Quantum Theory & the History of Light

Is Light a Ray, Wave or Particle? The question has been debated many times over the years dating back as far as Pythagoras.

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 www.src.wits.ac.za

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 Planck’s theory and experimental evidence show that as wavelength decreases, the amount of energy being radiated approaches zero! (per unit wavelength) Intensity Classical theory suggests that as the wavelength approaches zero, the amount of energy being radiated should be infinite! 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 frequency n = 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 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.) KEe = hf – hfo 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 (hf = hfo). Light intensity does not affect photoelectron emission if the threshold frequency has not been achieved. 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

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 CV 1 eV = 1.60 x 10-19 J This is Important!!

Wave-Particle Duality of Light Light has no mass, yet has momentum 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): E = hf ’ p = hf ’/c E = ½ mve2 p = mve - Collision Incident Photon = X-ray - Momentum p = hf/c E = hf This experiment validated Einstein’s Photoelectric effect. 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 diffraction & interference. Explained through reflection. Explained through refraction. Particle Theory: Explained through photoelectric emission. Explained through the Compton effect.

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/mv Where: 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 Particles Waves Mass Frequency Size Wavelength Kinetic Energy Amplitude Momentum 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.

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.