Lecture 10 Electron Configuration and the Periodic Table Beyond the Bohr Model: The Quantum Mechanical Model of the Atom 7.4 Quantum Numbers, Energy Levels, and Orbitals 7.5 Shapes of Atomic Orbitals 7.6 Atom Electron Configurations (I) 7.7 Lecture 10, Knowledge and Skills Know about and work with the wave nature of moving matter Know the meaning of the Heisenberg s uncertainty principle Know and work with Schr dinger s wave mechanical model of the hydrogen atom (and other atoms) Know the meaning of the term electron orbital Know the quantum numbers, n, l, ml, ms Significance of quantum numbers Know the shapes of orbitals: s, p, d Know about the internal structure of orbitals (nodes) Know the relative orbital energies Know the <a href="/keyword/pauli-exclusion-principle/" ><a href="/keyword/pauli-exclusion/" >pauli exclusion</a> principle</a> Know Hund s rule Determine the electron configuration of many-electron atoms Beyond the Bohr Model: Quantum Mechanics De Broglie (1924): All moving objects act as waves = h mv Electrons move in atoms as standing waves Beyond the Bohr Model: Quantum Mechanics Schr dinger (1926): Treats e- as standing waves Developed by analogy to classical equations for the motion of vibrations Called wave mechanics or quantum mechanics = wavelength (m) h = Planck s constant (J s) m = mass (kg) v = velocity (m s-1) For photon: Einstein: E = mc2 (m = mass of a photon) Planck: E = h = hc/ &gt;&gt; mc2 = hc/ &gt;&gt; = h/mc Schr dinger equation The solutions provide energies and wave functions ( ), which are characterized by quantum numbers. Beyond the Bohr Model: Quantum Mechanics Heisenberg Uncertainty Principle It is impossible to know both the exact position and exact momentum of an eWhy? Objects only seen by light with object size Electrons are very small Short is required Short = high = high E Energetic collisions alter the speed and direction of the eBorn Interpretation 2 Quantum Numbers Principal quantum number, n (n = 1, 2, 3, ) = probability of finding an e- at a point in space Most important in determining the orbital energy Defines the orbital size (average distance of electron from nucleus) Electron Orbital Orbitals with equal n are in the same shell 1 Quantum Numbers Angular momentum quantum number, l (l = 0 to n 1 ) Defines the shape of an orbital Orbitals with equal l (and equal n) are in the same subshell Code letters identify l l Code 0 s 1 p 2 d 3 f 4 g 5 h ... ... Quantum Numbers Magnetic quantum number, ml (ml = l to +l ) Defines the orientation of the orbital Example: List all sets of quantum numbers for an n = 3 el = 0, or 1, or 2 if n = 3 and l = 0 (3s), ml must be 0 if n = 3 and l = 1 (3p), ml is -1, 0, or 1 if n = 3 and l = 2 (3d), ml is -2, -1, 0, 1 or 2 Example: List all l for n = 1-4 ml Quantum Numbers: Electron Spin Experiments showed a 4th quantum number was needed Quantum Numbers: <a href="/keyword/pauli-exclusion-principle/" ><a href="/keyword/pauli-exclusion/" >pauli exclusion</a> principle</a> Assignment of quantum numbers: Every e- in an atom must have a unique set of quantum numbers (n, l, ml, ms) Each orbital has a different set of quantum numbers n, l, and ml Maximum of 2 electrons per orbital (opposite spins, ms) spin quantum number, ms + or only View electron as a spinning sphere A spinning charge acts as a magnet Quantum Numbers: <a href="/keyword/pauli-exclusion-principle/" ><a href="/keyword/pauli-exclusion/" >pauli exclusion</a> principle</a> The <a href="/keyword/pauli-exclusion-principle/" ><a href="/keyword/pauli-exclusion/" >pauli exclusion</a> principle</a> limits the maximum number of electrons in an electron shell with quantum number n. Shapes of Orbitals: s Orbitals l = 0 orbital: Every shell (n level) has one s orbital Spherical Larger n value = larger sphere Probability of finding e- at distance r from nucleus 2 2 6 2 6 10 2 8 18 1s 2s 3s Distance from nucleus, r (pm) 2 Shapes of Orbitals: p Orbitals Shapes of Orbitals: d Orbitals Three p orbitals (l = 1) Characterized by ml = -1, 0, +1: px, py and pz Every shell with n &gt;1 has three p orbitals Five d orbitals (l = 2): 3d xz 3d xy 3dyz 3d x 2 - y 2 3d z 2 Every shell with n &gt;2 has five d orbitals Hydrogen Atom Orbital Energies Energy of electron in H atom (from Schroedinger equation): equation) -2.179 x 10-18 n2 Note: Same result as Bohr E only depends on n (not l or ml ) All H atom subshells with equal n have the same E An ionized hydrogen atom has E = 0 Hydrogen Atom Orbital Energies E= (in J/atom) Orbitals: Radial Electron Distribution Electron orbitals have an internal structure (nodes) Orbitals: Radial Electron Distribution 2p 3p 1s 2s 3 Orbitals: Radial Electron Distribution Orbital Energies of Many-Electron Atoms 2s has greater penetration near the nucleus than 2p 4p 4s 3p 3s 2p 2s Energy 3d Note: E3s &lt; E3p &lt; E3d But: E3px = E3py = E3pz Also: 3d is above 4s (but E4s E3d) 1s In the presence of 1s electrons: E(2s) &lt; E(2p) Atom Electron Configurations Add e- to orbitals in increasing E order 1s 2s If sets of orbitals have equal E (degenerate use Hund s rule degenerate) Hund H He Li Be B C N Atom Electron Configurations 2p Electron configurations Expanded Condensed 1s1 1s2 1s22s1 1s22s2 1s22s22p1 1s22s22p12p1 1s22s22p12p1 2p1 1s22s22p22p1 2p1 1s22s22p22p2 2p1 1s22s22p22p2 2p2 1s1 1s2 1s22s1 1s22s2 1s22s22p1 1s22s22p2 1s22s22p3 1s22s22p4 1s22s22p5 1s22s22p6 1s Energy 3s 2s 3p 2p The most stable arrangement of e- in the same subshell has the maximum number of unpaired e-, all with the same spin Paired spins: + and Unpaired spins: all + ; or - O ; or F Ne Atom Electron Configurations 1s 2s 3s 4 s 3d 5 s 4d 6 s 5d 7 s 6d 4f 5f 3d 4d 5d 6d Transition elements d block 2p 3p 4p 5p 6p 7p Main group p block 1s Writing Atom Electron Configurations The first 20 elements have only s and p electrons Full Configuration N 1s2 2s2 2p3 P 1s2 2s2 2p6 3s2 3p 3 Ca 1s2 2s2 2p6 3s2 3p 6 4s2 Noble Gas Notation [He] 2s2 2p 3 [Ne] 3s2 3p 3 [Ar] 4s2 Main group Lanthanides and actinides s block f block 4