Transcript Physical Chemistry

Physical Chemistry
Quantum Chemistry
Quantum Mechanics – Historical Background
» Physics in the Late 19th Century (prior to quantum mechanics
(QM))
• Atoms are basic constituents of matter
• Newton’s Laws apply universally
• The world is deterministic
» Physics was complete except for a few decimal places !
• Newtonian mechanics explained macroscopic behavior
of matter --planetary motion, fluid flow, elasticity, etc.
• Thermodynamics had its first two laws and most of their
consequences
• Basic statistical mechanics had been applied to chemical
systems
• Light was explained as an electromagnetic wave
» However there were several experiments that could not be
explained by classical physics and the accepted dogma !
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Blackbody radiation
Photoelectric effect
Discrete atomic spectra
The electron as a subatomic particle
» � Inescapable conclusions would result from these problems
• Atoms are not the most microscopic objects
• Newton’s laws do not apply to the microscopic world of
the electron
• OUTCOME � New Rules!!!
Quantum Mechanics!
• Describes rules that apply to electrons in
atoms and molecules
• Non-deterministic, probabilistic ! A new
philosophy of nature
– � Explains unsolved problems of late 19th century
physics
– � Explains bonding, structure, and reactivity in
chemistry
The DEMISE of CLASSICAL PHYSICS
– (a) Discovery of the Electron
» In 1897 J.J. Thomson discovers the electron and measures (eme)
(and inadvertently invents the cathode ray (TV) tube)
» Faraday (1860’s – 1870’s) had already shown using
electrochemistry that amounts of electric current proportional to
amounts of some substances could be liberated in an electrolytic
cell. The term “electron” was suggested as a natural “unit” of
electricity.
» But Thomson experimentally observes electrons as particles with
charge & mass.
» Thomson found that results are independent of (1)
cathode material
» (2) residual gas composition
» � “electron” is a distinct particle, present in all
materials!
» Classical mechanics � force on electron due to
deflector voltage:
» (b) 1909 Mulliken oil drop experiment determines
e, me separately
» (c) Where are the electrons? What’s the structure
of the atom?
» Angstrom (10-10 m) atomic size scale already
inferred from gas kinetics First “jellium” model didn’t
last long
• Rutherford backscatterng experment
» (1) He2+ nucleus verysmall, << 10-10 m (Rutherford
estimated 10-14 m)
• (2) Au atoms are mostly empty!
» BUT model not consistent with classical electrodynamics:
Accelerating charge emits radiation! (centripetal
acceleration = v2/r) And since light has energy, Emust be
getting more negative with time
» R must be getting smaller with time!
» Electronspiralsintonucleusin~1010s!
» Also, as rdecreases, vshould increase Frequency � of
emitted light = frequency of rotation
» atom should emit light at all frequencies – that is it should
produce a continuous spectrum
» BUT emission from atoms was known to be discrete,
not continuous!
» For the H atom, Rydberg showed that the spectrum
was consistent with the simple formula:
Summary: Rutherford’s model of the atom
• (1) Is not stable relative to collapse of
electron into nucleus
• (2) Does not yield discrete emission lines,
• (3) Does not explain the Rydberg formula
The DEMISE of CLASSICAL PHYSICS
(cont’d)
• (a) Blackbody radiation --All things emit light when
heated up!
» Classically: (1) Radiation from a blackbody is the result of
electrons oscillating with frequency
Oscillating charged particle
antennae
» (2) The electrons can oscillate (& radiate) equally well at any
frequency
• Rayleigh-Jeans Law for spectral density ρ(ν), where intensity of
emitted light in frequency range from ν to ν+ dν is I(ν)~ ρ(ν) dν
• k = Boltzmann’s constant [= R/NA (gas constant per
molecule)] c = speed of light
Planck (~1900) First “quantum” ideas
• (1) The energy of the oscillator frequency
• (2) The energy an integral multiple of
» h becomes a “quantum” of energy
» Planck used statistical mechanics (5.62) to derive the
expression for black body radiation
» (b) Photoelectric effect
» Einstein (1905) proposed:
• (1) Light is made up of energy “packets: “photons”
• (2) The energy of a photon is proportional to the light
frequency
E = hv h Planck’s constant
» New model of photoelectric effect:
» Comparing to exp’t, value of “h” matches the one
found by Planck! This was an extraordinary result !
