Quiz 4 8:30-8:50am TODAY Have your calculator ready. Cell phone calculator NOT allowed. Closed book...

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.

Normal Matter : ParticlesNormal Matter : ParticlesBouncing Around!Bouncing Around!

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.


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


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


Po

ten

tia

l En

erg

y


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.



Flattening: atoms have negligible forcesat large separation.

r


Po

ten

tia

l En

erg

y


ro

Do atoms a very long distance apart attract or repel?



r


Po

ten

tia

l En

erg

y


ro

What happens as the atom Separation decreases?

?

Slope of PE curve : Force : |F|=|d(PE)/dr|


direction of force





direction of force



On this side force pushes up

On this side force pushes down

Equilibrium

Forces from potentials point in direction

that (locally) lowers PE




r


Po

ten

tia

l En

erg

y


ro

As the atom-atom separation decreases, force from the potential increases.

~ attracting each other when they area little distance apart



r


Po

ten

tia

l En

erg

y


ro

What happens when the atom separation decreases less than the equilibrium separation?



Repulsive: Atoms push apart as they get too close

r


Po

ten

tia

l En

erg

y


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


pair-wise

~ 10-21 J

~ 10-10m = 1Å

Etot

10Separation (10-10 m)

Ene

rgy

(10-2

1 J)

Separation (10-10 m)

Ene

rgy

(10-2

1 J)

Etot

PE

KE

Etot


Ene

rgy

(10-2

1 J)

PE

KE

Etot

Inaccessible Inaccessible


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


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

Closed Book

Make sure above boxes are filled!

Quiz 4 8:30-8:50am TODAY Have your calculator ready. Cell phone calculator NOT allowed. Closed book...

Documents

Transcript of Quiz 4 8:30-8:50am TODAY Have your calculator ready. Cell phone calculator NOT allowed. Closed book...