Chapter 6: Quantum Mechanics (note: these notes include a review of Chemistry I Honors, the AP notes are in dark red)

The Bohr Atom
Thompson: plum pudding
Rutherford: nucleus in a sea of electrons.
Bohr: planetary model.
Wave velocity = (wavelength)(frequency).
Review of wave mechanics.
The electromagnetic spectra: The type of wave is determined by its wavelength and frequency.
Speed of light = 2.998 x 108 m/s
A light wave has a frequency of 1.74 x 1017 hertz. What is its wavelength? What type of light is it?

Planck’s Hypothesis
Light is given off in bundles of energy called quanta.
E = h(
Energy = planck’s constant * wave frequency h = 6.626 x 10-34 J/hz

Energy Problems
A photon of light is found to have 3.63 x 10-22 Joules of energy. What is the wavelength of this light wave?
A photon of light is found to have a wavelength of 5.00 x 102 nm. What is the energy of a photon of this light wave?

Planck’s Hypothesis
Atomic Spectra: produced when an electron moves from a higher to lower energy level, giving off light in the process. (E = Ehi - Elo = h( = hc/(
Ex. For the yellow line in the sodium spectra (( = 589.0 nm), find its frequency, quantum energy, and the energy released by one mol of sodium electrons.What is the energy difference between two energy levels of Na?

Planck’s Hypothesis
( ( 5.090 x 1014s-1
(E = 3.373 x 10-19 J
For one mol of electrons: (E = 203.1 kJ
Hence a two energy level difference = 203.1 kJ/mol

Bohr Model
Bohr postulated that an electron moves about the nucleus in a circular orbit of a fixed radius.
The emission spectra of hydrogen: hydrogen absorbs energy when excited then gives it off when it returns to its ground state.
The ground state of an electron represents its lowest orbit. The excited state represents any other possible orbit.
Hydrogen only emits this absorbed energy at certain visible wavelengths. Bohr reasoned this related to certain allowed electron orbits.
To calculate the energy of an allowed energy level: En = (-2.180 x 10-18 J)/n2, where n = 1, 2, 3, …
RH = Rydberg constant = 2.180 x 10-18 J
In the Bohr atom, calculate the energy released as an electron moves from the third to the second energy level. What is the wavelength of the emitted light? E3 = -2.422 x 10-19 J; E2 = -5.450 x 10-19 J
Ehi - Elo = 3.028 x 10-19 J ( = hc/(E = 6.560 x 10-7 m = 656.0 nm (how does this compare to the Balmer series?)
Modern Atomic Structure
Bohr: emission spectra turned out to be several lines at each level, not singular lines.
De Broglie: wavelengths can be predicted based on the mass and velocity of a particle.
Wave/particle duality.
Planck - waves can act like particles E=h(
DeBroglie - hey… then particles can act as waves, mc2 = E = h(, (( h/mv.
Experiments can only demonstrate one of these qualities at a time.
Particle behavior: photoelectric effect (solar powered calculator).
Wave behavior: refraction (changes speed in different media), defraction (bends around barriers), reflection
Heisenberg Uncertainty Principle: both the momentum and position of a particle can not be precisely known at the same time.
Therefore, we can only refer to the probability of finding an electron in a region; we cannot specify the path.
Schrodinger: wave equations ((() can be used to predict the region of probability for locating an electron.
An Electron moves at high velocities usually on the surface of this region.
An electron effectively fills the surface. (fan analogy)
Quantum numbers are used to describe the location of electrons in atoms.
Importance: model of atoms and bonding theory.
Principle Quantum Number, n: energy level.
The higher the number the larger the region.
Corresponds to the periodic table.
Modern Atomic Structure
Principle energy level: the value of n is the main factor that determines the energy of an electron and its distance from the nucleus.
Maximum electron capacity of a level = 2n2
Modern Atomic Structure
Second Quantum Number, l: refers to energy sublevels.
The number of sublevels equals the principal quantum number.
Sublevels do not have the same energy.
Sublevels from one principal level can overlap sublevels from another. Figure 6.7, p. 151
3rd Quantum Number, m: refers to the orientation of the suborbital. s,p,d and f orbitals.
Degenerate orbitals (geometries and orientations - capacities)
Each orbital has the capacity of two electrons. The s orbitals are spherically symmetric about the nucleus; p orbitals are dumbell shaped and at right angles to each other.
4th Quantum Number: refers to the spin. ms = 1/2 or -1/2
Modern Atomic Structure
Pauli Exclusion Principle: each electron can be described by a unique set of 4 quantum numbers. n = primary energy level l = sublevels
0 = s-orbital
1 = p-orbital
2 = d-orbital. m = orientation of the orbital ( -l to +l) ex. p-orbital px = -1 py = 0 pz = +1 spin = +1/2 or -1/2 ex: 1st electron = 1 0 0 +1/2.
2nd electron = 1 0 0 -1/2
3rd electron = 2 0 0 +1/2
Hund’s Rule: electrons fill unoccupied degenerate orbitals before pairing. Find the quantum numbers for the 5th and 7th electrons.
Basic electron configurations.
Orbital diagrams.
Core configurations.
Note: 1. 2 e- in an orbital have opposed spins.
2. When several orbitals of the same sublevel are available, electrons enter one at a time with parallel spins.
Pneumonic device for remembering the filling order.
Use the periodic table to locate the outermost electrons of an atom.
S-block and p-block elements match the row.

