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Quiz 4 8:30-8:50am TODAYHave your calculator ready.
Cell phone calculator NOT allowed.Closed book
Quiz 1 & 2 grade available on the course website(last 4 digits of your student ID)Quiz 1 average 8.69, Quiz 2 average 7.22Quiz 3 graded, scores being recorded.
Next lecture February 12Quiz 5 will cover the material from today’s lecture,material from DLM7&8, including FNTs for DLM9.
QuickTime™ and a decompressor
are needed to see this picture.
Particle Model of MatterParticle Model of Matter
All matter is comprised of tiny particles(atoms and molecules) that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.
If all scientific information were to be lost, these wouldbe the most valuable ideas to pass on to future generations.
R.P. Feynman, Physics Nobel Laureat in 1965
QuickTime™ and a decompressor
are needed to see this picture.
Particle Model of MatterParticle Model of Matter
All matter is comprised of tiny particles(atoms and molecules) that move around in Perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.
If all scientific information were to be lost, these wouldbe the most valuable ideas to pass on to future generations.
R.P. Feynman, Physics Nobel Laureat in 1965
QuickTime™ and a decompressor
are needed to see this picture.
Particle Model of MatterParticle Model of Matter
All matter is comprised of tiny particles(atoms and molecules) that move around in Perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.
If all scientific information were to be lost, these wouldbe the most valuable ideas to pass on to future generations.
R.P. Feynman, Physics Nobel Laureat in 1965
Particle Model of MatterParticle Model of Matter
We will model real atoms of liquids and solids as oscillating masses and springs r
Goal : To understand macroscopic phenomena (e.g. melting, vaporizing) and macrocopic properties of matter such as phases, temperature, heat capacities, in terms of microscopic constituents and its behavior.
Atom 1(anchored)
Atom 2(bonded)
Model Bonded Atoms Model Bonded Atoms as Masses on Springas Masses on Spring
~ two atomic size particles interacting via“pair-wise potential” a.k.a. Lennard-Jones Potential
Intro to Particle Model of MatterIntro to Particle Model of MatterPotential Energy between two atomsPotential Energy between two atoms
“pair-wise potential” a.k.a. Lennard-Jones “pair-wise potential” a.k.a. Lennard-Jones PotentialPotential
r
Distance between the atoms (r)
Po
ten
tia
l En
erg
y
Equilibrium separation
ro
Displacement from equilibrium y[+][-]
Equilibrium separation : ro
Mass- Spring Oscillator analogy
Slope of PE curve (d(PE)/dy) is zero,
i.e., force on the massis zero.
Intro to Particle Model of MatterIntro to Particle Model of Matter
Potential Energy between two atomsPotential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential“pair-wise potential” a.k.a. Lennard-Jones Potential
r
Distance between the atoms (r)
Po
ten
tia
l En
erg
y
Equilibrium separation
ro
Equilibrium separation: ro
The force the two particlesexert on each other is zero.If the particles move from
this separation, larger or smaller,The force pushes/pulls them back.
Intro to Particle Model of MatterIntro to Particle Model of Matter
Potential Energy between two atomsPotential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential“pair-wise potential” a.k.a. Lennard-Jones Potential
Flattening: atoms have negligible forcesat large separation.
r
Distance between the atoms (r)
Po
ten
tia
l En
erg
y
Equilibrium separation
ro
Do atoms a very long distance apart attract or repel?
Intro to Particle Model of MatterIntro to Particle Model of Matter
Potential Energy between two atomsPotential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential“pair-wise potential” a.k.a. Lennard-Jones Potential
r
Distance between the atoms (r)
Po
ten
tia
l En
erg
y
Equilibrium separation
ro
What happens as the atom Separation decreases?
?
Slope of PE curve : Force : |F|=|d(PE)/dr|
Mass- Spring Oscillator analogy
direction of force
Displacement from equilibrium y[+][-]
Slope of PE curve : Force : |F|=|d(PE)/dr|
Mass- Spring Oscillator analogy
Displacement from equilibrium y[+][-]
direction of force
Slope of PE curve : Force : |F|=|d(PE)/dr|
Mass- Spring Oscillator analogy
On this side force pushes up
On this side force pushes down
Equilibrium
Forces from potentials point in direction
that (locally) lowers PE
Displacement from equilibrium y[+][-]
Intro to Particle Model of MatterIntro to Particle Model of Matter
Potential Energy between two atomsPotential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential“pair-wise potential” a.k.a. Lennard-Jones Potential
r
Distance between the atoms (r)
Po
ten
tia
l En
erg
y
Equilibrium separation
ro
As the atom-atom separation decreases, force from the potential increases.
