Lecture 9 Quantum Mechanics (made fun and easy)

Why the world needs quantum mechanics

Quantum Mechanics in Action 2 nm CdS (‘cadmium yellow’) CdS nanocrystal

Quantum Weirdness: The Zeno Effect

Quantum Weirdness: superposition of states

Light as a particle (Newton, )

The classical view of light as an electromagnetic wave. An electromagnetic wave is a traveling wave with time-varying electric and magnetic fields that are perpendicular to each other and to the direction of propagation. Light as a Wave (1861: Maxwell)

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Light as a wave Intensity of light wave = energy flowing per unit area per second Traveling wave description k=wavevector c= ω/k = λ ν

Schematic illustration of Young’s double-slit experiment. Constructive interference occurs when n λ L=xd Young’s Double Slit Experiment L d x

X-ray diffraction involves constructive interference of waves being "reflected" by various atomic planes in the crystal. X-ray Diffraction

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Bragg’s Law Bragg diffraction condition The equation is referred to as Bragg’s law, and arises from the constructive interference of scattered waves.

Diffraction patterns obtained by passing X-rays through crystals can only be explained by using ideas based on the interference of waves. (a) Diffraction of X-rays from a single crystal gives a diffraction pattern of bright spots on a photographic film. (b) Diffraction of X-rays from a powdered crystalline material or a polycrystalline material gives a diffraction pattern of bright rings on a photographic film. X-ray Diffraction

The Photoelectric Effect (1921 Nobel Prize) Illuminate cathode and monitor generated current as a function of applied voltage

Photoelectric current vs. voltage when the cathode is illuminated with light of identical wavelength but different intensities ( I ). The saturation current is proportional to the light intensity Results: Photocurrent versus voltage & intensity Photocurrent

The stopping voltage and therefore the maximum kinetic energy of the emitted electron increases with the frequency of light ν. Results: Photocurrent versus voltage & wavelength Photocurrent

When an electron traverses a voltage difference V, it’s potential energy changed by eV. When a negative voltage is applied to the anode, the electron has to do work to get to this electrode This work comes from the electrons kinetic energy just after photoemission When the negative anode voltage V is equal to Vo, which just “extinguishes” the current I, the potential energy gained by the electron balances the kinetic energy lost by the electron eV o = 1 / 2 mv 2 =KE m Interpretation I:

Since the magnitude of the saturation photocurrent depends on the light intensity, only the number of ejected electrons depends on the light intensity. Interpretation II: Photocurrent

The effect of varying the frequency of light and the cathode material in the photoelectric experiment. The lines for the different materials have the same slope h but different intercepts Results: Kinetic energy & light frequency

Photoelectric Effect Photoemitted electron’s maximum KE is KE m Work function, F 0 The constant h is called Planck’s constant.

The PE of an electron inside the metal is lower than outside by an energy called the workfunction of the metal. Work must be done to remove the electron from the metal. First full interpretation: 1905, Einstein Ø=hc/e λ o, where λ o is the longest wavelength for photoemission

Light Intensity (Irradiance) Classical light intensity Light Intensity Photon flux (# photons crossing a unit area per unit time)

X-ray image of an American one-cent coin captured using an x-ray a-Se HARP camera. The first image at the top left is obtained under extremely low exposure and the subsequent images are obtained with increasing exposure of approximately one order of magnitude between each image. The slight attenuation of the X-ray photons by Lincoln provides the image. The image sequence clearly shows the discrete nature of x-rays, and hence their description in terms of photons. SOURCE: Courtesy of Dylan Hunt and John Rowlands, Sunnybrook Hospital, University of Toronto. X-rays are photons

Quantum Weirdness II: Young’s Double Slit Experiment, Revisited L d x What happens when we observe which slit the photon goes through?