Lecture3(Quantum Chem) Ks

K. Sumithra CHEMISTRY I (CHEM C141) Lecture 3: 9/8/2010


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Transcript of Lecture3(Quantum Chem) Ks

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K. Sumithra


Lecture 3: 9/8/2010

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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

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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

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Bohr model of hydrogen-like 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,….

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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,….


Could explain Rydberg’s formula

Theoretical background for Line Spectra

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Bohr model – Inadequacies

Primitive Model


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.

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Waves and Particles

Main experiment showing light as particles are the Photoelectric effect

Black body radiation

Two properties of waves are:


If electron is acting as a wave, We should see diffraction and interference of matter waves

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Wave-Particle Duality

Double-slit ExperimentInterference: Superposition of two or more waves to generate new patterns

Constructive; destructive

Wave-Particle duality shows:Light can act like a particle.Particles can act as waves

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The wavefronts resulting from two slits.

Young’s double-slit experiment can be done with electrons

Electron behaving as a wave!

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Two waves in phase

Two waves 180° out of phase


wave 1

wave 2

constructive destructive


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Electron DiffractionFiring electron at an object and observing the

scattering (analogous: X-ray 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

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Bragg’s lawnλ=2d sin(θ)

λ- wavelength of the electron wave

A pattern of sharp reflected beams from the crystal

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Girl friend or her Granny?

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wave-particle duality

The ability for something to behave as a wave and a particle at the same time is known as wave-particle duality.

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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

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Matter-Wave Duality

Orthodox Quantum physicist : Duality is a phenomenon that can be viewed in one way or in another, but not both simultaneously.

Second-order consequence of various limitations of the observer

Wave–particle duality is deeply embedded into the foundations of quantum mechanics

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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.

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Evidence for wave-particle duality

Electron diffraction Interference of matter-waves

Photoelectric effect Compton effect

“ There are therefore now two theories of light, both indispensable, and … without any logical connection.” 

Einstein, 1924

Evidence for wave-nature of matter, light

Evidence for particle-nature of light

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Light comes in discrete units (photons) with particle properties (energy and momentum) that are related to thewave-like properties of frequency and wavelength. 


Prince Louis de Broglie 1923Postulate :

Ordinary matter can have wave-like properties, with the wavelength λ related to momentum p.

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Wave-Particle Duality

p = h/

A particle moving with linear momentum p, has an associated ‘matter-wave’ of wave length: = h/p

Matter waves

de Broglie:

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= h/p

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Calculate the wavelength of an electron in a 10-MeV 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 10-31 kg x10 x106 x 1.602 x 10-19 kg m2 s-2)½

= 1.7 x 10-21 kg m s-1

λ= h/p = (6.626 x 10-34 J s)/(1.7 x 10-21 kg m s-1) λ = 3.9 x 10-13 m = 0.39 pm

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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: 680-682, 1999

Largest object for which quantum-mechanical wave-like properties have been directly observed in diffraction.

BuckminsterfullereneBucky ball

University of Vienna, Austria.

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Are there waves associated with macroscopic objects?

Wavelengths are immeasurably small

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A human being weighing 70 kg, and moving with a speed of 25 m/s ~ 3.79 x 10-37 meters.

A ball weighing 100 g, and moving with a speed of 25 m/s ~ 2.65 x 10-34 meters.

An electron accelerated through a potential difference of 50 V ~ 1.73 x 10-10 meters.

Some Typical de Broglie wavelengths

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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

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A property of Conjugate variables :

– share an uncertainty relation

Time and Frequency

Position and Momentum


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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

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Uncertainty Principle

Definite wavelength Definite momentum but since wave is spread out everywhere, no information about position.

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Hard to understand duality, matter waves, uncertainty?