1. 1 Electronic Structure of Atoms (i.e., Quantum Mechanics) Brown, LeMay Ch 6 AP Chemistry

2. 2 6.1: Light is a Wave Electromagnetic spectrum: –A form of radiant energy (can travel without matter) –Both electrical and magnetic (properties are perpendicular to each other) Speed of Light: c = 3.0 x 10 8 m/s (in a vacuum) Wavelength ( ): distance between wave peaks (determines “color” of light) Frequency ( ): # cycles/sec (measured in Hz) c = 

3. 3 6.2: Light is a Particle (Quantum Theory) Blackbody radiation: * Blackbody: object that absorbs all EM radiation that strikes it; it can radiate all possible wavelengths of EM; below 700 K, very little visible EM is produced; above 700 K visible E is produced starting at red, orange, yellow, and white before ending up at blue as the temperature increases –discovery that light intensity (energy emitted per unit of time) is proportional to T 4 ; hotter = shorter wavelengths “Red hot” < “white hot” < “blue hot” Max Planck (1858-1947) Planck’s constant: Blackbody radiation can be explained if energy can be released or absorbed in packets of a standard size he called quanta (singular: quantum). where Planck’s constant (h) = 6.63 x 10 -34 J-s

4. 4 The Photoelectric Effect Spontaneous emission of e- from metal struck by light; first explained by Einstein in 1905 –A quantum strikes a metal atom and the energy is absorbed by an e-. –If the energy is sufficient, e- will leave its orbital, causing a current to flow throughout the metal. Albert Einstein (1879-1955)

5. 5 6.3: Bohr’s Model of the H Atom (and only H!) Atomic emission spectra: –Most sources produce light that contains many wavelengths at once. –However, light emitted from pure substances may contain only a few specific wavelengths of light called a line spectrum (as opposed to a continuous spectrum). –Atomic emission spectra are inverses of atomic absorption spectra. Hydrogen: contains 1 red, 1 blue and 1 violet. Carbon:

6. 6 Niels Bohr theorized that e-: –Travel in certain “orbits” around the nucleus, or, are only stable at certain distances from the nucleus –If not, e- should emit energy, slow down, and crash into the nucleus. Allowed orbital energies are defined by: principal quantum number (n) = 1, 2, 3, 4, … Rydberg’s constant (R H ) = 2.178 x 10 -18 J Niels Bohr (1888-1962) Johannes Rydberg (1854-1919)

7. As n approaches ∞, the e- is essentially removed from the atom, and E ∞ = 0. ground state: lowest energy level in which an e - is stable excited state: any energy level higher than an e - ’s ground state Increasing Energy, EPrincipal Quantum Number, n 5432154321 E5E4E3E2E1E5E4E3E2E1

8. 8 n i = initial orbital of e- n f = final orbital of e- in its transition

9. Figure 1: Line series are transitions from one level to another. Series Transition down to (emitted) or up from (absorbed)… Type of EMR Lyman1UV Balmer2Visible Paschen3IR Brackett4Far IR 5432154321 n Theodore Lyman (1874 - 1954) Johann Balmer (1825 – 1898) Friedrich Paschen (1865 - 1947) Frederick Brackett (1896 – 1988) ?

10. 10 6.4: Matter is a Wave Planck said: E = h c / Einstein said: E = m c 2 Louis DeBroglie said (1924):h c /  m c 2 h /  m c Therefore: m = h / c Particles (with mass) have an associated wavelength  h / mc Waves (with a wavelength) have an associated mass and velocity Louis de Broglie (1892 - 1987)

11. IBM – Almaden: “Stadium Corral” This image shows a ring of 76 iron atoms on a copper (111) surface. Electrons on this surface form a two-dimensional electron gas and scatter from the iron atoms but are confined by boundary or "corral." The wave pattern in the interior is due to the density distribution of the trapped electrons. Their energies and spatial distribution can be quite accurately calculated by solving the classic problem of a quantum mechanical particle in a hard-walled box. Quantum corrals provide us with a unique opportunity to study and visualize the quantum behavior of electrons within small confining structures.

