De Broglie Waves, Uncertainty, and Atoms Physics 102: Lecture 23 De Broglie Waves, Uncertainty, and Atoms 1

Photoelectric Effect Summary Each metal has “Work Function” (W0) which is the minimum energy needed to free electron from atom. Light comes in packets called Photons E = h f h=6.626 X 10-34 Joule sec Maximum kinetic energy of released electrons K.E. = hf – W0 All puzzles explained with quantum theory.

Photoelectric Effect Summary Maximum kinetic energy of released electrons K.E. = hf – W0 hf W0 KE All puzzles explained with quantum theory.

Compton Scattering This experiment really shows photon momentum! Pincoming photon + 0 = Poutgoing photon + Pelectron Electron at rest Experiment: Outgoing photon has longer wavelength  Incoming photon has momentum, p, and wavelength l Recoil electron carries some momentum and KE Momentum of a photon Energy of a photon

Compton Scattering Incident photon loses momentum, since it transfers momentum to the electron Lower momentum means longer wavelength This is proof that a photon has momentum

Is Light a Wave or a Particle? Electric and Magnetic fields act like waves Superposition, Interference, and Diffraction Particle Photons Collision with electrons in photo-electric effect Compton scattering from electrons BOTH Particle AND Wave

ACT: Photon Collisions Photons with equal energy and momentum hit both sides of the plate. The photon from the left sticks to the plate, the photon from the right bounces off the plate. What is the direction of the net impulse on the plate? 1) Left 2) Right 3) Zero

Radiometer Incident photons Black side (absorbs) Shiny side (reflects) Preflight 23.1 Photon A strikes a black surface and is absorbed. Photon B strikes a shiny surface and is reflected back. Which photon imparts more momentum to the surface? Photon A Photon B

Ideal Radiometer Photons bouncing off shiny side and sticking to black side. Shiny side gets more momentum so it should rotate with the black side leading

Our Radiometer Black side is hotter:gas molecules bounce off it with more momentum than on shiny side-this is a bigger effect than the photon momentum

Are Electrons Particles or Waves? Particles, definitely particles. You can “see them”. You can “bounce” things off them. You can put them on an electroscope. How would know if electron was a wave? Look for interference!

Young’s Double Slit w/ electron 2 slits-separated by d JAVA Electrons produce interference pattern just like light waves. Go to physics 2000 web site for JAVA version Source of monoenergetic electrons L Screen a distance L from slits

Electrons are Particles and Waves! Depending on the experiment electron can behave like wave (interference) particle (localized mass and charge) If we do an experiment that tells us which slit the electron went through, then there is no interference pattern

De Broglie Waves So far only photons have wavelength, but De Broglie postulated that it holds for any object with momentum- an electron, a nucleus, an atom, a baseball,…... Explains why we can see interference and diffraction for material particles like electrons!!

Preflight 23.3 Which baseball has the longest De Broglie wavelength? (1) A fastball (100 mph) (2) A knuckleball (60 mph) (3) Neither - only curveballs have a wavelength Lower momentum gives higher wavelength. p=mv, so slower ball has smaller p.

ACT: De Broglie Wavelength A stone is dropped from the top of a building. What happens to the de Broglie wavelength of the stone as it falls? 1. It decreases 2. It stays the same 3. It increases

Some Numerology 1 eV = energy gained by a charge e when accelerated through a potential difference of 1 Volt e = 1.6 x 10-19 C so 1 eV = 1.6 x 10-19 J h = 6.626 x 10-34 J-sec c = 3 x 108 m/s hc = 1.988 x 10-25 J-m = 1240 eV-nm Mass of electron m = 9.1 x 10-34 kg mc2 = 8.2 x 10-13 J = 511,000 eV = 511 keV

Comparison: Wavelength of Photon vs. Electron Example Comparison: Wavelength of Photon vs. Electron Say you have a photon and an electron, both with 1 eV of energy. Find the de Broglie wavelength of each. Equations are different - be careful! Photon with 1 eV energy: Big difference! Electron with 1 eV kinetic energy: Solve for

Preflights 23.4, 23.5 Photon A has twice as much momentum as Photon B. Compare their energies. EA = EB EA = 2 EB EA = 4 EB Electron A has twice as much momentum as Electron B. Compare their energies. EA = EB EA = 2 EB EA = 4 EB

ACT: De Broglie Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy. (1) lbowling > lgolf (2) lbowling = lgolf (3) lbowling < lgolf

Heisenberg Uncertainty Principle Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa. This seems weird but… OK this is weird but…… it is also true.

Heisenberg Uncertainty Principle: A Consequence of the Wave Nature of Particles screen Number of electrons arriving at screen w Dpy = p sinq p q p q electron beam Dy = w = l/sinq y x Use de Broglie l

The “Uncertainty in py” is Dpy h/w. Electron diffraction electron beam screen Number of electrons arriving at screen w x y py Electron entered slit with momentum along x direction and no momentum in the y direction. When it is diffracted it acquires a py which can be as big as h/w. The “Uncertainty in py” is Dpy h/w. An electron passed through the slit somewhere along the y direction. The “Uncertainty in y” is Dy  w.

electron beam screen Number of electrons arriving at screen w x y py If we make the slit narrower (decrease w=Dy) the diffraction peak gets broader (Dpy increases). “If we know location very precisely, we lose knowledge of momentum, and vice versa.” Remember earlier we saw that a particle whose momentum (and therefore wavelength) is known precisely is very uncertain in position.

to be precise... Preflight 23.7 Of course if we try to locate the position of the particle along the x axis to Dx we will not know its x component of momentum better than Dpx, where and the same for z. Preflight 23.7 According to the H.U.P., if we know the x-position of a particle, we can not know its: (1) y-position (2) x-momentum (3) y-momentum (4) Energy 51% correct