Quantum Mechanical Model

Limitations of the Bohr Model

e- DO NOT travel in fixed paths around the nucleus!!!

e- found in certain regions around the nucleus!

These regions (orbitals) are based on probability where e- can be found.

e- behave like waves instead of particles.Only works for atoms with 1 e-

It is not possible to determine the location & momentum of an e- at the same time (Heisenburg Uncertainty Principle).

Quantum Numbers

UPPER LEVEL

• Four Quantum Numbers:–Specify the “address” of each electron

in an atom

Quantum Numbers

1. Principal Quantum Number ( n )

– Energy level

– Size of the orbital

– n2 = # of orbitals in the energy level

Quantum Numbers

s p d f

2. Angular Momentum Quantum # ( l )– Energy sublevel

– Shape of the orbital

Quantum Numbers

n = # of sublevels per leveln2 = # of orbitals per levelSublevel sets: 1 s, 3 p, 5 d, 7 f

Quantum Numbers

3. Magnetic Quantum Number ( ml )

– Orientation of orbital

– Specifies the exact orbitalwithin each sublevel

Quantum Numbers

px py pz

Quantum Numbers

• Orbitals combine to form a spherical shape.

2s

2pz2py

2px

Quantum Numbers

4. Spin Quantum Number ( ms )

– Electron spin +½ or -½

– An orbital can hold 2 electrons that spin in opposite directions.

Quantum Numbers

1. Principal #

2. Ang. Mom. #

3. Magnetic #

4. Spin #

energy levelsublevel (s,p,d,f)orbitalelectron

• Pauli Exclusion Principle–No two electrons in an atom can have the

same 4 quantum numbers.

–Each e- has a unique “address”:

n = principal quantum #

# = Energy n = 1

n = 2

n = 3If you recall:

Each energy level consists of one or more sublevels.

s < p < d < fEnergy Energy

There is a maximum # of e- that can occupy each sublevel. s = 2 e-

p = 6 e-

d = 10 e-

f = 14 e-

As previously stated, e- are located in regions (orbitals) where they have the highest probability of being found!