12. 12 Heisenberg’s Uncertainty Principle (1927) It is impossible to determine the exact position and exact momentum (p) of an electron. p = m v To determine the position of an e-, you have to detect how light reflects off it. But light means photons, which means energy. When photons strike an e-, they may change its motion (its momentum). Werner Heisenberg (1901 – 1976)

13. 13 Electron density distribution in H atom

14. 14 6.5: Quantum Mechanics & Atomic Orbitals Schrödinger’s wave function: Relates probability (   ) of predicting position of e- to its energy. Where: U = potential energy x = positiont = time m = massi =√(-1) Erwin Schrödinger (1887 – 1961)

15. 15 Probability plots of 1s, 2s, and 3s orbitals

16. 16 6.6: Representations of Orbitals s orbital p orbitals

17. d orbitals f orbitals: very complicated

18. Figure 2: Orbital Quantum Numbers SymbolNameDescriptionMeaningEquations n Principle Q.N. Energy level (i.e. Bohr’s theory) Shell number n = 1, 2, 3, 4, 5, 6, 7 n = 1, 2, 3, … l Angular Momentum Q.N. General probability plot (“shape” of the orbitals) Subshell number l = 0, 1, 2, 3 l = 0 means “s” l = 1 means “p” l = 2 means “d” l = 3 means “f” l = 0, 1, 2, …, n – 1 Ex: If n = 1, l can only be 0; if n = 2, l can be 0 or 1.

19. SymbolNameDescriptionMeaningEquations mlml Magnetic Q.N. 3-D orientation of the orbital s has 1 p has 3 d has 5 f has 7 m l = -l, -l +1, …, 0, l, …, +l There are (2l + 1) values. msms Spin Q.N. Spin of the electron Parallel or antiparallel to field m s = +½ or -½ * s, p, d, and f come from the words sharp, principal, diffuse, and fundamental.

20. 20 Permissible Quantum Numbers (4, 1, 2, +½) (5, 2, 0, 0) (2, 2, 1, +½) Not permissible; if l = 1, m l = 1, 0, or –1 (p orbitals only have 3 subshells) Not permissible; m s = +½ or –½ Not permissible; if n = 2, l = 0 or 1 (there is no 2d orbital)

21. 21 1.Aufbau principle: e - enter orbitals of lowest energy first (* postulated by Bohr, 1920) 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 3d 4d 5d 6d 4f x 7 5f x 7 Increasing Energy 7p 6.7: Filling Order of Orbitals Relative stability & average distance of e- from nucleus

22. 22 1.Aufbau principle: e - enter orbitals of lowest energy first Increasing Energy 1s 2s 3s 4s 5s 6s 7s 3d 4d 5d 6d 4f x 7 5f x 7 2p 3p 4p 5p 6p 7p Relative stability & average distance of e- from nucleus 6.7: Filling Order of Orbitals

23. 23 Use the “diagonal rule” (some exceptions do occur). Sub-level maxima: s = 2 e- p = 6 e- d = 10 e- f = 14 e- … 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p

24. 24 2.Pauli exclusion principle (1925): no two e- can have the same four quantum numbers; e- in same orbital have opposite spins (up and down) 3.Hund’s rule: e- are added singly to each equivalent (degenerate) orbital before pairing Ex: Phosphorus (15 e-) has unpaired e- in the valence (outer) shell. 1s 2s 2p 3s 3p Wolfgang Pauli (1900 – 1958) Friedrich Hund (1896 - 1997)

25. 6.9: Periodic Table & Electronic Configurations s blockp blockd blockf block s1s1 s2s2 p1p1 p2p2 p3p3 p4p4 p5p5 p6p6 d2d2 d3d3 d5d5 d5d5 d6d6 d7d7 d8d8 d 10 f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7 f8f8 f9f9 f 10 f 11 f 12 f 13 f 14 s2s2 1s 2s 3s 4s 5s 6s 7s 2p 3p 4p 5p 6p 7p 4f 5f 3d 4d 5d 6d 3d 4d 5d 6d d1d1

26. 26 Electronic Configurations ElementStandard Configuration Noble Gas Shorthand Nitrogen Scandium Gallium [He] 2s 2 2p 3 [Ar] 4s 2 3d 1 [Ar] 4s 2 3d 10 4p 1 1s 2 2s 2 2p 3 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 1 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 1

27. 27 ElementStandard Configuration Noble Gas Shorthand Lanthanum Cerium Praseodymium [Xe] 6s 2 5d 1 [Xe] 6s 2 5d 1 4f 1` 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 5d 1 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 5d 1 4f 1 [Xe] 6s 2 4f 3 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 3

28. 28 Notable Exceptions Cr & Mo: [Ar] 4s 1 3d 5 not [Ar] 4s 2 3d 4 Cu, Ag, & Au: [Ar] 4s 1 3d 10 not [Ar] 4s 2 3d 9