QUANTUM MECHANICS

Predicting the most probable position of an electron.

BOHR’s MODEL

Cannot successfully predict line spectra for any other element besides hydrogen.Electrons must not be moving in circular orbits at set distances from the nucleus.

BACK TO THE 3 ?’s ABOUT e-

How are the electrons moving?As wavesNOT in orbits

Where are they located?

In ORBITALS Areas of high probability based on the wave motion and energy of an electron

Every orbital has an “address” given by a set of 4 QUANTUM NUMBERS.

How much energy do they have?

Determined by the n value (like Bohr).Higher n = higher energy level = more energy = further from the nucleus.

SCIENTISTS CONTRIBUTING to QUANTUM THEORY

DeBROGLIE 1924 French Proposed the particle wave duality to describe electron motion.

HEISENBERG 1927Proposed the Heisenberg uncertainty principle.The more you know about the e- position, the less you know about it’s velocity.

SCHRODINGER 1926 AustrianProposed a complex mathematical relationship to predict where an e- is located.

SCHRODINGER EQUATIONA calculus problem.

We will deal only with the answers.

4 answers to the Schrodinger equation are known as QUANTUM NUMBERS.

4 QUANTUM NUMBERS

nlml

ms

1. Prinicpal Quantum Number

Symbol: nTells what energy level the electron is in.Possible values: n = 1 to infinity

2. Orbital Quantum Number

Symbol: l (small cursive l)Tells about the shape of the orbital where the electron is housed.Possible values: 0 to (n-1)

Orbital Quantum Number and Shapes

L = 0 s orbital sphericalL = 1 p orbital peanut

shapedL = 2 d orbital daisy

(cloverleaf)

L = 3 f orbital flower

s orbital

p orbitals

d orbitals

3. Magnetic Quantum Number

Symbol: ml

Tells about the orientation of the orbital around the nucleus (around the axis).Possible values

- l to + l including 0

Values of ml

s orbital – 1 orientation, 1 ml value (0)

p orbital – 3 orientations, 3 ml values (-1, 0, 1)

d orbital – 5 orientations, 5 ml values (-2,-1,0,1,2)

4. Spin quantum number

Symbol: ms

Tells the direction of electron spin within an orbital.Possible values: +1/2 or –1/2+1/2 clockwise spin- 1/2 counter clockwise spin

RULES for QUANTUM NUMBERS and ELECTRONS

Pauli Exclusion Principle Every electron in an atom must have a unique set of quantum numbers.

Electrons in the same orbital must have opposite spins.

ENERGY LEVEL DIAGRAMA way to keep track of electrons.Includes lines or boxes that represent orbitals.Also shows orbital types and energy levels.Once filled, it is possible to find the quantum number set for any electron in the atom.

RULES FOR FILLING AN ENERGY LEVEL DIAGRAM

AUFBAU PRINCIPLEMeaning: “Building up”Electrons must be filled in from the lowest energy level to the highest.

Do not move to the next sublevel until the one below has been completely filled.

HUND’S RULE

Electrons will fill an unoccupied orbital within a sublevel before pairing up with another electron in an orbital.This minimizes electron repulsion and leads to stability.

OCTET RULE

Atoms become stable when their outermost energy level contains 8 electrons.

Noble gases have a full OCTET.

The outermost electrons are called VALENCE ELECTRONS.