Quiz 4 8:30-8:50am TODAY Have 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 7.22 Quiz 3 graded, scores being recorded. Next lecture February 12 Quiz 5 will cover the material from today’s lecture,material from DLM7&8, including FNTs for DLM9.

Normal Matter : Particles Bouncing Around!

Particle 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 would be the most valuable ideas to pass on to future generations. R.P. Feynman, Physics Nobel Laureat in 1965

Particle 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 would be the most valuable ideas to pass on to future generations. R.P. Feynman, Physics Nobel Laureat in 1965

Particle 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 would be the most valuable ideas to pass on to future generations. R.P. Feynman, Physics Nobel Laureat in 1965

Particle 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 as Masses on Spring ~ two atomic size particles interacting via“pair-wise potential” a.k.a. Lennard-Jones Potential

Intro to Particle Model of Matter Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential r Distance between the atoms (r) Potential Energy Equilibrium separation r o

Displacement from equilibrium y[+][-] Equilibrium separation : r o Mass- Spring Oscillator analogy Slope of PE curve (d(PE)/dy) is zero, i.e., force on the mass is zero.

Intro to Particle Model of Matter Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential r Distance between the atoms (r) Potential Energy Equilibrium separation r o Equilibrium separation: r o The force the two particles exert 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 Matter Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential Flattening: atoms have negligible forces at large separation. r Distance between the atoms (r) Potential Energy Equilibrium separation r o Do atoms a very long distance apart attract or repel?

Intro to Particle Model of Matter Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential r Distance between the atoms (r) Potential Energy Equilibrium separation r o 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 Matter Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential r Distance between the atoms (r) Potential Energy Equilibrium separation r o As the atom-atom separation decreases, force from the potential increases. ~ attracting each other when they are a little distance apart

Intro to Particle Model of Matter Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential r Distance between the atoms (r) Potential Energy Equilibrium separation r o What happens when the atom separation decreases less than the equilibrium separation?

Intro to Particle Model of Matter Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential Repulsive: Atoms push apart as they get too close r Distance between the atoms (r) Potential Energy Equilibrium separation r o ~ but repelling upon being squeezed one another Is 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 Potential

 roro  = atomic diameter r o = equilibrium separation “Pair-wise potential” a.k.a. Lennard-Jones Potential * ‘Not to scale’

Energy r (atomic diameters) r   is the atomic diameter roro   is the well depth r o is the equilibrium separation  Potential Energy between two atoms “pair-wise potential” a.k.a. Lennard-Jones Potential pair-wise  ~ J  ~ m = 1Å

E tot 10 Separation ( m) Energy ( J)

Separation ( m) Energy ( J) E tot

Separation ( m) Energy ( J) E tot

PE KE E tot Separation ( m) Energy ( J)

PE KE E tot Inaccessible Separation ( m) Energy ( J) This is what is meant by a “bond” - the particles cannot escape from one another

PE KE E tot Inaccessible 10 Separation ( m) Energy ( 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.E tot  0 B.E tot  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.E tot  0

r Energy ( J) Distance between the atoms E tot Pair-wise potential When E tot ≥ 0, What is true about KE at very large r?

What is the change in bond energy (∆E bond ) by removing the red atom? 2.2 A 4.4 A 6.6 A -8 x J -0.5 x J ~ 0 J 8.8 A 11 A ~ 0 J Bond energy For each atom-atom pair, Pair-wise potential exists Separation ( m)

E bond for a substance is the amount of energy required to break apart “all” the bonds i.e. we define E bond = 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. E bond = ∑ all pairs (PE pair-wise ) Multiple 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… Phases under Microscope

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