Periodic properties of the elements Chapter 8

Quantum numbers Principal quantum number, n Determines size and overall energy of orbital Positive integer 1, 2, 3 . . . Corresponds to Bohr energy levels

Quantum numbers Angular momentum quantum number, l Determines shape of orbital Positive integer 0, 1, 2 . . . (n–1) Corresponds to sublevels l letter s 1 p 2 d 3 f

Quantum numbers Magnetic quantum number, ml Determines number of orbitals in a sublevel and orientation of each orbital in xyz space integers –l . . . 0 . . . +l

What type of orbital is designated by each set of quantum numbers? n = 5, l = 1, ml = 0 5p n = 4, l = 2, ml = –2 4d n = 2, l = 0, ml = 0 2s Write a set of quantum numbers for each orbital 4s n = 4, l = 0, ml = 0 3d n = 3, l = 2, ml = –2, –1, 0, +1, or +2 5p n = 5, l = 1, ml = –1, 0, or +1

Electron configurations Electrons exist within orbitals, given by three quantum numbers n, l, and ml

Electron configurations Configuration shows which orbitals are occupied Aufbau principle: e– takes lowest available energy Hund’s rule: if there are 2 or more orbitals of equal energy (degenerate orbitals), e– will occupy all orbitals singly before pairing

Electron configurations Electron has spin, either “up” or “down” Electron spin given by 4th quantum number, ms Pauli exclusion principle: no two e– in an atom can have the same set of 4 quantum numbers ⇒ 2 e– per orbital, one up ↑ and one down ↓

Magnetic properties Atom or ion with unpaired e– is attracted to a magnetic field = paramagnetic Atom or ion with all e– paired is slightly repelled by a magnetic field = diamagnetic

Effective nuclear charge: Zeff Electron experiences attraction of nucleus and repulsion of other e– in the atom Outer e– is partially shielded from full charge of nucleus Zeff = actual nuclear charge – charge shielded by other e–

Effective nuclear charge: Zeff Core e– effectively shield outer e– from nuclear charge Outer e– do not shield other outer e– very efficiently Thus, Li outer e– experiences Zeff ≈ 3–2 = +1 Be outer e– experience Zeff ≈ 4–2 = +2

Trends in atomic radius Atomic radius increases down a group Same Zeff Outer e– in higher principal energy level = larger orbital Atomic radius decreases across a period Same principal energy level Increasing Zeff pulls in outer e–

Trends in atomic radius Transition metal radii stay roughly constant across a period Outer e– stay same Adding protons to nucleus and electrons to n–1 (core) orbital, so Zeff stays about constant

Ions and ionic radii Elements may lose or gain outer e– to form ions Metals lose e– → cations Nonmetals gain e– → anions The ions in these examples are isoelectronic (same e– configuration)

Transition metal ions Transition metals lose their ns e– before losing their (n–1)d e–

Ions and ionic radii A cation is much smaller than its parent atom

Ions and ionic radii An anion is much larger than its parent atom

Ions and ionic radii For isoelectronic species, the one with the highest nuclear charge will have the smallest radius S2– 18 electrons 16 protons 184 pm Cl1– 17 protons 181 pm K1+ 19 protons 133 pm Ca2+ 20 protons 99 pm

Ionization energy Ionization energy (IE) = energy needed to remove e– from atom/ion in gaseous state IE always positive (endothermic) Successive IE values always increase IE increases dramatically when begin to remove core e–

Trends in 1st ionization energy IE1 decreases down a group Same Zeff Outer e– in higher principal energy level = farther from nucleus, easier to remove IE1 generally increases across a period Increasing Zeff pulls outer e– closer to nucleus, harder to remove

Two important exceptions 1st e– in p sublevel 3s orbital penetrates closer to nucleus 3p e– somewhat more shielded from nuclear charge, easier to remove e– begin pairing in p sublevel P S

Electron affinity (EA) EA = energy change when gaseous atom/ion gains an e– Trends less regular but generally becomes more exothermic across a period

Summary of periodic trends Across a period atomic radius decreases IE1 (always endothermic) increases (with two important exceptions) EA generally becomes more exothermic Down a group atomic radius increases IE1 decreases