Lecture notes: CHEM103 Spring 2008 – October 7, 2008

0) Review: uncertainty principle: probability NOT location!

1) electrons as a 3-D wave

a. Schrodinger’s equation – yikes!

b. orbital shapes (waveforms) of electrons

c. describing them with 4 quantum numbers

EXAMPLE: Sodium atoms in fireworks

What is the energy level of sodium (in its 1^st excited state)?

GIVEN:

Emission of 589.3 nm light

Photoionization requires 495.8 kJ/mole

è E_∞ = 0

E₂ = ?

è DE = emission of photon

E₁ = ?

(hint: what is the energy level of the ground state?)

A 1-dimensional wave is familiar…

…so is a 2-dimensional wave

A 3–dimensional wave?

A 2-dimensional probability wave?

A 3–dimensional probability wave!

Mapping PROBABILITY of electron location…

These can be calculated using Schrodinger’s equation for the electron WAVE in 3-D space

Where: Y² is proportional to the probability of electron

(note: this is very hard to do mathematically for any atom containing more than 1 electron…)

These are “ORBITALS” – NOT “ORBITS”!

This is a vastly different idea (and improved, too) than Bohr!

ß WRONG!!!

Lithium Sodium

Instead:

probability “shapes” resulting from solutions to Schrodinger’s equation:

These odd shapes describe the

PROBABILITY of finding electron IN A VOLUME around the nucleus…

and are described by 4 QUANTUM NUMBERS:

Abbreviation:	Technical name:	...more simply…	Notes:	what it identifies:
n	principal quantum number	“energy level”	think energy diagram…	shell
L	angular momentum quantum number	“shape”	also: number of nodal planes	sub-shell
ml	magnetic quantum number	“axis”	also: indicates # of orbitals	orbital
ms	spin quantum number	“spin”	2 electrons per orbital MAXIMUM	electron