The Transition Metals d-block elements (groups 3-12).
Energy sublevel overlap: ex - 4s vs. 3d
Multiple valence
Brightly colored compounds and solutions.
The Periodic Table
Lanthanoids: elements 57-70, begins 4f block.
Actinoids: elements 89-102, begins 5f block.
Rare earth metals.

Nature tends towards stability.
Atoms seek bonding situations that result in stable electron configurations (ex. Share electrons).
Octet rule: eight electrons in the outer level (s & p’s?) render an atom unreactive.
Atoms seek to lose, gain, or share electrons to seek a stable octet of electrons.
The Periodic Table
An atom having a filled or half-filled sublevel is slightly more stable than an atom without.
Full sublevels are more stable than half-filled.
The Periodic Table
Full outer levels are more stable than full sublevels.
The Periodic Table
Electron promotion: an electron can be promoted to a slightly higher sublevel in order to produce a full or half filled sublevel.
Ex - Cr and Cu

Groups = families: columns of related elements. Each family has a similar outer electron configuration. Ex. s2 and p5 elements.
The properties are predictable and repeat themselves. They are based on electronic configuration.

Atomic Radii
The distance from the nucleus to the outermost orbital.
Increases as you move down a group; increased principle energy level.
Decreases as you move across a period.
Z effective - the larger the charge of a nucleus, the greater the pull on the electrons. This greater attractive force pulls the electrons slightly closer to the nucleus and accounts for the trend in atomic radii across a period.
Radii of Ions
Ions: charged particles which are the result of adding or subtracting electrons from a neutral atom.
Radii of Ions
Cations: ions with a positive charge (metals).
Anions: ions with a negative charge (non-metals).
Atoms will add or subtract electrons to complete their outermost energy level (they seek stability; a full octet of electrons).
Radii of Ions
Nature does whatever is easiest.
Ex. It is easier for potassium to lose 1 electron rather than gain 7 to complete its octet.

Ionic radii is based on whether an atom will add or subtract electrons when it ionizes.
Cations are smaller than their neutral atoms.
Anions are larger than their neutral atoms.
Radii of Ions
Ionic radii increase down a group and decrease across a period. p. 252 (notice the group 18 elements)

Oxidation Numbers
Predicting oxidation states: for the main group elements (groups 1-2, 13-18) this will be based on the tendency of the group towards stability.
Predicting oxidation states: for the transition elements - theory vs reality
Ex. Zn and Ag
Transition elements:
1. Can lose one or both of its two s-shell electrons first.
2. Can lose each individual d-shell electrons only after the outer s-shell is empty
3. Will not lose d-electrons if that shell is half-filled.
Ex. Scandium (+2, +3) vs Titanium (+2, +3, +4)
Vs Copper (+1, +2)

Ionization Energy
Ionization energy: the energy required to remove one electron from a gaseous atom.
Trends: decreases down a group, increases across a period ( takes more energy to remove an electron from an element that usually forms an anion).
Ionization Energy
Factors affecting ionization energy:
Nuclear charge
Shielding effect
Radius
Sublevel

Nuclear charge: the larger the Z effective, the greater the force attracting the electrons; greater ionization energy.
Shielding effect - core electrons shield the attractive nuclear force from outer electrons, lessening ionization energy. Electron/electron repulsion can increase the effect.
Radius- the greater the atomic radii, the lower the ionization energy.
Sublevels- removing an electron from a half-filled or full sublevel requires more energy.

Electron Affinity
Electron Affinity: an atoms ability to attract additional electrons.
Electron Affinity
Metals have low electron affinities. Non-metals have high electron affinities. The trend: increase across a period and decreases down a group. Why?
Ionization Energy
Multiple ionization energies: the second and third ionization energies can give clues as to atomic structure. Ex. Al vs Mg vs Na