physics 102: lecture 23, slide 1 de broglie waves, uncertainty, and atoms physics 102: lecture 23

Physics 102: Lecture 23, Slide 1

De Broglie Waves, Uncertainty, and Atoms

Physics 102: Lecture 23


Three Early Indications of Problems with Classical Physics

• Blackbody radiation

• Photoelectric effect

• Wave-particle duality

Lecture 22: Quantum Mechanics

• Compton scattering

• DeBroglie

• Heisenberg Uncertainty Principle

Today


Experiment: Outgoing photon has longer wavelength

Recoil electron carries some momentum and KE

Incoming photon has momentum p, and wavelength

This experiment really shows photon momentum!

Electron at rest

Compton Scattering

Pincoming photon + 0 = Poutgoing photon + Pelectron

hc

hfE h

p

Photon energy

Photon momentum

E = pc


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

h

p


Is Light a Wave or a Particle?• Wave

– 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 CollisionsPhotons 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


Incident photons

Radiometer

Preflight 23.1Photon 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

Black side (absorbs)

Shiny side (reflects)


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

Ideal Radiometer


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


Electrons are Particles and Waves!• Depending on the experiment electron can behave

like– wave (interference)

– particle (localized mass and charge)

• Recall Young’s double slit experiment: – If we measure which slit the electron went through,

then there is no interference pattern!!


h

p

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!!

De Broglie Waves

ph


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

Preflight 23.3


ACT: De Broglie Wavelength

A stone is dropped from the top of a building.

1. It decreases

2. It stays the same

3. It increases

What happens to the de Broglie wavelength of the stone as it falls?


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

Standard units (m, kg, s) are not convenient for talking about photons & electrons


• Photon with 1 eV energy:

Comparison:Wavelength of Photon vs. Electron

hc

E Ehc nm 1240

eV 1nm eV 1240

You have a photon and an electron, both with 1 eV of energy. Find the de Broglie wavelength of each.

• Electron with 1 eV kinetic energy:

KE

12

mv2 and p =mv, so KE =p2

2mK.E.)(2mp Solve for

KE)(2mh

KE)(2 2mc

hceV) 1)(eV 000,511(2

nm eV 1240 nm23.1

Big difference!

Eq

uati

on

s are

diff

ere

nt

- b

e

care

ful!


X-ray diffraction e– diffraction

From College Physics, Vol. Two

Identical pattern emerges if de Broglie wavelength of e– equals the X-ray wavelength!

X-ray vs. electron diffraction

Demo


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) bowling > golf

(2) bowling = golf

(3) bowling < golf


Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa.

Heisenberg Uncertainty Principle

2h

ypy

Recall: Quantum Mechanics tells us nothing is certain, everything is probability

Uncertainty in position (along y)

Uncertainty in momentum (along y)


Number of electrons arriving at screen

screen

w

x

y

p

py = p sinp

= y

sinsin pypy p h

w = /sin

electron beam

Electron diffractionElectron beam traveling through slit will diffract

Recall single-slit diffraction 1st minimum:

sin = /w

Using de Broglie

Single slit diffraction pattern


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 py h/w.

An electron passed through the slit somewhere along the y direction. The “Uncertainty in y” is y w.

electron beam

screen


w

x

y py w h

py

py y h


electron beam

screen


w

x

y

py

py y h

If we make the slit narrower (decrease w =y) the diffraction peak gets broader (py increases).

“If we know location very precisely, we lose knowledge of momentum, and vice versa.”


to be precise... pyy

h2

Of course if we try to locate the position of the particle along the x axis to x we will not know its x component of momentum better than px, where

pxx

h2

and the same for z.

Preflight 23.7According 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

physics 102: lecture 23, slide 1 de broglie waves, uncertainty, and atoms physics 102: lecture 23

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