Lecture notes: CHEM103 Spring 2008 – October 9, 2008

1) FOUR quantum numbers – what rules govern these and what do they MEAN???

a. Pauli exclusion principle

b. Aufbau rule

c. Madelung’s rule

d. Hund’s rule

2) how do you write electronic configurations of neutral atoms?

a. “spdf” notation (text only with sub- & super-scripts)

b. abbreviated “spdf” notation (using Noble gases)

c. orbital box notation (boxes or lines w/arrows)

d. energy level notation

Rules for first 3 quantum #s:

n (non-zero) integers: 1, 2, 3, 4, 5, 6 -- energy level

l possible values: from 0 up to (n-1) -- shape (s, p, d, f, etc.)

m_l possible values: from –l to + l -- “axis” (but no fixed frame of reference)

Other orbital shapes:

the “p” orbital

the “d” orbital

NOTE: “l” also indicates the number of nodal planes.

an “f” orbital

m_s possible values: either +1/2 or –1/2 -- up or down

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

Analogy: addresses

state, city, street, apartment number

Pauli exclusion principle:

EVERY orbital, filled or empty has a UNIQUE set of quantum numbers

(so that every electron within an atom has a unique set of quantum numbers)

Exercise: For n=1, how many electrons possible?

For n=2, how many orbitals possible?

For n=3, how many sub-shells possible; how many orbitals possible; how many electrons possible?

These 'magic' numbers inevitably arise from the underlying quantum mechanics,

but as Richard Feynman told us (here): "I think I can safely say that nobody understands quantum mechanics."

SO, WHAT DO THESE SHAPES AND NUMBERS HAVE TO DO WITH ENERGY?!?

DIFFERENT ORBITALS HAVE DIFFERENT ENERGIES!

As you go UP in values of “n” and “l”, the orbital energy increases.

a SINGLE electron (e.g. hydrogen) can be “promoted” to higher energy orbitals

They increase in energy with increasing (n + l), NOT just in values of n. (Madelung’s rule)

for orbitals with the same value of (n + l), they increase in energy with increasing values of “n”

(note: this is for NEUTRAL atoms, not for cations)

This has some IMPORTANT and confusing implications for the relative energy levels of orbitals

Comment: the spacing of these energy levels is completely fictitious, but helpful for visualization…

In reality, they grow exponentially closer as the energy levels increase!

Check out: http://www.meta-synthesis.com/webbook/34_qn/qn_to_pt.html

NOW: multi-electron atoms…

FIRST: know that these orbitals are all possible REGARDLESS of the number of electrons in the atom:

(Similarly, an atom with more electrons simply fills more orbitals… but IN SEQUENCE:

electrons fill up in order from lowest energy orbital to highest energy (aufbau principle)

FINALLY: electron-electron repulsion (Hund’s rule)

(This is particularly true within an orbital, but is also important within sub-shells – see this later…)

Alternate representations:

Text (“spdf” notation) – & abbreviated!

Lines/Boxes (orbital line/box diagrams)

Energy levels

Write electron configurations for: Be (beryllium), P (phosphorous), Rb (rubidium)

BUT – this model has predictive power – explains the form (shape) of the periodic table…

Note: we can USE the periodic table to “predict” (or “remember” – on an exam!)

the orbital filling order (for most configurations)

Periodic Table as it SHOULD BE:

http://nexus.webelements.info/?q=node/980