Quantum Mechanics (made fun and easy)

Lecture 7 Quantum Mechanics (made fun and easy)

Why the world needs quantum mechanics

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

Quantum Weirdness: The Zeno Effect

Quantum Weirdness: superposition of states

Light as a particle (Newton, 1643-1727)

Light as a Wave (1861: Maxwell) 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.

E y Light as a wave Traveling wave description ( x, t ) E sin( i( kx t ) o k=wavevector c=ω/k = λν Intensity of light wave = energy flowing per unit area per second I 1 2 c o E 2 o From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw-Hill, 2005)

Young s Double Slit Experiment http://www.youtube.com/watch?v=dfpeprq7ogc t / t h? x d L Schematic illustration of Young s double-slit experiment. Constructive interference occurs when nλl=xd

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

Bragg s Law Bragg diffraction condition 2 d sin θ nλ n 1, 2, 3,... The equation is referred to as Bragg s law, and arises from the constructive interference of scattered waves. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw Hill, 2005)

X-ray Diffraction 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 h 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.

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

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

Interpretation I: 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 V o, which h 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 II: Photocurrent Since the magnitude of the saturation photocurrent depends on the light intensity, only the number of ejected electrons depends on the light intensity. n it

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

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

First full interpretation: 1905, Einstein 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. Ø=hc/eλ o, where λ o is the longest wavelength for photoemission

Photoelectric effect: Light is a particle with energy Red photons no current; blue photons measured current Light = energy packets (photons) with energy E=hν Photoemission only occurs when E > workfunction Ø Ø=hc/eλ o, where λ o is the longest wavelength for photoemission Work function of a metal keeps the electron in the material

Light Intensity (Irradiance) Classical light intensity I 1 c 2 o E 2 o Light Intensity I phh Photon flux (# photons crossing a unit area per unit time) ph N ph A t

X-rays are photons 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, y, and hence their description in terms of photons. SOURCE: Courtesy of Dylan Hunt and John Rowlands, Sunnybrook Hospital, University of Toronto.

Quantum Weirdness II: Young s Double Slit Experiment, Revisited What happens when we observe which slit the photon goes through? x d L http://www.youtube.com/watch?v=dfpeprq7ogc

Compton effect: Light also has momentum 1927 Nobel prize Holly Compton found that X- ray wavelengths increase due to scattering of the photon by free electrons in the material further demonstrates the particle nature of light

Compton s experiment and results

Compton scattering Scattering of an X-ray yphoton by a free electron in a conductor. Since the electron has a momentum, by conservation of momentum, the x-ray must also have momentum. h KE m h h' p

Summary equations: light as a particle & wave Energy: E h Wavevector:k 2 Momentum: p h k 1 Intensity: I h ce0 2 2 0

The solar spectrum Absorption by H and He in the sun Absorption by molecules in the atmosphere What causes the overall shape?

Blackbody radiation Blackbodies absorb all electromagnetic radiation Appear black when cold As they heat up, begin to emit radiation Color depends on temperature the hotter the temperature, the higher the emitted photon energy

Blackbody radiation (1900, Max Planck) Schematic illustration i of black body radiation i

Blackbody radiation Classical theory Planck s radiation law Spectral irradiance vs. wavelength at two temperatures (3000K is p g p ( about the temperature of the incandescent tungsten filament in a light bulb.)

Classical Theory ( Rayleigh-Jeans law ) Thermal vibrations and rotations give rise to radiated electromagnetic waves that will interfere with each other, giving i rise to many standing electromagnetic waves in the oven Each standing wave contributes ~kt of energy (from kinetic molecular theory) By calculating the number of standing waves, find irradience I 4 λ ~ T ~ 1/λ

Planck s Theory Assumed radiation in oven involved emission and absorption of discrete amounts of light energy by the oscillation of molecules. l Assumed the probability of a molecule (an oscillator) possessing an energy nhν (n an integer) was proportional to the Boltzmann factor (think kinetic molecular theory) I 5 2 2 hc hc exp kt 1

Stefan s Law Integrating the irradiance over all wavelengths yields the total radiated power P S emitted by a blackbody per unit surface area at a temperature T: P S S T 4 S Stefan s constant 5 4 2 k 8 2 4 5.67010 W m K 2 3 15c h

Stefan s law for real surfaces Electromagnetic radiation emitted from a hot surface P radiation = total radiation power emitted (W = J s -1 ) S[ 4 4 radiation 0 P S [ T T ] S σ S = Stefan s constant, W m -2 K -4 ε = emissivity of the surface ε = 1 for a perfect black body ε < 1 for other surfaces S = surface area of emitter (m 2 ) From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap ( McGraw Hill, 2005)

Temperature of a lightbulb filament 100 Watt lightbulb emissivity ε=0.35. Filament length of 57.9cm, diameter of 31.7 microns. S=2π(31.7x10-6 m)(0.579m)=1.15 15 x 10-4 m 2 P s =100 W =Sεσ S (T F4 -T 04 ) s S( F 0 ) T 0 =300K T F =2573 K = 2300 o C

Wein s displacement law As the temperature of a blackbody increases, the peak emission i shifts to shorter wavelengths: λ*t=2.89x10-3 m*k Classical l theory Planck s radiation law

The solar spectrum Absorption by H and He in the sun Absorption by molecules in the atmosphere What causes the overall shape? Blackbody emission at ~6000K!