Quantum Numbers and Shapes Chapter 10

principal energy level sublevels orbital's electron spin Chpt 10 – Quantum Numbers An orbital is an orientation in space, so a series of steps (quantum numbers) are used to describe various properties of the orbital. The steps are: principal energy level sublevels orbital's electron spin

principal energy level Chpt 10 – Quantum Numbers principal energy level Has whole numbers (1, 2, 3,…) that relate to the size and energy of the orbital. The orbital becomes larger with an increase in the principle energy level number, thus the electron spends more time away from the nucleus. The energy is higher because the electron is not as tightly bound by the nucleus.

“s” sublevels *contains 1 orbital “p” sublevels *contains 3 orbitals Chpt 10 – Quantum Numbers sublevel’s “s” sublevels *contains 1 orbital “p” sublevels *contains 3 orbitals “d” sublevels *contains 5 orbitals “f” sublevels *contains 7 orbitals

Chpt 10 – Quantum Numbers orbital’s Relates to the orientation of the orbital in space. (Example: (p- sublevel) x, y, z) An orbital is the area that there is a 90% chance of finding the electron in that area. The orbital’s of different sublevels have different shapes based upon mathematical models.

S orbitals are spherical in shape 90% boundary: Inside this lies 90% of the probability nodes

P-orbitals Node at nucleus

The Boundary Surface Representations of All Three 2p Orbitals

The Boundary Surfaces of All of the 3d Orbitals

Representation of the 4f Orbitals in Terms of Their Boundary Surfaces

THE MULTI-ELECTRON ATOM ENERGY LEVEL DIAGRAM Remember the energies are < 0 1s E 2s 2p 3s 3p 3d 4s 4p 5s 4d

Sublevels and orbitals based on the Periodic Table

Alternative Periodic Table

ELECTRONIC CONFIGURATIONS THE BUILDING-UP PRINCIPLE. GROUND STATE lowest energy electronic configuration assign electrons to orbitals one at a time Electrons go into the available orbital of lowest energy. At least one electron is in each orbital of a sublevel before a second electron is added to the orbital. A maximum of two electrons per orbital.

Order of Filling Orbitals

THE AUFBAU (BUILDING-UP) PRINCIPLE: electrons are added to hydrogen-like atomic orbitals in order of increasing energy 1s E 2s 2p 3s 3p 3d 4s 4p 5s 4d The electron configuration of any atom or ion….... can be represented by an orbital diagram

   ORBITAL DIAGRAM Hydrogen has its one electron in the 1s orbital: 1s 2s 2p H: 1s1  Helium has two electrons: both occupy the 1s orbital Pauli principle with opposite spins: 1s 2s 2p He:   1s2 1s 2s 2p He:

ORBITAL DIAGRAM Hydrogen has its one electron in the 1s orbital: 1s 2s 2p H: 1s1  Helium has two electrons: both occupy the 1s orbital Pauli principle with opposite spins: 1s 2s 2p He:   1s2 helium ground state Helium can also exist in an excited state such as: 1s 2s 2p He:  1s12s1  Now onto the next atoms

Lithium has three electrons, so it must use the 2s orbital: Beryllium has four electrons, which fill both the 1s and 2s orbitals: Boron’s five electrons fill the 1s and 2s orbitals, and begin to fill the 2p orbitals. Since all three are degenerate, the order in which they are filled does not matter. 1s 2s 2p Li: 1s22s1 1s 2s 2p Be: 1s2 2s2 1s 2s 2p B: 1s22s22p1

CARBON Z=6 A CHOICE OR How can we decide????? 1s 2s 2p C: 1s22s22p2

ELECTRONS OCCUPY DEGENERATE ORBITALS SEPARATELY HUND’S RULE FOR THE GROUND STATE ELECTRONS OCCUPY DEGENERATE ORBITALS SEPARATELY THE SPINS ARE PARALLEL SO FOR CARBON THE GROUND STATE IS 1s 2s 2p C: 1s22s22p2

ENERGY LEVEL DIAGRAM FOR A MULTI-ELECTRON ATOM BROMINE ELECTRONIC CONFIGURATION 1s E 2s 2p 3s 3p 3d 4s 4p 5s 4d                  [Ar] 4s23d104p5 

Every element in a group has The valence electron configuration of the elements in the periodic table repeat periodically! H He 1s1 1s2 Li Be B C N O F Ne 2s1 2s2 2p1 2p2 2p3 2p4 2p5 2p6 Na Mg Al Si P S Cl Ar 3s1 3s2 3p1 3p2 3p3 3p4 3p5 3p6 Every element in a group has the same valence electron configuration!

Chpt 10 – Quantum Numbers Electron Spin The concept of electron spin was developed to account for a magnetic moment. Classical physics indicates that a moving (spinning) charge produces a magnetic moment (field). Opposite spins produce opposite magnetic fields.

Electron Spin

This 2-valued electron spin can be shown in an experiment In silver (and many other atoms) there is one more “spin up” electron than “spin down” or vice versa. This means that an atom of silver can interact with a magnetic field and be deflected up or down, depending on which type of spin is in excess.

Transition Metal Demonstration The chromium, manganese, and iron ions will exhibit magnetic character because of the high number of unpaired electrons in the 3d orbitals. Will zinc show any magnetic character?