Chemistry 4521

Time is flying by: only 15 lectures left!! Six quantum mechanics Four Spectroscopy Third Hour exam Third Hour exam Three statistical mechanics Review Final Exam Wednesday May 4 7:30 10 PM Final Exam, Wednesday, May 4, 7:30 – 10 PM

Quantum MechanicsOverall goals:Introduce QM and qualitatively solve limited problems in 1D; extend to 3DParticle in a box (translation quantization)

ll ( l l b )Harmonic oscillator (molecular vibration)Rigid rotor (molecular rotation)Atomic and molecular electronic energy levelsApply these results to spectroscopic analyses and statistical equilibrium

Lecture 1 (today) Classical mechanics, optics, wave motion, thermodynamics

Apply these results to spectroscopic analyses and statistical equilibrium

p yFailures when extending to short distances, small massesBlackbody radiation ( existence of photons)Wave –particle duality

Diff ti h t l t i ff tDiffraction, photoelectric effectMatter (deBroglie) waves, electron diffractionQualitative QM

Bohr atomBohr atomParticle in a box

All were partial answers, leading Schrödinger to wave mechanics

Classical Physics/MechanicsClassical Physics/Mechanics Predicts precise trajectory for particles with precisely

ifi d l ti d t t h i t tspecified locations and momenta at each instant

Allows the translational, rotational and vibrationalmodes of motion to be excited to any energy, simplyby controlling forces that are applied

Shattered by three observations involving matter and

Considers matter and energy as distinct

Shattered by three observations involving matter and light, all indicating the presence of discrete energy states • Blackbody radiation

Ph t l t i ff t• Photoelectric effect• Atomic line spectra

Quantum MechanicsCircumference = 2r=n

r

Describes the "Wave-Particle" Duality

Light is an electromagnetic wave described by Maxwell’s equationLight is an electromagnetic wave, described by Maxwell s equation- but it can also behave like a particle

Particles - also have wavelike nature (manifest only when mass is tiny)Th ti f ti l b d ib d b The wave properties of particles can be described by a modified form of Maxwell’s equations for wave motion, known as the Schrödinger equation.

Pre-Quantum Mechanics1890'sI. Classical MechanicsGeneral Equations (F= ma on steroids)q (F m )LaGrangeHamiltonII Electricity & MagnetismII. Electricity & MagnetismMaxwell's EquationsElectromagnetic Waves:

Central theses of the time: No real conceptual issues remain unresolved.C t ti l t b li bl h d h !Computations on real systems were unbelievably hard, however!

Traveling WavegWave amplitude is orthogonalto the direction of propagationto the direction of propagation

Single vertical pulse moves on horizontal string

2, sinY x t A x vt

With only five lectures, we must ignore timedependence and restrict o rsel es to those

vwithfrequency

dependence, and restrict ourselves to thosestates characterized by standing waves.Time-independent quantum mechanics

Wave Motion in Restricted Systemsy

One-half wavelength (/2) i h (/2) is the “quantum” of the guitar guitar string’s vibration

X X

Pre-Quantum MechanicsII. Electricity & MagnetismMaxwell's EquationsLight:Light:

III. Thermodynamics(you know all about this!)

IV. OpticsWave Diffraction( ~ object size)( object size)Two slit diffraction:Geometrical Optics( >> object size)

Failures of Classical Physics(waves behaving as particles)(waves behaving as particles)

1. Blackbody radiation

Bl kb d R di tiBlackbody Radiation

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Smoldering coal1000 K

Electric heating coil1500 K

Light bulb filament2000 K

Radiation from a Cavityi Bl kb d R di tiis Blackbody Radiation

Atoms in solid vibrate Atoms in solid vibrate and produce radiationRadiation in cavity has a at on n ca ty has range of frequencies,

Treated rigorouslywith classical

thermodynamics thermodynamics and E & M

Rayleigh-Jeans Blackbody Calculationy g y(rigorous thermo and E&M)

2

B38 k T d

c

B4

c8 k T d

H ll did it k?

