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2. Atomic Structure

Remember!? Dmitri I. Mendeleev’s Periodic Table (17 Feb. 1869 )

2.1 Historical Developmentof Atomic Theory

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2.1.1 The Periodic Tableof the Elements

2.1.2 Discovery of SubatomicParticles & the Bohr Atom

Each element emits lightof specific energies when excited by electric dischargeor heat. For the H-atom

(Balmer, 1885):

654

3

2

n =

3

2.1.2 Discovery of SubatomicParticles & the Bohr Atom

Johann Jacob Balmer(Physicist, 1825 – 1899)

The Hydrogen Spectrum:

2.1.2 Discovery of SubatomicParticles & the Bohr Atom

Bohr Model (1913 ~ 1923) of the Hydrogen Atom:

Note, Rydberg’s“constant” is f(mn)

principle quantum numbers!

Niels Bohr(1885 - 1962)

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2.1.2 Discovery of SubatomicParticles & the Bohr Atom

Theodore Lyman(1874 - 1954)

Friedrich Paschen(1865-1940)

Energy levels only valid for hydrogen!

2.1.2 Discovery of SubatomicParticles & the Bohr Atom

All Moving Particles have Wave Properties (de Broglie , 1920):

Energy of spectral lines (electron)can be measured with great precision(Δpx is small) -> Uncertainty in location of the electron is large.

No exact orbits but orbitals with probability to find the electron

Louis de Broglie(1892-1987 )

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2.1.2 Discovery of SubatomicParticles & the Bohr Atom

“The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.”(Heisenberg, 1927)

Uncertainties in the Location and Momentum of a Moving Particle (Heisenberg , 1927):

Δt ΔE >= h/4πNot quite correct…there is no operator in presenting Δt (time)

Werner Heisenberg(1901-1976 )

2. 2 The Schrödinger Equation

Erwin Schrödinger(1887-1961)

Wave Properties of an Electron in Terms of Position, MassTotal Energy, and Potential Energy:

Wave function, Ψ, describes electron wave in space.

Hamiltonian operator, H, includes derivatives that operate on Ψ

Each orbital, characterized by its own Ψ, has a characteristic energy

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The “Solvay Congress”in Copenhagen 1927

Heisenberg, standing front left, next to P.A.M. Dirac, in front of A.H. Compton. Univ. of Chicago, 1929.

Bohr in intense discussion with Heisenberg and Pauli(L to R) in Copenhagen

…but don’t forget good old “Al”!

The “Solvay Congress”in Copenhagen 1927

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The “Solvay Congress”in Copenhagen 1927

2. 2 The Schrödinger Equation

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Unlimited solutions…but for a physically realistic solution for Ψ:

Each Ψ describes the wave properties of a given electron in a particular orbital . The probability of finding anelectron at a given point in space is proportional to Ψ2

2. 2 The Schrödinger Equation

2.2.1 Particle in a Box

Particle in a Box n = 3

n = 2

n = 1

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2.2.2 Quantum Numbers& Atomic Wave Functions

*

* lines in alkali metal spectra are doubledbeam of alkali metal atoms splits into two if it passess through H

2.2.2 Quantum Numbers& Atomic Wave Functions

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2.2.2 Quantum Numbers& Atomic Wave Functions

2.2.2 Quantum Numbers& Atomic Wave Functions

R(r): Radial Function “R”: Electron Density @ Different Distances from the Nucleus. Determined by n and l

The Radial Probability Function 4πr2R2 describes theprobability of finding the electron at a given distancefrom the nucleus, summed over all angles

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2.2.2 Quantum Numbers& Atomic Wave Functions

The Angular Functions:

Angular Functions “ΘΦ” Y: Describe the Shape of the Orbital and its Orientation in space: Y(θφ) -> s, p, d Orbitals

Determined by l and ml

How does the probability change from point to point at a given distance?

2.2.2 Quantum Numbers& Atomic Wave Functions

The Nodal Surfaces:

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2.2.2 Quantum Numbers& Atomic Wave Functions

2.2.2 Quantum Numbers& Atomic Wave Functions

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2.2.2 Quantum Numbers& Atomic Wave Functions

taken from Harvey & Potter“Introduction to Physical

Inorganic Chemistry”Wesley 1963

note thedifference

2.2.2 Quantum Numbers& Atomic Wave Functions

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2.2.2 Quantum Numbers& Atomic Wave Functions

2.2.2 Quantum Numbers& Atomic Wave Functions

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2.2.2 Quantum Numbers& Atomic Wave Functions

The s and p-orbitals…that’s the way we like them most!

2.2.2 Quantum Numbers& Atomic Wave Functions

electron densityon the axes!

The s and p-orbitals…that’s the way we like them most!

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2.2.2 Quantum Numbers& Atomic Wave Functions

The five d-orbitals…my favorite ones!

2.2.2 Quantum Numbers& Atomic Wave Functions

electron densityon the axes!

electron density in between the axes!

The five d-orbitals…my favorite ones!