de broglie waves, uncertainty, and atoms sections 30.5 – 30.7 physics 1161: lecture 29
TRANSCRIPT
Outgoing photon has momentum p and 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 Energy of a photon
Photons with equal energy and momentum hit both sides of a metal 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 2 3
0% 0%0%
1. Left2. Right3. Zero
Photons with equal energy and momentum hit both sides of a metal 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 2 3
0% 0%0%
1. Left2. Right3. Zero
Photon that sticks has an impulse p Photon that bounces has
an impulse 2p!
h
p
So far only for 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 29.1
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 29.1
ph
Lower momentum gives higher wavelength.
p=mv, so slower ball has smaller p.
A stone is dropped from the top of a building. What happens to the de Broglie wavelength of the stone as it falls?
1 2 3
0% 0%0%
1. It decreases.2. It increases.3. It stays the same.
A stone is dropped from the top of a building. What happens to the de Broglie wavelength of the stone as it falls?
1 2 3
0% 0%0%
1. It decreases.2. It increases.3. It stays the same.
p
h
hp
Speed, v, and momentum, p=mv, increase.
• Photon with 1 eV energy:
Comparison:Wavelength of Photon vs. Electron
hc
E Ehc nm 1240
eV 1nm eV 1240
Say 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!
Equa
tions
are
diff
eren
t - b
e ca
refu
l!
Preflights 28.4, 28.5
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
Preflights 28.4, 28.5
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
m
pmvKE
22
1 22
hc
E phand so cpE
double p then quadruple E
double p then double E
Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy.
1 2 3
0% 0%0%
1. bowling > golf
2. bowling = golf
.bowling < golf
Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy.
1 2 3
0% 0%0%
1. bowling > golf
2. bowling = golf
.bowling < golf
KE)(2mh
ph
Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa.
If we know the momentum p, then we know the wavelength , and that means we’re not sure where along the wave the particle is actually located!
y
Heisenberg Uncertainty Principle
2h
ypy
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 29.2According 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
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 29.7According 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
Early Model for Atom
But how can you look inside an atom 10-10 m across?
Light (visible) = 10-7 m
Electron (1 eV) = 10-9 m
Helium atom = 10-11 m
--
--
+
+
+
+
• Plum Pudding– positive and negative charges uniformly
distributed throughout the atom like plums in pudding
Rutherford ScatteringScattering He++ nuclei (alpha particles) off of gold. Mostly go through, some scattered back!
Atom is mostly empty space with a small (r = 10-15 m) positively charged nucleus surrounded by cloud of electrons (r = 10-10 m)
(Alpha particles = He++)
Only something really small (i.e. nucleus) could scatter the particles back!
Atomic Scale
• Kia – Sun Chips Model– Nucleons (protons and neutrons) are like Kia Souls
(2000 lb cars) – Electrons are like bags of Sun Chips (1 lb objects)– Sun Chips are orbiting the cars at a distance of a
few miles• (Nucleus) BB on the 50 yard line with the
electrons at a distance of about 50 yards from the BB
• Atom is mostly empty space• Size is electronic