B4 Correct atlarge

How well did it work?

The “Ultraviolet Catastrophe”

Blackbody Radiationy

Radiation emitted from object increases and shifts to shorter wavelengths at higher temperaturesshorter wavelengths at higher temperatures

Not quantitatively explained by classical physics

i t f is energy at a frequency , per unit volume, andper unit frequency range

Planck's Idea that OscillatorEnergy is QuantizedEnergy is Quantized

Max Planck "fixed it up" by trial and error, in the process incorporating a "non-physical" assumption:p g p y p

Photons can behave like particles under some conditions, and have a relationship between their frequency and energy given byE = h = h c/, where h is a constant.

S b i i hi h h i i h R l i h J h h Substituting this hypothesis into the Rayleigh - Jeans theory, he obtained

8 1( ) hcT

Planck simply adjusted h and found one value 6 6 x 10-27 erg s

5( , )1

hckT

Te

Planck simply adjusted h, and found one value, 6.6 x 10 7 erg s,that fit the experimental data! It was later known as Planck's constant.

No one took it seriously.

Comparison of Planck and Rayleigh-Jeans equations

R l i h J ( i d )Rayleigh Jeans (non-quantized energy):28 k T

Pl k ( ti d )

B3 k Tc

28 h

Planck (quantized energy):

3Bexp(h / k T) 1c

A constant (later called h) reappeared in the photoelectric A constant (later called h) reappeared in the photoelectric effect and in the diffraction of “matter waves,”in each case with the same numerical value! A clue!

Failures of Classical Physics(waves behaving as particles)(waves behaving as particles)

2. Photoelectric effect

Light Electron

Photoelectric EffectLight Electron,

mass mmass mespeed u

Electron emission depends on frequency of light,NOT on intensity of light

Light acts as if it is a beam of particles that has energy hOne-to-one relationship between photon absorbed and e– emitted

h = 1/2 mu2 + w k (E )

p p m

where w = e= work function (E required to remove e–)and 1/2 meu2 = KE of ejected e–

Experimental Characteristics of the Photoelectric Effect

h = 1/2 mu2 + e

1. There is a threshold frequency for electron ejection. Neither the threshold nor KE depends on intensity of the light

KE depends on intensity of the light.2. KE of ejected electrons increases with frequency .3. There is no time lag for electron ejection

4. e is the “work function” (e- binding energy) of the metal

5. Nobel prize for Einstein!

ConcepTest # 1ConcepTest # 1The kinetic energy of the photo-y pelectron is plotted versus the frequency of incident radiation for potassium, rubidium and sodium. F l ft t i ht id tif th From left to right, identify the lines.

A. K, Rb, Na

B Rb Na KB. Rb, Na, K

C. Rb, K, Na

D N K RbD. Na, K, Rb

Failures of Classical Physics(particles behaving as waves)(particles behaving as waves)

3. X-ray and Electron Diffractiond e- me

x ray V

e

Led to deBroglie

matterh

p

d

Au

d

V

p = momentum = mv

mattermatterp

4. Atomic Line Emission seems to indicate discrete energy states Dispersion of visible light

Au Au

Dispersion of light from excited atomsp f g f

Photons as waves and particles

Light particles with energy h known as photons

Dual theory of radiationy

Diffraction and interference depends onWAVE properties of lightWAVE properties of light

Photoelectric effect depends onPARTICLE properties of lightPARTICLE properties of light

Matter: particles & wavesMatter with mass m and velocity v seems to have a wave of wavelength D = h/p associated with it.g D p

Matter behaves “normally” (F=ma) when it interacts with objects with dimensions >> D

Matter displays diffraction and interference effects when it interacts with objects with di i dimensions D.(constructive and destructive interference leading to the concept of stationary states)p y )

Dhp

The Schrödinger equation is essentially a wave equation applied to matter waves.