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1 Announcements Print worksheet #10 prior to your Thursday discussion section LON-CAPA assignment #6 due Tuesday, Oct. 5 at 9am Next week s quiz will be on Tuesday atomic history and electron configurations Online gradebook now includes Exam 1 raw and scaled scores LON-CAPA grades for assignments 1-5 Clicker points for lectures 3-9 Quizzes 1-4 (5?) Please check for errors now

2 Quantum Mechanics and Atomic Orbitals During the last lecture we discussed Bohr and Einstein de Broglie particle nature of light wave nature of particles Now let s meet some more scientists. These are the founders of quantum mechanics! Schrödinger Heisenberg Dirac

3 Quantum Mechanics 101 quantum mechanics focuses on theoretical and probabilistic descriptions of atoms Solutions to Schrödinger s Equation tell us everything we need to know about an atom Ĥ Ψ = E Ψ Ĥ is known as the Hamiltonian operator Ψ is called a wavefunction When the Hamiltonian operator is applied to a wavefunction, the result is a constant (energy) times the wavefunction

4 Quantum Mechanics 101 The tricky part of quantum mechanics is determining the equation for Ψ this often involves very complex differential equations Don t worry, we won t actually solve Schrödinger s Equation in this class (but you can look forward to that in Chem 442) You need to know three things at this point: 1. Every allowed electron state has a unique Ψ 2. Specific Ψ s are called orbitals 3. An orbital is NOT the same as a Bohr orbit

5 Quantum Mechanics 101 So how does this help us understand atomic structure? Quantum mechanics tells us that we do not know exactly how an electron travels around an atom (but it definitely is not confined to a circular orbit!). Ψ 2 = the probability of finding an electron at a particular distance from the nucleus of an atom 1s orbital

6 orbitals require 3 quantum numbers n l m l address magnetic -l,, l orientation angular momentum 0, 1, 2,, (n -1) shape principal 1, 2, 3, size and energy

7 orbitals require 3 quantum numbers n l m l The principal quantum number determines the size of an orbital, as well as its energy as n increases, orbitals become larger, and the probability of finding an electron further from the nucleus increases n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7

8 orbitals require 3 quantum numbers n l m l The angular momentum quantum number determines the shape of an orbital (designated by letters) n = 1 l = 0 n = 2 l = 0, 1 n = 3 l = 0, 1, 2 n = 4 l = 0, 1, 2, 3 l = 0 l = 1 l = 2 l = 3 s orbital p orbital d orbital f orbital

9 The periodic table can be divided into s, p, d and f regions l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 s d p f

10 orbitals require 3 quantum numbers n l m l The magnetic quantum number ranges from l, -l+1 l-1, l and determines the orientation of an orbital Row 1 of the periodic table is associated with the principal quantum number n=1: n = 1 l = 0 m l = 0 (1s) Row 2 of the periodic table is associated with the principal quantum number n=2: n = 2 l = 0 m l = 0 (2s) l = 1 m l = -1, 0, 1 (2p) Note: there are a total of three 2p orbitals

11 Row 3 of the periodic table is associated with the principal quantum number n=3: n = 3 l = 0 m l = 0 (3s) l = 1 m l = -1, 0, 1 (3p) l = 2 m l = -2, -1, 0, 1, 2 (3d) Note: there are a total of five 3d orbitals Each orbital can hold a total of 2 electrons. We need one more quantum number to distinguish between the two electrons within an orbital m s is the spin quantum number, and it can only have the values +1/2 (up) or -1/2 (down)

12 1s orbital ψ 2 s orbitals are spherical 2s and 3s ψ 2

13 p orbitals have a dumbbell shape These are the three 2p orbitals 3p, 4p, 5p etc. have similar shapes but are larger

14 Most d orbitals are shaped like a cloverleaf These are the five 3d orbitals 4d, 5d etc. have similar shapes but are larger

15 Atoms with more than 1 electron (polyelectronic) The Pauli Exclusion Principle states that no 2 electrons can have the same set of 4 quantum numbers Electron configurations are constructed by filling the orbitals with the lowest energy (starting with 1s) until all electrons have been assigned Hydrogen has 1 electron 1s 1 Helium has 2 electrons 1s 2 Which orbital fills next?

16 H He Li Be B C N O F Ne 1s 2s 2p x 2p y 2p z 3s 3p x 3p y 3p z 4s 3d 3d 3d 3d 3d Place 2 electrons into each s orbital before moving on to the next orbital When you get to the p orbitals, place one electron into each orbital before going back and adding the second electron Noble gas shorthand notation can reduce repetition. Write the symbol for a noble gas in brackets and then write the configuation for the remaining electrons Na [Ne] Cr and Cu do NOT follow the standard rules (see Wkst #10)