Overview

We assign quantum numbers by looking at the last electron of an atom.

Orbitals with same energy level are called degenerate.

Quantum Numbers

Principal Quantum Number

(n)

Principal Quantum Number (n) The shell

Describes size and energy level of orbitals - corresponds to period (row) on the periodic table

Refers to most outermost electron shell.

• Means electrons have higher energy.

Anything that falls within d-block:

• n = $$\text{period} - 1$$

Anything that falls within f-block:

• n = $$\text{period} - 2$$

Angular Momentum Quantum Number

(l)

Angular Momentum Quantum Number (l) The sub-shell

Defines 3d shape of orbitals.

Any integer from 0 to $$n-1$$

Magnetic Quantum Number

$$m_l$$

Magnetic Quantum Number ($$m_l$$) Orbitals

Defines spatial orientation

Total number of possible orbitals in subshell = 2l + 1 = num possible M_l

Ml can have values from -l to +l.

When l = 1, $$m_l$$ can be -1, 0, or +1

Orbitals

Lobes

Where electrons can be found.

Nodes

Electrons can never be found.

More nodes = higher energy (negative space)

Total nodes = $$n - 1$$

Angular Nodes

Planes separating phases/lobes

Radial Nodes

Spherical nodes between shells

Spin Quantum Number ($$m_s$$)

Spin Quantum Number ($$m_s$$) Electron Spin

Tells us the spin of last electron.

Either up or down.

• Up = $$+\frac{1}/{2}$$

• Down = $$-\frac{1}{2}$$

• Each orbital (value of $$m_l$$) can have two electrons and they cannot have the same spin.

Electron Configuration

• $$n + 1 + \text{subscript of number of atoms in that group}$$.

Aufbau Principle

Lower energy orbitals fill up first.

Noble Gas Configuration

Allows us to start at the last noble gas

Examples

Ne Electron Configuration

$$12^22s^22p^6$$

O Electron Configuration

$$12^22s^22p^4$$

Mg Electron Configuration

$$12^22s^22p^63s^2$$

Ti Electron Configuration

$$12^22s^22p^63s^23p^64s^23d^2$$

Ti Electron Configuration

$$[Ar]4s^23d^2$$

Valence Electrons

Valence Electrons Outermost Electrons

Electrons in the outermost shell that participate in binding.

Number of Valence Electrons

Find highest n-value of s & p orbitals ... find largest n value and add all superscripts in s and p orbitals for that n-value.

Octet

When an atom has 8 valence electrons.

Mg Electron Configuration

$$1s^{2} 2s^{2} 2p^{6} 3s^{2}$$

Has two valence electrons.

Periodic Table

s-block s-orbitals

l = 0

p-block

l = 1

d-block

l = 2

f-block

l = 3

Trends

Ionic Radius

As we add more electron shells - the atomic radius increases

As we add more protons - the atomic radius decreases

• As we move DOWN and the the LEFT, the atomic radius INCREASES.

• Atomic radius decreases as you move to the right.