~ attracting each other when they area little distance apart
Intro to Particle Model of MatterIntro to Particle Model of Matter
Potential Energy between two atomsPotential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential“pair-wise potential” a.k.a. Lennard-Jones Potential
r
Distance between the atoms (r)
Po
ten
tia
l En
erg
y
Equilibrium separation
ro
What happens when the atom separation decreases less than the equilibrium separation?
Intro to Particle Model of MatterIntro to Particle Model of Matter
Potential Energy between two atomsPotential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential“pair-wise potential” a.k.a. Lennard-Jones Potential
Repulsive: Atoms push apart as they get too close
r
Distance between the atoms (r)
Po
ten
tia
l En
erg
y
Equilibrium separation
ro
~ but repelling upon being squeezed one anotherIs it possible to squosh one atom
Completely into one another?
separation
Flattening: atoms have negligible forces at large separation.
r
PE
Distance between the atoms
Repulsive: Atoms push apart as they get too close
““pair-wise potential” a.k.a. Lennard-Jones Potentialpair-wise potential” a.k.a. Lennard-Jones Potential
ro = atomic diameterro = equilibrium separation
““Pair-wise potential” Pair-wise potential” a.k.a. Lennard-Jones Potentiala.k.a. Lennard-Jones Potential
* ‘Not to scale’
Energy
r (atomic diameters)
r
is the atomic diameter
ro
is the well depth ro is the equilibrium separation
Potential Energy between two atomsPotential Energy between two atoms“pair-wise potential” a.k.a. Lennard-Jones Potential“pair-wise potential” a.k.a. Lennard-Jones Potential
pair-wise
~ 10-21 J
~ 10-10m = 1Å
PE
KE
Etot
Inaccessible Inaccessible
Separation (10-10 m)
Ene
rgy
(10-2
1 J)
This is what is This is what is meant by a “bond” - meant by a “bond” - the particles cannot the particles cannot escape from one escape from one anotheranother
PE
KE
Etot
Inaccessible Inaccessible
10
Separation (10-10 m)
Ene
rgy
(10-2
1 J)
The bond is an abstraction: Atoms that don’t have enough energy cannot escape the potential (force), so we treat them as bound until we add enough energy to free them.
Question : What does it mean to break a bond?
If a bond is “broken” in an atom-atom potential, which of the following must be true:
A. Etot 0
B. Etot 0
C. PE 0
D. PE 0
E. KE 0
Question : What does it mean to break a bond?
If a bond is “broken” in an atom-atom potential, which of the following must be true:
B. Etot 0
r
Energy (10-21 J)
Distance between the atoms
Etot
Pair-wise potentialPair-wise potential
When Etot ≥ 0, What is true about KE at very large r?
What is the change in bond energy (∆Ebond) by removing the red atom?
2.2 A
4.4 A
6.6 A
-8 x 10-21J
-0.5 x 10-21J
~ 0 J8.8 A
11 A~ 0 J
~ 0 J
Bond energy
For each atom-atom pair, Pair-wise For each atom-atom pair, Pair-wise potential existspotential exists
Separation (10-10m)
• Ebond for a substance is the amount of energy required to break apart “all” the bondsi.e. we define Ebond = 0 when all the atoms are separated
• The bond energy of a large substance comes from adding all the potential energies of particles at their equilibrium positions.
Ebond = ∑all pairs(PEpair-wise)
Multiple atom systemMultiple atom system
Liquid: Molecules can move around, but are loosely held together by molecular bonds. Nearly incompressible.
Gas: Molecules move freely through space. Compressible.
Solid: Rigid, definite shape. Nearly incompressible.
Umm some things are starting to make sense… Umm some things are starting to make sense…
Phases under MicroscopePhases under Microscope