1.6 QM Model

1. 1.6 QM Model

2. Quantum Numbers • According to the QM Model, each electron in an atom can be described by 4 quantum numbers (arrived at by solving Schrödinger’s equation) • 3 specify the probability of finding the e- at various points in space • 1 refers to the magnetic property of electrons • QUANTUM ORGANIZATION • Energy Level (shell) • Sublevel (subshell) • Atomic Orbital • Spin

3. Principal QN • Symbolized by “n”,it denotes the energy level (shell) in which an electron is located • Also known as the Energy Level QN • ALLOWED VALUES: positive, whole number values (n = 1, 2, …, 7) (only 7 EL’s) • Maximum number of electrons • in any one energy level = 2n2 • The energy of an electron in • an atom depends principally • on n: The larger the value of • n, the higher the energy of • the e-

4. Angular Momentum QN • Within each energy level (shell) there are sublevels (subshells) • Schrödinger’s wave equation describes shapes within each sublevel where there is a high probability of finding electrons • These shapes are called atomic orbitals • There are four types of orbitals (s, p, d, f) • The sublevels are named for the energy level they are in and the type of atomic orbital they contain • 1s – sublevel on the 1st EL containing an s orbital • 3d – sublevel on the 3rd EL containing d orbitals

5. Angular Momentum QN (cont.) • Symbolized by “l”,it denotes the sublevel an electron is located in (determines the shape of the orbital) • Also known as the Sublevel QN • ALLOWED VALUES: integer values from 0 to n-1 Letters p d f l0 1 2 3 • Although energy of an electron is principally determined by n, energy also depends on l • General rule: Energy increases as l increases

6. Atomic Orbitals

7. Atomic Orbitals

8. Atomic Orbitals

9. Atomic Orbitals

10. Magnetic Quantum QN • Each orbital can hold a maximum of 2 electrons • Each pair of electrons in a given sublevel has a different place (orientation) in space. • Symbolized by “ml”,it denotes the electron’s orientation in space around the nucleus (specifies the orbital an electron is located in) • Also known as the Orbital QN • ALLOWED VALUES: integers from -l to +l • For l = 0 (s), ml = 0: only 1 orientation of the orbital in an s-sublevel • For l = 1 (p), ml = -1, 0, 1: 3 orientations of the orbitals in a p-sublevel

11. Spin QN • Symbolized by “ms”,it denotes the spin of the e-: clockwise, ms=+1/2 or counterclockwise, ms=-1/2 • Used to distinguish between e-in the same orbital • ALLOWED VALUES: +1/2 or -1/2 • If two electrons occupy the same orbital, they MUST have opposite spins; if they do not, these two electrons would have identical quantum numbers!