Lecture3(Quantum Chem) Ks

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Transcript of Lecture3(Quantum Chem) Ks
K. Sumithra
CHEMISTRY I (CHEM C141)
Lecture 3: 9/8/2010
SUMMARY OF THE LAST LECTURE
Black Body Radiation  features
• Planck’s Distributions:
• Concept of QuantizationPhotoelectric Effect: Ek = h = h( 0)• Particle nature of light
Line Spectra: ΔE = E2 – E1 = hν• Convincing evidence for Quantization
Bohr Atom Model
Atomic and Molecular Spectra
The energy of the atoms or molecules is confined to discrete values, so energy can be discarded only in packets.
A region of spectrum of radiationemitted by exited iron atoms
Spectrum due to sulphur dioxidemolecules
Bohr model of hydrogenlike atom
•To account for the line spectrum, Bohr proposed stable orbits (or energy levels), for the electron, given by the quantization condition for angular momentum
mvr = nh/2 = nħ, n = 1,2,3,….
Bohr Model
1. Specific orbits, discrete quantized energies.
2. The electrons do not continuously lose energy, but gain or lose by jumping from one orbit to another
3. quantization of angular momentum
L = mvr = nh/2 = nħ, n = 1,2,3,….
Success
Could explain Rydberg’s formula
Theoretical background for Line Spectra
Bohr model – Inadequacies
Primitive Model
Semiclassical
The spectra of larger atoms.
The relative intensities of spectral lines.
The existence of fine and hyperfine structure in spectral lines.
The Zeeman effect  changes in spectral lines due to external magnetic fields.
Waves and Particles
Main experiment showing light as particles are the Photoelectric effect
Black body radiation
Two properties of waves are:
InterferenceDiffraction
If electron is acting as a wave, We should see diffraction and interference of matter waves
WaveParticle Duality
Doubleslit ExperimentInterference: Superposition of two or more waves to generate new patterns
Constructive; destructive
WaveParticle duality shows:Light can act like a particle.Particles can act as waves
The wavefronts resulting from two slits.
Young’s doubleslit experiment can be done with electrons
Electron behaving as a wave!
Two waves in phase
Two waves 180° out of phase
combinedwaveform
wave 1
wave 2
constructive destructive
Interference
Electron DiffractionFiring electron at an object and observing the
scattering (analogous: Xray and neutron diffraction): Davisson and Germer 1925
investigation of the angular distribution of electrons scattered from nickel. :
electron beam was scattered by the surface atoms at the exact angles predicted for the diffraction of waves, with a typical wavelength
Bragg’s lawnλ=2d sin(θ)
λ wavelength of the electron wave
A pattern of sharp reflected beams from the crystal
Duality
Girl friend or her Granny?
waveparticle duality
The ability for something to behave as a wave and a particle at the same time is known as waveparticle duality.
It combines two contradictory features or qualitiesThat does not mean that it is false! It is a fundamental property of the universe.
Duality is a paradox
MatterWave Duality
Orthodox Quantum physicist : Duality is a phenomenon that can be viewed in one way or in another, but not both simultaneously.
Secondorder consequence of various limitations of the observer
Wave–particle duality is deeply embedded into the foundations of quantum mechanics
It is difficult to draw a line separating wave–particle duality from the rest of quantum mechanics.
1. In electron microscopy where the small wavelengths associated with the
electron can be used to view objects much smaller than what is visible using visible light.
Applications of Duality
2. Neutron Diffraction uses neutrons with a wavelength of about 1 Ǻ, the typical spacing of atoms in a solid, to
determine the structure of solids.
Evidence for waveparticle duality
Electron diffraction Interference of matterwaves
Photoelectric effect Compton effect
“ There are therefore now two theories of light, both indispensable, and … without any logical connection.”
Einstein, 1924
Evidence for wavenature of matter, light
Evidence for particlenature of light
Light comes in discrete units (photons) with particle properties (energy and momentum) that are related to thewavelike properties of frequency and wavelength.
MATTER WAVES
Prince Louis de Broglie 1923Postulate :
Ordinary matter can have wavelike properties, with the wavelength λ related to momentum p.
WaveParticle Duality
p = h/
A particle moving with linear momentum p, has an associated ‘matterwave’ of wave length: = h/p
Matter waves
de Broglie:
= h/p
Calculate the wavelength of an electron in a 10MeV particle accelerator. (1 MeV = 106 eV) Solution: We need to find the momentum, p, from the energy, E. The relationship between them is p = (2mE)½
P = (2 x 9.11 x 1031 kg x10 x106 x 1.602 x 1019 kg m2 s2)½
= 1.7 x 1021 kg m s1
λ= h/p = (6.626 x 1034 J s)/(1.7 x 1021 kg m s1) λ = 3.9 x 1013 m = 0.39 pm
C60 fullerene’s wave manifestation:
Large, massive object
(diameter is in nanometer range)
de Broglie wavelength is 2.5 pm i.e. about 400 times smaller than diameter.
•Journal: Nature 401: 680682, 1999
Largest object for which quantummechanical wavelike properties have been directly observed in diffraction.
BuckminsterfullereneBucky ball
University of Vienna, Austria.
Are there waves associated with macroscopic objects?
Wavelengths are immeasurably small
A human being weighing 70 kg, and moving with a speed of 25 m/s ~ 3.79 x 1037 meters.
A ball weighing 100 g, and moving with a speed of 25 m/s ~ 2.65 x 1034 meters.
An electron accelerated through a potential difference of 50 V ~ 1.73 x 1010 meters.
Some Typical de Broglie wavelengths
Uncertainty Principle No physical phenomena can be described by only ‘classic point particle’ or ‘wave’ Neither the wave or particle description is fully and exclusively accurate
Duality ; Consequence
A property of Conjugate variables :
– share an uncertainty relation
Time and Frequency
Position and Momentum
Uncertainty
Heisenberg’s Uncertainty Principle
It is impossible to specify simultaneously, with arbitrary precision, (a given Cartesian component of) the momentum and position of a particle.
px x ħ/2
•Complementary variables, increase in the precision of one possible only at the cost of a loss of precision in the other.
x uncertainty in positionp uncertainty in momentum
mΔv.Δx ≥ h/4π ħ=h/2π
Uncertainty Principle
Definite wavelength Definite momentum but since wave is spread out everywhere, no information about position.
Hard to understand duality, matter waves, uncertainty?