Today’s class:
Quantum tunneling and radioactive decay
Radioactive decay
George Gamow: 1928
Announcements
• Midterm next week. No homework this
week. There will be one next week.
• Reading 8.1-8.3
Application of quantum tunneling: Scanning
Tunneling Microscope  'See' single atoms!
Use tunneling to measure very(!) small changes in distance.
Nobel prize winning idea: Invention of “scanning tunneling
microscope (STM)”. Measure atoms on conductive surfaces.
Measure current
between tip and
sample
Look at current from sample to tip to measure gap.
Tip
SAMPLE METAL
SAMPLE
(metallic)
Electron tunnels from sample
to tip.
-
energy
x
How would U(x) look like after an
electron tunneled from the sample
to the tip if sample and tip were
isolated from each other?
a. same as before.
b. U in tip higher, U sample lower.
c. U in tip lower, U sample higher.
d. U same on each side as before
but barrier higher.
sample
tip
ans. b. electron piled on top (in energy) of many other electrons
that contribute to U(x). Add electron, makes higher U(x),
remove makes lower. So what does next electron want to do?
Correct picture of STM-- voltage applied between tip and
sample. Holds potential difference constant, electron current.
Figure out what potential energy looks like in different regions
so can calculate current, determine sensitivity to gap distance.
+
sample
I
I
SAMPLE
SAMPLE METAL
(metallic)
energy
Tip
What does U tip look like?
a. higher than U sample
b. same as U sample
c. lower than U sample
d. tilts downward from left to right
V e. tilts upward from left to right
tip
applied voltage
Correct picture of STM-- voltage applied between tip and
sample.
Potential energy in different regions so can calculate current,
determine sensitivity to gap distance.
What is potential in air gap
approximately?
+
sample
I
I
SAMPLE
SAMPLE METAL
(metallic)
energy
Tip
tip
V
linear connection
Notice changing V will
change barrier, and hence
tunneling current.
applied voltage
Current vs. Position.
•
•
•
•
Tuneling
Controversy
STM now
Superconductors
STM (picture with reversed voltage, works exactly the same)
end of tip always
atomically sharp
Piezoelectricity
• Electric dipole • Ordered domains
linked to lattice
(like ferromagnetism)
• Electric field ≈
strain ≈
displacement
– Applications in sensors, lighters, actuators
– Length-scales involved can be ~nm/V
Piezoelectric actuators and
sensors are everywhere!
Buzzers in electronic gadgets and in smoke alarms.
Microphones in cell-phones.
Quartz crystals.
BBQ grills and lighters.
Knock sensors in car engines.
Seismology.
Concrete compactors
Sonar devices (Submarines, Robotics, Automatic doors)
STM results
0
300 Å
• Atomic lattices and surface structure
Si(111) 7x7 reconstruction
Trenary: UIC
Gold surface
B. Barker: LPS
STM results
0
0
200 Å
300 Å
• Atomic lattices and surface structure
Can selectively “write” on surface
~10nm lengths
Charge Density Wave
on TaSe2
Jixia Dai Colorado
STM results
• Electrons are waves
Fe on Cu(111)
? on Cu(111)
D. Eigler: IBM Almaden
As approached, voltage pulse, 100nm away, and
How
does CDW
react to
somewhere
with 1T phase
200Ǻ
100Ǻ
0
0
disorder?
We have been writing large
scale defects into these surfaces
We can also induce a structural
transition to write 50nm bits into
the surface… Bad memory
Slow scan
0
100Ǻ
Whatcopper
aboutatoms
doping
with
Dragging
across
the
surface
Cu?
We have also learned to manipulate the dopant Cu atoms to create defined
structures
Application of Quantum
Tunneling:
Radioactive decay
George Gamow: 1928
Radioactive decay
(Quantum tunneling – George Gamow)
Nucleus is unstable  ejects alpha particle (2 netrons, 2 protons)
Typically found for large atoms with lots of protons and neutrons.
Polonium-210
84 protons,
126 neutrons
Proton (positive charge)
Neutron (no charge)
Nucleus has lots of protons and lots of
neutrons.
Two forces acting in nucleus:
- Coulomb force .. Protons really close
together, so very big repulsion between
protons due to coulomb force.
- Nuclear force (attraction between nuclear
particles is very strong if very close
together) … called the STRONG Force.
Radioactive decay
Proton (positive charge) In alpha-decay, an alpha-particle is
Neutron (no charge)
emitted from the nucleus.
Polonium-210
84 protons,
126 neutrons
Lead-206
82 protons,
124 neutrons
This raises the ratio of neutrons
to protons … makes for a more
stable atom.
(Neutrons are neutral.. no
coulomb repulsion, but nuclear
force attraction)
How to figure out what's going on?
Starting point: Always look at potential energy curve for particle!
+
KE
New nucleus
Nucleus
Alpha particle
(Z-2 protons,
(Z protons,
(2 protons,
& bunch of neutrons) bunch of neutrons-2) 2 neutrons)
Now look at this system… as the
distance between the alpha particle
and the nucleus changes.
As we bring the a particle closer to the core,
what happens to potential energy?
As bring a closer, what happens to potential energy?
U=0 At a great distance
r
A
U(r)
C
D. Something else
U(r)
B
U(r)
r
r
Potential energy curve for the α particle
+
KE
New nucleus
Nucleus
Alpha particle
(Z-2 protons,
(Z protons,
(2 protons,
& bunch of neutrons) bunch of neutrons) 2 neutrons)
Strong attractive force
(Nuclear forces)
U(r)
Look at this system… as the
distance between the alpha particle
and the nucleus changes.
As we bring the a particle closer to the core,
what happens to potential energy?
r
Coulomb repulsion:
Nucleus:
(Z-2) protons
kq1q2 k ( Z  2)(e)(2e)
U (r ) 

