Chapter 5Chapter 5

Section 5.3 & 5.4Section 5.3 & 5.4

The Quantum ModelThe Quantum Model

Problems with the Bohr ModelProblems with the Bohr Model

1.1. Worked well for predicting hydrogen Worked well for predicting hydrogen spectrum, but not for elements with more spectrum, but not for elements with more than one electron.than one electron.

2.2. Did not explain a “fine structure” to Did not explain a “fine structure” to spectral lines that became apparent as spectral lines that became apparent as spectrometers improved.spectrometers improved.

3.3. Did not explain chemical behavior of Did not explain chemical behavior of atoms.atoms.

Louis deBroglie:Louis deBroglie:

If light waves can behave like particles If light waves can behave like particles then particles (electrons) can behave like then particles (electrons) can behave like waves.waves.

Electron beams can be bent, or Electron beams can be bent, or diffracteddiffracted..

Electron beams can Electron beams can interfereinterfere (overlap) (overlap) with each other, just like light.with each other, just like light.

Werner HeisenbergWerner Heisenberg

Heisenberg Uncertainty Principle: It is Heisenberg Uncertainty Principle: It is impossible to know simultaneously both impossible to know simultaneously both the position and the velocity of an electron the position and the velocity of an electron (how an electron is moving).(how an electron is moving).

To “see” an electron, it must be struck by a To “see” an electron, it must be struck by a photon of light. The photon adds energy to photon of light. The photon adds energy to the electron and the electron’s position the electron and the electron’s position changes.changes.

Erwin Schrödinger:Erwin Schrödinger:

Quantum mechanical model (most Quantum mechanical model (most current view) A mathematical “wave current view) A mathematical “wave equation” describes the probable equation” describes the probable locations of electrons.locations of electrons.

1.1. electrons may be found anywhere electrons may be found anywhere outside nucleus. There are regions of outside nucleus. There are regions of high probability called high probability called orbitalsorbitals..

2.2. Electron orbitals correspond to 3-D Electron orbitals correspond to 3-D regions in space with different shapes.regions in space with different shapes.

3. Certainty of the Bohr model is replaced 3. Certainty of the Bohr model is replaced with the region in space where an electron with the region in space where an electron may be found 90% of the time.may be found 90% of the time.

4. Radii of the orbits predicted by Bohr 4. Radii of the orbits predicted by Bohr correspond to distances from the nucleus correspond to distances from the nucleus where electrons are likely to be found.where electrons are likely to be found.

Schrödinger model of the atom identifies the Schrödinger model of the atom identifies the probable locations where electrons will be probable locations where electrons will be found using found using four quantum numbersfour quantum numbers..

Each set of 4 quantum numbers results in a Each set of 4 quantum numbers results in a unique “address” for locating an electron.unique “address” for locating an electron.

nn = Principle Quantum Number = Principle Quantum Number

Values allowed: n = 1,2,3, ….Values allowed: n = 1,2,3, ….Gives the main energy level occupied by Gives the main energy level occupied by

the electron / distance from nucleusthe electron / distance from nucleusLowest energy level is n = 1, as in BohrLowest energy level is n = 1, as in Bohr

ll = angular momentum quantum = angular momentum quantum numbernumber

Values allowed: Values allowed: ll = integers from 0 to ( = integers from 0 to (n n --1)1)

Gives the Gives the sublevel sublevel within the energy levelwithin the energy levelSublevel gives the shape of the orbitalSublevel gives the shape of the orbitalSublevel described by letters: s p d f (Sublevel described by letters: s p d f (ll = =

0,1, 2, 3)0,1, 2, 3)

mm = magnetic quantum number = magnetic quantum number

Values allowed: Values allowed: mm = integers from – = integers from –ll to + to +ll Gives the orientation of the Gives the orientation of the orbitalorbital in space in space

(along the x, y, z axis)(along the x, y, z axis) Tells how many orbitals there are in each Tells how many orbitals there are in each

sublevelsublevel Example if Example if ll = 0 there is only one position, if = 0 there is only one position, if ll = 1 then magnetic = 1 then magnetic

numbers = -1, 0, 1. indicate there are 3 orbital positionsnumbers = -1, 0, 1. indicate there are 3 orbital positions

ss pp dd ff

11 33 55 77

ss = spin quantum number = spin quantum number

Gives direction of spin of electrons in an Gives direction of spin of electrons in an orbitalorbital

Values allowed: Values allowed: ss = +½ or –½ = +½ or –½

Electron Filling Order ChartElectron Filling Order Chart1s

2s 2p

3s 3p 3d

4s 4p 4d 4f

5s 5p 5d 5f

6s 6p 6d 6f 6g

7s 7p 7d 7f

8s 8p 8d

Electron Configuration of Electron Configuration of OxygenOxygen

Oxygen, Z = 8Oxygen, Z = 8

1s1s222s2s222p2p44

Orbital Filling DiagramsOrbital Filling Diagrams

Show how electrons are distributed in Show how electrons are distributed in orbitals.orbitals.

Each box or horizontal line represents the Each box or horizontal line represents the unoccupied orbital.unoccupied orbital.

Each arrow represents an electronEach arrow represents an electron

Aufbau Principle:Aufbau Principle:

An electron occupies the lowest energy An electron occupies the lowest energy orbital that can receive it.orbital that can receive it.

Pauli Exclusion Principle:Pauli Exclusion Principle:

No 2 electrons in the same atom can have No 2 electrons in the same atom can have the same set of 4 quantum numbersthe same set of 4 quantum numbers

Hund’s RuleHund’s Rule

Orbitals of equal energy are each Orbitals of equal energy are each occupied by one e- before any orbital is occupied by one e- before any orbital is occupied by a second e- and all electrons occupied by a second e- and all electrons in singularly occupied orbitals must have in singularly occupied orbitals must have the same spin.the same spin.

Example: write the orbital diagram for Example: write the orbital diagram for carbon, Z= ___ and fluorine, Z= ___carbon, Z= ___ and fluorine, Z= ___

Carbon, Z = 6Carbon, Z = 6

___ ___ ___ ___ ______ ___ ___ ___ ___

1s 2s 2p1s 2s 2p

↑↓↑↓ ↑↓↑↓ ↑ ↑ ↑ ↑ ______

1s 2s 2p1s 2s 2p

Fluorine, Z = 9Fluorine, Z = 9

___ ___ ___ ___ ______ ___ ___ ___ ___

1s 2s 2p1s 2s 2p

↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↑

1s 2s 2p1s 2s 2p