Quantum Mechanics

Electron Density

• Gives the probability that an electron will be found in a particular region of an atom

• Regions of high electron density represent a high probability of locating the electron

Representation of the electron density distribution surrounding the nucleus in

the hydrogen atom; shows a high probability of finding the electron closer

to the nucleus

Based on Heisenberg uncertainty principle and Schrodinger wave equation

Atomic Orbital

• Way to distinguish Bohr’s model from the current quantum mechanical model

• Probability of locating the electron in 3D space around the nucleus

• Has a characteristic energy

Quantum numbers

used to describe atomic orbitals and to label electrons that reside in them

• Principle quantum number (n)• Angular momentum quantum number• Magnetic quantum number• Electron spin quantum number

5

n = 1, 2, 3, 4, ….

n=1 n=2 n=3

distance of e- from the nucleus

Principal Quantum Number n

Energy levels are like rungs of a ladder. You cannot be in

between a rung

Energy levels in an atom’s electron are unequally spaced.

The higher energy levels are closer together.

Angular Momentum Quantum Number

Shape of the “volume” of space that the e- occupies

s orbitalp orbitald orbitalf orbital

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Magnetic Quantum Number

•Describes the orientation of the orbitals in space•All orientations are identical in energy

s orbitalSphere

p orbitaldumbbell3 orientations

d orbitalDouble dumbbell5 orientations

f orbital7 orientations

Electron Spin Quantum Number

•Electrons are thought to be spinning on their own axes-clockwise, or counterclockwise.

•The up and down arrows denote the direction of the spin.

Energy of Orbitals

depends on principle and angular momentum quantum numbers

Shielding Effect

• Why is the 2s orbital lower in energy than the 2p?

• “shielding” reduces the electrostatic attraction

• Energy difference also depends on orbital shape

Electron Configuration vs Orbital diagram

1s1

principal quantumnumber n

Shape

number of electronsin the orbital

Orbital diagram

H

1s1

Aufbau Principle

“fill up” the lowest energy level first

Orbitals in the Periodic Table

Pauli Exclusion Principle

• No two electrons can have the same 4 quantum numbers

• Only two electrons may occupy the same atomic orbital, and these electrons must have opposite spins

• Electrons that have opposite spins are said to be paired

Orbital name # of orientations Total # of electronsspdf

Hund’s Rule•The most stable arrangement of electrons in an orbital is the one with the greatest number of parallel spins

•e- will occupy singly before filling with opposite spins

PracticeFill in the orbital diagram, and write the electron

configuration for the following atoms

Example of Exceptions to the Rules

Element Should be Actually isCopper 1s22s22p63s23p63d44s2 1s22s22p63s23p63d54s1

Chromium 1s22s22p63s23p63d94s2 1s22s22p63s23p63d104s1

•These are not the only two exceptions.

•The rules are violated because half-filled sublevels are not as stable as filled sublevels, but they are more stable than other configurations

Noble Gas Configuration

What is the electron configuration for Ne?Ne: What is the electron configuration for Mg?Mg:

What do both electron configurations have in common?

To figure out which noble gas to use find the noble gas that is closest to the element without

going over in atomic number

Which noble gas is closest without going over?RbClRa

PracticeWrite the noble gas electron configuration for the

following atoms:

Na:

Mn:

Co:

Sn:

Valence Electrons

• Electrons in the outermost s and p orbitals (highest n shell)

• These electrons participate in chemical reactions