r
r
V=0 for r  ∞
Energy
very small r (~1fm):
nuclear force dominates
~30 MeV
‘Large’ r: coulomb force dominates
U(r)
kq1q2 k ( Z  2)(e)(2e)
U (r ) 

r
r
1 to 10 MeV
r
Edge of the nucleus (~8x10-15 m),
Nuclear (‘Strong’) force starts acting
strong attraction between nucleons.
Potential energy drops dramatically.
Energy
What’s the kinetic energy of this particle inside the
nucleus?
U(r)
D
C
B
x
A
E: Something else
Review: Radioactive decay
Energy
Small r: Nuclear
force dominates
~30 MeV
Large r: coulomb force dominates
U(r)
kq1q2 k ( Z  2)(e)(2e)
U (r ) 

r
r
1 to 10 MeV
r
Edge of the nucleus (~8x10-15 m),
Nuclear (‘Strong’) force starts acting
strong attraction between nucleons.
Potential energy drops dramatically.
Energy
What would the kinetic energy of that particle be after it
tunneled out from the nucleus?
U(r)
D
C
B
x
A
E: Something else
Energy
So we found that the particle has less kinetic energy
outside than inside the nucleus. Did it loose energy?
U(r)
KEoutside
x
KEinside
A) Yes.
B) No.
C) Impossible to tell. Need to
solve Schröd. equ. first.
Energy
Wave function picture:
U(r)
~100MeV
of KE inside
the nucleus
Exponential decay in the barrier
~1-10MeV of KE
outside
Wave function of the free particle:
‘small’ KE  Large wavelength
Wave function of the particle
inside the potential well: Large
KE  small Wavelength
U(r)
Energy
Observations show Alpha-particles from the same
chemical element exit with a range of energies.
9 MeV KE
4 MeV KE
Different KE in different isotopes
# neutrons influence nuclear potential
Observe a particles from different isotopes (same # protons,
different # neutrons), exit with different amounts of energy.
2m
a
(U  E )
2

U(r)
Energy
30 MeV
1. Less distance to tunnel
2. U-E is smaller (smaller a)
 Wave function doesn’t
decay as much before reaches
other side … more probable!
9MeV KE
4MeV KE
x
The 9 MeV electron more probable…
Isotopes that emit higher energy alpha
particles, have shorter lifetimes!!!
Solving Schrodinger
equation for this
potential energy is hard!
V(x)
Square barrier is much easier…
and get almost the same answer!
V(x)