Quantum Mechanical Models of the Atom

Terms

Pauli Exclusion Principle: No two electrons in an atom can have the same four quantum numbers.; Pauli’s Principle prevents two electrons with the same spin from existing in the same subshell, each subshell will be filled with one spin direction before they are filled with the opposite spin. This is the second of Hund’s Rules.
Aufbau Principle: This pattern of orbital filling is known as the aufbau principle （the German word aufbau means “build up”）.
Hund’s rule: When filling degenerate orbitals, electrons fill them singly first, then with parallel spins.; I.e. start by filling boxes with single 'upward' arrows, and then once all of such boxes are maxed out, then you add double arrows pointing in opposite directions.; Pauli’s Principle prevents two electrons with the same spin from existing in the same subshell, each subshell will be filled with one spin direction before they are filled with the opposite spin. This is the second of Hund’s Rules.
Coulomb’s Law

Pauli's Exclusion Principle

Each election has a unique set of four quantum numbers （i.e. see quantum numbers）. They are

Overview

Values

Name	Symbol	Unit	Description	Range
Wavelength		Any unit for distance	Distance between two analogous points	Always Positive
Frequency	or （nu）		Number of cycles	Always Positive
Energy		（joule）	Amount of energy （） in a light packet

Constants

Name	Symbol	Unit	Value
Speed of Light
Planck's constant		Energy multiplied by time joule-seconds

Other Formulas

Heisenberg's Uncertainty Principle

Where

is the uncertainty in position.
is the uncertainty in velocity.
is the mass of the particle.
is the plank's constant.

In general it states that the more you know about an electrons position, the less you know about it's velocity.

Energy of an Electron in an Orbital with Quantum Number in a Hydrogen Atom

Energy of an Electron in an Orbital with Quantum Number for any atom

Where is the atomic number of the given element.

Change in Energy That Occurs in an Atom When It Undergoes a Transition between Levels （Further Details）

and

If is negative, energy is being released.
If is positive, energy is being absorbed.

Ionization Energy

Where

is the electron number
the point on the table where you see the highest difference/delta.

Atomic Spectroscopy

The Principal Quantum Number （n）（Hydrogen Atom）

For the hydrogen atom, the energy of an electron in an orbital with quantum number is given by

Therefore the difference in energy is given by the following

The Principal Quantum Number （n）（Any Atom）

For the hydrogen atom, the energy of an electron in an orbital with quantum number is given by

TODO

Where is the atomic number of the given element.

Electron Configuration

Examples

Electron configuration for

Since the electron configuration for Argon is

Electron configuration for

Beginning with the electron configuration for

Remove the electrons from the term with the higher electron state. Warning! Do not just remove the electrons from the rightmost term since the rightmost term may be a lower electron state. For instance given

is in a higher electron state
is in a lower electron state

Alternatively, to compute the lowest energy orbital, add the principle quantum number （） to the The angular momentum quantum number （） to get the orbital with the lowest energy. Therefore

Given and

NVM this is an exception to the rule...

TODO move this somewhere else...

As shown

Therefore the electron configuration for is:

Electron configuration for

It would appear that the electron configuration for would be

But this is wrong! It's actually

How-tos

What are the valence electrons?

Given

The valance electrons will be the ones in the highest energy state. Therefore

Therefore there are valence electrons.

Given

The valance electrons will be the ones in the highest energy state. Therefore

Therefore there are valence electrons.

Quantum Numbers

Overview

Symbol	Description
	The principle quantum number
	The angular momentum quantum number
	The magnetic quantum number
	The spin quantum number

The Principle Quantum Number （）

Value of	Value of	Orbital Sublevel

Angular Momentum Quantum Number

Value	Result

Value of	Value of