» Summary:
• (1) Structure of atom can’t be explained
classically
• (2) Discrete atomic spectra and Rydberg’s
formula can’t be explained
• (3) Blackbody radiation can be “explained” by
quantifying energy of
• oscillators E = h
• (4) Photoelectric effect can be “explained” by
quantifying energy of light
• E=h
The ATOM of NIELS BOHR
» Niels Bohr, a Danish physicist who established the
Copenhagen school.
– (a) Assumptions underlying the Bohr atom
• (1) Atoms can exist in stable “states” without radiating. The states
have discrete energies En, n= 1, 2, 3,..., where n= 1 is the lowest
energy state (the most negative, relative to the dissociated atom at
zero energy), n= 2 is the next lowest energy state, etc. The number
“n” is an integer, a quantum number, that labels the state.
• (2) Transitions between states can be made with the absorption or
emission of a photon of frequency where ν = ΔE/ h
.
» These two assumptions “explain” the discrete
spectrum of atomic vapor emission. Each line in the
spectrum corresponds to a transition between two
particular levels. Thisisthebirthofmodernspectroscopy.
» (3) Angular momentum is quantized: l = nh where h =
h /2π
• Angular momentum
» For H atom withn= 1, r=a0= 5.29x10-11m = 0.529 Å (1 Å = 1010m)
» Take Rutherford’s energy and put in r,
» Energies are quantized!!!
» For H atom, emission spectrum
WAVE-PARTICLE DUALITY of LIGHT and MATTER
• MATTER(A)Light (electromagnetic radiation)
• Light as a waveFor now neglect polarization vector
orientationPropagating in x-direction:
Young’s 2-slit experiment
日本 Hitachi 公司 的 Tonomura 利用 Electron
Phase Microscope 所做的雙狹縫實驗
• Double-slit experiment
Fig. 1
Double – slit experiment with single electrons
Fig. Single electron events build up to from an interference pattern in
2
the double-slit experiments.
» Light as a particle
• Light can behave both as a wave and as a particle!! Which aspect is
observed depends on what is measured.
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(B) Matter
Matter as particles
Matter as waves
obvious from everyday experience
(deBroglie, 1929, Nobel Prize for his Ph.D. thesis!)
» Same relationship between momentum and wavelength
forlightandformatter
» Consequences (I)
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As Bohr had assumed angular momentum is quantized!!!
WAVE-PARTICLE DUALITY of MATTER
» Consequences (II)
» Heisenberg Uncertainty Principle
» Consider diffraction through a single slit
» Now consider a beam of electrons with de Broglie
wavelength .The slit restricts the possible positions
of the electrons in the x direction: at the slit, the
uncertainty in the electron x-position is
» This means the electrons must go through the slit
with some range of velocity components Vx
» So the position and momentum of a particle cannot
both be determined with arbitrary position! Knowing
one quantity with high precision means that the other
must necessarily be imprecise!
» The conventional statement of the Heisenberg
Uncertainty Principle is
» Implications for atomic structure
» Apply Uncertainty Principle to e-in H atom
» Basically, if we know the e-is in the atom, then we
can’t know its velocity at all!
» Bohr had assumed the electron was a particle with a
known position and velocity. To complete the picture
of atomic structure, the wavelike properties of the
electron had to be included.
» So how do we properly represent where the particle
is??
» Schrodinger (1933 Nobel Prize)
» A particle in a “stable” or time-independent state can
be represented mathematically as a wave, by a
“wavefunction” (x) (in 1-D) which is a solution to
• the differential equation
» We cannot prove the Schrödinger equation. But we can motivate why it might
be reasonable.
» Similarly, a left-traveling wave can be represented as
» Both are solutions to the wave equation
» As in a vibrating violin string, the node positions are
independent of time. Only the amplitude of the fixed
waveform oscillates with time.
» More generally, we can write wave equation
solutions in the form
» We now have the outline of:
» a physicalpictureinvolving wave and particle duality
of light and matter !
» a quantitativetheoryallowing calculations of stable
states and their properties !