginning it was dark and cold.

No sun No light No earth No solar system.

~ 4.5 billion years ago, a huge cloud of gas and dust was formed. This cloud contracted and grew into a central molten

mass of plasma that became our SUN. Through the process of thermonuclear hydrogen

fusion, the sun began to shine.

Is Light a Ray, Wave or Particle? The question has been debated many times over the

years dating back as far as Pythagoras.

History of Light 582 – 500 BC: Pythagoras theorized that light travels in

particles where he assumed that every visible object emits a steady stream of particles, that bombard the eye.

427 – 347 BC: Plato suggested that vision was produced by rays of light that originate in the eye and then strike the object being viewed.

384 – 322 BC: Aristotle suggested that light travels in waves.

320 – 275 BC: Euclid said that light travels in rays which came from the eyes in straight lines.

~300 BC: First lenses made by Greeks and Romans consisting of glass spheres filled with water.

History of Light (cont.) ~1000 AD: al Hathan said that light enters the eye from

an outside source rather than originating from within. ~1000 AD – early 1600’s: Many inventions occurred in

the area of optics (glasses and telescopes) and an overall general understanding of the nature of light (Law of Reflection and Law of Refraction).

Wave Theory of Light Christian Huygens (1629 – 1695): Light travels in

wavelets Huygen's Wavelets

Corpuscle Theory of Light: Sir Issac Newton (1642 –1727) Newton believed that bodies emitted energy in particles or

corpuscles that traveled in straight lines. 1666: Performed an experiment with a prism that showed that the

sun’s light is white light consisting of all of the colors of the spectrum.

Wave Theory of Light: Thomas Young (1773 – 1829)-revisited

1801: Through use of the Double-Slit Experiment, the wave properties of light were first experimentally shown to exist.

Experiment demonstrated that light undergoes interference and diffraction in much the same way that water and sound waves do.

Used source of monochromatic light to eliminate the problems with phase differences associated with incoherent light.

Young Double-Slit Experiment

Huygen’s Wavelets

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Wave Theory of Light: James Clerk Maxwell (1831 – 1879) 1860: James Maxwell hypothesized that electric fields

changing in time would create magnetic fields and vice-versa.

These fields travel together in space as waves. Electromagnetic Wave

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Max Planck & Blackbody Radiation All matter, whether cool or hot emits electromagnetic

waves. The light radiated from an incandescent body changes

with temperature. The higher the temperature, the greater the intensity and

frequency of the light emitted. Why does incandescent light come in all wavelengths

then? Incandescent light is produced by vibrating atoms, which

are systems far more complex than a single electron. Thus they are able to emit many different energies because f can vary linearly, producing a largely continuous energy spectrum.

Blackbody Radiation

Classical theory suggests that as the wavelength approaches zero, the amount of energy being radiated should be infinite!

Planck’s theory and experimental evidence show that as wavelength decreases, the amount of energy being radiated approaches zero!

Blackbody Radiation

Quantization of Energy Energy exists in discrete quantities Atoms oscillate at discrete frequencies that reflect discrete energy

levels. Energy is absorbed and emitted in the form of photons of radiation.

E = nhf

Where: h = Planck’s Constant (6.626 x 10-34J•s)f = vibrational frequencyn = 0, 1, 2, 3, …

Note: Energy is not permitted for values other than those which satisfy the equation (You cannot have ½ of a photon).Each value of n can be thought of as a photon; where 1 photon would be 1hf and two photons would be 2hf; and so on….

The Photoelectric Effect Einstein proposed that light (electromagnetic

radiation) consists of energy packets (Photons or Quanta) where E = hf.

If a photon had a sufficiently high enough frequency (or high enough energy) it could cause an electron to be ejected by the atom it is incident upon.

Photon of light

The Photoelectric Effect (cont.) The threshold frequency (fo) is the minimum

frequency of a photon of light required to free an electron from an atom.

At the threshold frequency, the electron will have no kinetic energy.

Light intensity does not affect photoelectron emission if the threshold frequency has not been achieved. In other words, if the frequency is below the

threshold frequency, it does not matter how bright the light is; electrons will not be ejected.

The Photoelectric Effect

The Photoelectric Effect(cont.) The maximum kinetic energy of an emitted electron is

determined by the relationship of conservation of energy where:

KEe = hf – hfo

Note: this relationship implies that the photon has particle properties.

