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2. Atomic Structure 2.1 Historical Development of Atomic Theory Remember!? Dmitri I. Mendeleev’s Periodic Table (17 Feb. 1869 ) 1 2.1.1 The Periodic Table of the Elements 2.1.2 Discovery of Subatomic Particles & the Bohr Atom Each element emits light of specific energies when excited by electric discharge or heat. For the H-atom (Balmer, 1885): n= 6 5 4 3 2 2 2.1.2 Discovery of Subatomic Particles & the Bohr Atom The Hydrogen Spectrum: Johann Jacob Balmer (Physicist, 1825 – 1899) 2.1.2 Discovery of Subatomic Particles & the Bohr Atom Bohr Model (1913 ~ 1923) of the Hydrogen Atom: Note, Rydberg’s “constant” is f(mn) Niels Bohr (1885 - 1962) principle quantum numbers! 3 2.1.2 Discovery of Subatomic Particles & the Bohr Atom Theodore Lyman (1874 - 1954) Friedrich Paschen (1865-1940) Energy levels only valid for hydrogen! 2.1.2 Discovery of Subatomic Particles & 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 ) 4 2.1.2 Discovery of Subatomic Particles & the Bohr Atom Uncertainties in the Location and Momentum of a Moving Particle (Heisenberg , 1927): “The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.” (Heisenberg, 1927) Δt ΔE >= h/4π Not quite correct…there is no operator in presenting Δt (time) Werner Heisenberg (1901-1976 ) 2. 2 The Schrödinger Equation Wave Properties of an Electron in Terms of Position, Mass Total 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 Erwin Schrödinger (1887-1961) 5 The “Solvay Congress” in Copenhagen 1927 Bohr in intense discussion with Heisenberg and Pauli (L to R) in Copenhagen Heisenberg, standing front left, next to P.A.M. Dirac, in front of A.H. Compton. Univ. of Chicago, 1929. The “Solvay Congress” in Copenhagen 1927 …but don’t forget good old “Al”! 6 The “Solvay Congress” in Copenhagen 1927 2. 2 The Schrödinger Equation 7 2. 2 The Schrödinger Equation 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 an electron at a given point in space is proportional to Ψ2 2.2.1 Particle in a Box Particle in a Box n=3 n=2 n=1 8 2.2.2 Quantum Numbers & Atomic Wave Functions * * lines in alkali metal spectra are doubled beam of alkali metal atoms splits into two if it passess through H 2.2.2 Quantum Numbers & Atomic Wave Functions 9 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 the probability of finding the electron at a given distance from the nucleus, summed over all angles 10 2.2.2 Quantum Numbers & Atomic Wave Functions The Angular Functions: How does the probability change from point to point at a given distance? 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 2.2.2 Quantum Numbers & Atomic Wave Functions The Nodal Surfaces: 11 2.2.2 Quantum Numbers & Atomic Wave Functions 2.2.2 Quantum Numbers & Atomic Wave Functions 12 2.2.2 Quantum Numbers & Atomic Wave Functions note the difference taken from Harvey & Potter “Introduction to Physical Inorganic Chemistry” Wesley 1963 2.2.2 Quantum Numbers & Atomic Wave Functions 13 2.2.2 Quantum Numbers & Atomic Wave Functions 2.2.2 Quantum Numbers & Atomic Wave Functions 14 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 The s and p-orbitals…that’s the way we like them most! electron density on the axes! 15 2.2.2 Quantum Numbers & Atomic Wave Functions The five d-orbitals…my favorite ones! 2.2.2 Quantum Numbers & Atomic Wave Functions The five d-orbitals…my favorite ones! electron density on the axes! electron density in between the axes! 16