QUANTUM NUMBERS developed after work of a guy named Schrödinger purpose : to locate any electron in any atom (if only a “probability”) Analogy: like finding your seat at a big concert (you need section, row, seat, etc. to locate yourself)

1st quantum number: principal quantum number symbol is n describes distance from nucleus (or size of electron cloud) also states what energy level or shell and electron is in n = 1,2,3,4,5,6,7 (always whole #’s) this corresponds to 7 rows on the periodic table the row on the periodic table tells the highest energy level an electron can be in for that atom’s ground state alternative letter labels: K,L,M,N,O,P,Q 2n2 will calculate max # of e-’s in each level [n2 calculates max # of orbitals] as n increases, distance from nucleus increases, energy increases, reactivity increases, stability decreases

2nd quantum number: subshell quantum number symbol is l describes the shape of e- cloud (and sublevels within main energy level) number of subshells in main energy level = n l = 0,1,2,3,4,5,6 (one less than n) = alternative letter labels: s,p,d,f,g,h,i

these letters come from spectral analysis s comes from the word sharp p comes from the word principal d comes from the word diffuse f comes from the word fundamental distribution of electrons: s can hold 2 e- p can hold 6 e- d can hold 10 e- f can hold 14 e- g can hold 18 e- h can hold 22 e- i can hold 26 e-

each orbital can hold 2 electrons m values go from -l to +l 3rd quantum number: orbital quantum number (aka “magnetic” quantum number) symbol is m or ml describes the region in 3-D space where an electron might be (definition of “orbital”) each orbital can hold 2 electrons m values go from -l to +l distribution of electrons: s holds 2 e-’s in one orbital p holds 6 e-’s in three orbitals d holds 10 e-’s in five orbitals etc

Max # of orbitals in an energy level can be calculated using n2 max # of orbitals in a sublevel can be calculated using 2l + 1 degenerate orbitals - orbitals of equal energy (in the same sublevel) shapes: s orbitals are spherical shaped p orbitals are hourglass / dumbbell shaped

“s orbitals” (orbitals in the s sublevel) are spherical shaped

“p orbitals” (orbitals in the p subshell) are hourglass shaped

4th quantum number: spin quantum number symbol is s or ms describes the direction of spin of an electron (either clockwise or counterclockwise) s = -1/2 or +1/2

Pauli’s Exclusion Principle: A max of 2 electrons can occupy a single atomic orbital and only if they have opposite spins. Each electron has its own unique set of quantum numbers (no 2 electrons can have the same location)

Hund’s Rule: Single electrons with the same spin must occupy each equal-energy orbital before additional electrons with opposite spins can occupy the same orbital. (or: don’t pair up electrons in degenerate orbitals unless you have to) (don’t put 2 people in a seat unless each person has his own seat first)

Aufbau Principle: each electron occupies the lowest energy orbital available. Electrons are added in order, starting with the lowest energy

Electron Configurations Lewis Electron Dot Diagrams and How to do: Electron Configurations Lewis Electron Dot Diagrams and Orbital Filling Diagrams Slide 3

Electron Configurations An electron configuration is an arrangement of all of the electrons in an atom. For instance, an electron configuration for iron (Z=26) would show where all of the 26 electrons would be in that atom. Slide 3

Use the “diagonal rule” to do an electron configuration Be neat and write out all of the maximum values for quantum numbers. Use notation like this: 4d10 Where “4” is the n value (energy level number) “d” is the l value (letter for the sublevel) and “10” is the maximum number of electrons that the sublevel can hold Slide 3

The Diagonal Rule: 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 5f14 5g18 6s2 6p6 6d10 6f14 6g18 6h22 7s2 7p6 7d10 7f14 7g18 7h22 7i26

Do electron configuration for each: N (Z = 7) Fe (Z = 26) As (Z = 33) In (Z = 49) Bi (Z = 83) Fr (Z = 87) Am (Z = 95) Slide 3

Noble gas notation: a shortcut electron configuration that uses the prior noble gas. Ex: sodium may be 1s22s22p63s1 or [Ne]3s1

Lewis Electron Dot Diagrams Show only the outer shell (or valence electrons) (ie, those electrons that are in the outermost energy level) These will only ever include s and p electrons (because of overlap). Max dots in a Lewis e- dot diagram is therefore 8 because 2(from s) plus 6 (from p) equals 8 You must have an electron configuration done first! Each “side” of the four sides represents an orbital. (and therefore can hold only 2 electrons) Follow Hund’s rule for the p electrons. Slide 3

Do a dot diagram for N (Z = 7) Fe (Z = 26) As (Z = 33) In (Z = 49) Bi (Z = 83) Fr (Z = 87) Am (Z = 95) Slide 3

Orbital Filling Diagrams Each orbital is represented as a box (or sometimes a circle) Each electron is represented as an arrow Follow Hund’s rule and Pauli’s Exclusion Principle. Slide 3

Exceptions to predicted configurations: Exceptions occur due to the unusual stability of full and half full sublevels. Example: Chromium Example: Copper