Wave Properties of Matter

DeBroglie (1924) proposed that matter has wavelike properties.

l = h/(mv) = wavelength associated with a particle

Evidence for Wave Properties of Matter

Davisson and Germer (1927):

The Heisenberg Uncertainty Principle

We cannot know both the exact ________________________ of a particle simultaneously.

( Dx)( Dp) > h/(4p)

Dx = uncertainty in ________________

Dp = uncertainty in ________________

Implications

1. What if h were very large?

2. Determinism

Problems with determinism:

a)

b)

3. Electrons do not move along a well defined path.

Wave Mechanical Model of the Atom

Schrödinger (1926)

Assumption:

(see board)

Schrödinger Wave Equation

HY = EY

H is an operator.

E is the ____________ of the electron.

Y is the wave function of the electron and describes the properties of the electron.

The Hydrogen Atom

solutions: 1, 2, 3, ..., n

1. Only certain 3-d "waveforms" possible for the electron in H atom.

2. Each "waveform" is called an ___________ and describes a possible _______________ of the electron. It also tells us

Y ²(x,y,z) a electron density at (x,y,z)

You can think of an orbital as an electron cloud where the electron density is higher some places than others.

(Electrons in an atom do not move in orbits, in fact, to the extent they can be regarded as wavelike they do not "move" at all in the usual sense of the word. They do have momentum, however, which is a property of particles.)

3. Orbital shapes:

(see board & transparencies)

notation: 3s

3 determines the energy and size of the orbital

s determines the shape of the orbital

4. Orbital energies

Electron Configurations

1. Aufbau principle:

1s < 2s < 2p < 3s < 3p < 4s , 3d < 4p < 5s , 4d < 5p < 6s , 5d , 4f < 6p

2. Pauli exclusion principle:

3. Hund's rule: When electrons fill up orbitals with the same energy, they try to remain as unpaired as possible.