2. Atomic Structure. 2.1 Historical Development of Atomic Theory. Remember!? Dmitri I. Mendeleev s Periodic Table (17 Feb )

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1 2. Atomic Structure 2.1 Historical Development of Atomic Theory Remember!? Dmitri I. Mendeleev s Periodic Table (17 Feb ) 1

2 2.1.1 The Periodic Table of the Elements 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 =

3 2.1.2 Discovery of Subatomic Particles & the Bohr Atom The Hydrogen Spectrum: Johann Jacob Balmer (Physicist, ) Discovery of Subatomic Particles & the Bohr Atom Bohr Model (1913 ~ 1923) of the Hydrogen Atom: Note, Rydberg s constant is f(m n ) Niels Bohr ( ) principle quantum numbers! 3

4 2.1.2 Discovery of Subatomic Particles & the Bohr Atom Theodore Lyman ( ) Friedrich Paschen ( ) Energy levels only valid for hydrogen! 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 (Δp x is small) -> Uncertainty in location of the electron is large. No exact orbits but orbitals with probability to find the electron Louis de Broglie ( ) 4

5 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 ( ) 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 ( ) 5

6 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, The Solvay Congress in Copenhagen 1927 but don t forget good old Al! 6

7 The Solvay Congress in Copenhagen The Schrödinger Equation 7

8 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 Ψ Particle in a Box Particle in a Box n = 3 n = 2 n = 1 8

9 2.2.2 Quantum Numbers * * lines in alkali metal spectra are doubled beam of alkali metal atoms splits into two if it passess through H Quantum Numbers 9

10 2.2.2 Quantum Numbers Quantum Numbers R(r): Radial Function R : Electron Different Distances from the Nucleus. Determined by n and l The Radial Probability Function 4πr 2 R 2 describes the probability of finding the electron at a given distance from the nucleus, summed over all angles 10

11 2.2.2 Quantum Numbers 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 m l Quantum Numbers The Nodal Surfaces: 11

12 2.2.2 Quantum Numbers Quantum Numbers 12

13 2.2.2 Quantum Numbers note the difference taken from Harvey & Potter Introduction to Physical Inorganic Chemistry Wesley Quantum Numbers 13

14 2.2.2 Quantum Numbers Quantum Numbers 14

15 2.2.2 Quantum Numbers The s and p-orbitals that s the way we like them most! Quantum Numbers The s and p-orbitals that s the way we like them most! electron density on the axes! 15

16 2.2.2 Quantum Numbers The five d-orbitals my favorite ones! Quantum Numbers The five d-orbitals my favorite ones! electron density on the axes! electron density in between the axes! 16

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