Electronic Structure of an atom refers to the number and distribution of electrons around the nucleus.

Wave-Particle Nature of Light

Quotation: "Anyone who is not shocked by quantum theory has not understood it."

-Niels Bohr

The Delayed Choice Experiment (Scientific American Jan. 1988, p. 46)

Experimental setup.

Procedure:

1. The laser is fired and one photon is sent into the beam splitter.

2. If the photon behaves like a particle it will take either path A or A' as it leaves the beam splitter.

3. If the photon behaves like a wave it will "split" in two and take both paths and interfere with itself.

4. After the photon leaves the beam splitter the switch is triggered.

5. If the switch is turned to the "on" position the photon either takes path A or path A' and is detected by the photodetector. It behaves as a particle with a definite path.

6. If the switch is turned to the "off" position the photon takes both paths and produces an interference pattern. It behaves as a wave.

How does the photon decide how to behave?

Possible Explanations

1. The photon knows how the switch will be turned in advance and makes a decision before leaving the beam splitter.

(New Age)

2. The nature of the photon is indeterminate until the switch is turned and an observation is made: the photon becomes a wave or becomes a particle.

The observation makes the photon a wave or a particle.

(accepted by Bohr and most physists)

(Is reality objective? Do we create reality by observations?)

3. God controls both the "decision" of the photon and the experimenter.

Thought experiment with quasar.

DeBroglie (1924) proposed that matter has wavelike properties.

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

The smaller the particle, the smaller m is, the greater l is, and the more important wave properties are.

Evidence for Wave Properties of Matter

Davisson and Germer (1927): Showed that electrons can be diffracted by a nickel crystal. This indicates that electrons have wave properties.

X-ray diffraction; Electron diffraction

Al foil

Wave Mechanical Model of the Atom

Schrodinger (1926)

Assumption: Electrons in an atom behave as standing waves.

Guitar string analogy

(transparency/chalkboard)

Only certain wavelengths are possible for standing waves.

Schrodinger Wave Equation

HY = EY (analogous to eq. for mechanical waves)

H is an operator.

E is the energy of the electron.

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

Hydrogen atom

solutions: Y₁, Y₂, Y₃, ..., Y_n

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

2. Each "waveform" is called an orbital and describes the possible energy states of the electron. It also tells us where the electron can usually be found when in a given energy state. (orbitals have size, shape, & orientation)

Y²(x,y,z) a electron density at (x,y,z)

3. Each orbital can be specified by 3 quantum numbers which describe the various properties of the orbital.

n, principal quantum number: determines avg distance of e^- from nucleus,i.e., it determines the size of the orbital.

It also determines the energy of the orbital.

n = 1, 2, 3,..., 7

l, orbital angular momentum quantum no.: determines the shape of the orbital.

It also determines the energy of the orbital in atoms other than H.

l = 0, 1, 2,..., n - 1

l........designation of orbital

0.......s

1.......p

2.......d

3.......f

s orbital:

p orbital:

d_xy:

d_z2:

Sign of wave function does not affect electron density.

Sign of wave function is important for bonding and hybridization.

m_l, magnetic quantum number: determines the orientation of the orbital.

m_l = -l, -l + 1, ..., 0, ...,l - 1, l

There are 2l + l orbitals with quantum number l, each with a different orientation.

n, l, & m_l determine the orbital.

m_s, spin quantum number: within an orbital the electron can have one of two possible "spins" corresponding to m_s = +1/2 or -1/2

(table of orbitals)

Radial Distribution Functions

When orbitals have radial nodes the electron spends part of its time very close to the nucleus. The orbital is said to be penetrating and will be lower in energy in a many-electron atom.

ability to penetrate inner orbitals:

s > p > d > f

The Many-electron Atom

Orbitals similar to H orbitals except:

1. orbitals for heavier elements contracted & lower in energy

2. orbitals with different l values differ in energy

ns < np < nd < nf

ns is most penetrating so e^- experiences nuclear charge most so orbital lowest in energy

(orbital diagram for H vs many-electron atoms)

Many-electron (subshells split)

Electron Configurations

1. Aufbau principle: The electron configuration for an atom can be determined by filling orbitals in order of increasing energy:

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

(periodic table)

2. Pauli exclusion principle: No two electrons can have the same four quantum numbers, i.e., if two electrons are in the same orbital, they must have opposite spins.

hence a maximum of 2 electrons/orbital

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

(orbital diagrams)

(table of electron configurations)

Effective Nuclear Charge

(Bohr model of Li vs C)

Slater's Rules

effective nuclear charge = Z_eff = Z - s

where s is the shielding parameter and is calculated by empirical rules.

1. Write out the electron configuration as follows:

(1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(5s,5p)...

2. Electrons to the right of the group of electrons in question contribute nothing to the shielding of that group of electrons.

3. All other electrons in the same group shield the electron in question to an extent of 0.35 each.

4. If the electron in question is an s or p electron:

a) all electons in the n - 1 shell shield to an extent of 0.85 each

b) all electrons in shells n - 2 or less shield perfectly, i.e., their contribution is 1.00 each.

5. If the electron in question is a d or f electron: all electrons lying to the left of the nd or nf group contribute 1.00. (why?)

(example with N)

Z_eff is a major factor in determining periodic variation in atomic parameters:

Element.....Z_eff

Li...............1.3

Be..............1.95

B................2.60

C................3.25

N................3.90

O................4.55

F.................5.20

Ne...............5.85

steady increase in Z_eff

Element.....Z_eff

H.................1.0

Li................1.3

Na...............2.2

K.................2.2

Rb...............2.2

Cs...............2.2

slow increase in Z_eff

Atomic Radii, r_A

The the metallic radii and covalent radii are together referred to as the atomic radii:

Vertical change in size more rapid than horizontal.

Ionic Radii, r_I

Vertical trends:

1 Main group elements: r_I increases while descending a group since n increases:

Li⁺ < Na⁺ < K⁺ < Rb⁺ < Cs⁺

2. d block elements:

3d < 4d, 5d

Cr < Mo, W

Lanthanide Contraction: Z_eff increases as we go across the lanthanides making Z_eff for 5d metals larger than "normal". The result is that 5d metals are comparable to 4d metals in size.

Horizontal trends: isoelectronic series:

O^2- > F^- > Na⁺ > Mg²⁺ > Al³⁺ (each has [Ne] configuration)

Z increases so orbitals contract.

constant charge:

Ca²⁺ > Ti²⁺ > V²⁺

(anomalies not uncommon in d block)

Other trends:

anions > cations (why?)

(periodic table of ions)

For a given element, the greater the charge, the smaller the ion.

Cr²⁺ > Cr³⁺ > Cr⁶⁺

Electronegativity, c (Pauling)

(Periodic Table)