QUANTUM NUMBERS ORBITALS Quantum mechanical model Mathematical equations

QUANTUM NUMBERS & ORBITALS

Quantum mechanical model • Mathematical equations to determine probability of locating an electron in an atom • Electron cloud – region of space around a nucleus with high probability of locating an electron • Windmill/ fan analogy

Orbitals • Mathematical expression • Area of atom where electrons are likely to be found • Only 2 electrons per orbital

Quantum Numbers • Describe the distribution of electrons in the atom • Come from Schrödinger's wave equations • Types: • principal (n) • angular (l) (or azimuthal) • magnetic (ml) • spin (ms) (- ½ or + ½)

Principal Quantum Number (n) • Describes the size of the orbital • Distance from the nucleus • Orbitals get larger as move out from nucleus • Requires energy input to move an electron from an orbital to another orbital further out • Indirectly describes the energy of an orbital

Angular Quantum Number (l) • Describes the shape of the orbital • spherical (l = 0) • polar (l = 1) (or dumbbell) • cloverleaf (l = 2) • take on more complex shapes as the value of the angular quantum number becomes larger

Picturing Orbitals The subshells: s, p, d, f

Magnetic Quantum Number (m) • Describes the orientation in space of a particular orbital

Shells and Subshells Orbitals that have the same value of the principal quantum number (n) form a shell. Orbitals within a shell are divided into subshells that have the same value of the angular quantum number (l). ◦ lowercase letters are used to indicate different subshells s: l = 0 p: l = 1 d: l = 2 f: l = 3

Picturing Orbitals N = size L = shape M = orientation

S orbital http: //www. uky. edu/~holler/html/s. html

P orbitals http: //www. uky. edu/~holler/html/p. html

D orbitals http: //www. uky. edu/~holler/html/d. html

F orbitals http: //www. uky. edu/~holler/html/f. html

• http: //www. youtube. com/watch? v=K- j. Ngq 16 j. EY&feature=related

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Adding Electrons to Orbitals Pauli Exclusion Principle ◦ No two electrons in an atom can have identical quantum numbers The combination of n, l, m, and spin Only 2 electrons per orbital Aufbau Principle Electrons will enter the lowest energy level available Hund’s Rule ◦ Electrons on the same energy level will enter empty orbitals before pairing Electron spin ◦ Electrons in each orbital have opposite spins Spin up or spin down “facing” in opposite directions

Filling of Electron Orbitals

Distribution of the orbitals

Electron Configuration: 1 st 18 1 A 2 A 3 A 4 A 5 A 6 A 7 A 1 H 1 s 1 8 A 2 He 1 s 2 3 Li 1 s 2 2 s 1 4 Be 1 s 2 2 s 2 5 B 1 s 2 2 s 22 p 1 6 C 1 s 2 2 s 22 p 2 7 N 1 s 2 2 s 22 p 3 8 O 1 s 2 2 s 22 p 4 9 F 1 s 2 2 s 22 p 5 10 Ne 1 s 2 2 s 22 p 6 11 Na [Ne] 3 s 1 12 Mg [Ne] 3 s 2 13 Al [Ne] 3 s 23 p 1 14 Si [Ne] 3 s 23 p 2 15 P [Ne] 3 s 23 p 3 16 S [Ne] 3 s 23 p 4 17 Cl [Ne] 3 s 23 p 5 18 Ar [Ne] 3 s 23 p 6

Standards • 1998: • SC. A. 2. 4. 5 Elements are arranged into groups and families based on similarities in electron structure and their physical and chemical properties can be predicted. • NGSSS • SC. 912. P. 8. 5 Relate properties of atoms and their position in the periodic table to the arrangement of their electrons.