Also, only one photon can act on one electron at any given moment.

The work function is the minimum amount of energy required to remove an electron from an atom such that it does not have any kinetic energy.

Work Function

The Photoelectric Effect(cont.)

What is the relationship between light intensity and PE emission?

IntensityIntensity

(a) If the threshold frequency is achieved, then increasing the intensity will emit more photons.

(b) Increasing the intensity has no affect on the kinetic energy of the emitted photons.

(a) (b)

The Photoelectric Effect(cont.)

What is the relationship between the frequency of the photon and PE emission?

FrequencyFrequency

(a) If the threshold frequency is achieved, then increasing it will NOT emit more photoelectrons.

(b) Increasing the frequency will impart more kinetic energy to the electron once fo is achieved.

(a) (b)

Slope = h

Threshold Frequency

The Photoelectric Effect(cont.)

- E = hf - hfo

E = hf = hc/

Photon

Photoelectron

Cathode

Anode

+

_

Note: for an electron to reach the anode, it must have a sufficient amount of kinetic energy.

E

E

The Photoelectric Effect(cont.) Stopping Potential: The minimum electric potential required to

prevent an electron from reaching the anode. From electrostatics:

V = Ed Where:

E = electric field intensity (V/m)d = distance between two plates

W = KE

-qVo = ½mev2 Where:

Vo = stopping potentialq = charge of an electron

me = mass of an electronv = speed of electron

Applications of the Photoelectric Effect

Photocells – Used to operate switches and relays, alarms, door openers and boilers.

CCD (Charged Coupled Devices) – Low light imagery.

Solar Cells Research in quantum physics.

Quantum Energy Units The units for energy is Joules. Joules is very large for atomic systems. Use smaller unit instead – Electron Volt. One electron volt is equal to the energy of an

electron accelerated across a potential difference of one volt.

qe = 1.6 x 10-19 C

1 eV = (1.60 x 10-19 C)(1 V) = 1.60 x 10-19 CV

1 eV = 1.60 x 10-19 JThis isImportant!!

Wave-Particle Duality of Light Einstein’s theory suggests that although a

photon of light has no mass, it does possess kinetic energy.

Einstein further predicted that a photon of light should also have momentum as follows.

p* = hf/c = h/λ

The fact that a photon can have momentum again implies that it has particle properties.

*Momentum, p = mass x velocity

Wave-Particle Duality of Light

-

The Compton Effect (1922):

Incident Photon = X-ray

Collision

Momentump = hf/cE = hf

E = hf ’

p = hf ’/c

E = ½ mve2

p = mve

Conservation of Energy & Momentum: The energy and momentum gained by the electron equals the energy and momentum lost by the photon.

hf/c – hf ‘/c = mve

-

Particles vs. Waves (Light) Wave Theory:

• Explained through polarization.• Explained through reflection.• Explained through diffraction & interference.• Explained through refraction.

Particle Theory:• Explained through photoelectric emission.• Explained through the Compton effect.• Explained through reflection.• Explained through refraction.

Wavelike Behavior of Particles The photoelectric effect and Compton scattering

showed that electromagnetic radiation has particle properties.

Could a particle behave like a wave? The answer is yes!

p = mv = h/λ

λ = h/mvWhere:

λ = de Broglie wavelength

Wavelike Behavior of Particles Proof of the wavelike behavior of particles was

made by diffracting electrons off a thin crystal lattice.

The particles showed similar interference patterns to light when passed through a diffraction grating.

Particles vs. Waves

Physicists have demonstrated that light has both wavelike and particle characteristics that need to be considered when explaining its behavior.

Similarly, particles – such as electrons – exhibit wavelike behavior.

Particles WavesMass Frequency

Size Wavelength

Kinetic Energy Amplitude

Momentum

Key Ideas Objects that are hot enough will emit light

because of the charge particles inside their atoms.

The spectrum of light produced by an incandescent body is dependent on its temperature.

Planck suggested that the spectrum of an incandescent body can only be comprised of certain energy levels (E = nhf).

The photoelectric effect is the emissions of electrons from metals when exposed to EM radiation of a minimum frequency (fo).

Key Ideas The minimum energy required to free an

electron from the atom is the work function (E = hfo).

Light comes in discrete packets of energy called photons.

Photons of light have momentum (p = h/) - even though they are massless.

Energy and momentum are conserved in photon-electron collisions.

Particles have wavelike attributes similar to light.