Chapter 5 Section 5.3 & 5.4 The Quantum Model

Problems with the Bohr Model 1. Worked well for predicting hydrogen spectrum, but not for elements with more than one electron. 2. Did not explain a “fine structure” to spectral lines that became apparent as spectrometers improved. 3. Did not explain chemical behavior of atoms.

Louis deBroglie: If light waves can behave like particles then particles (electrons) can behave like waves. If light waves can behave like particles then particles (electrons) can behave like waves. Electron beams can be bent, or diffracted. Electron beams can be bent, or diffracted. Electron beams can interfere (overlap) with each other, just like light. Electron beams can interfere (overlap) with each other, just like light.

Werner Heisenberg Heisenberg Uncertainty Principle: It is impossible to know simultaneously both the position and the velocity of an electron (how an electron is moving). Heisenberg Uncertainty Principle: It is impossible to know simultaneously both the position and the velocity of an electron (how an electron is moving). To “see” an electron, it must be struck by a photon of light. The photon adds energy to the electron and the electron’s position changes. To “see” an electron, it must be struck by a photon of light. The photon adds energy to the electron and the electron’s position changes.

Erwin Schrödinger: Quantum mechanical model (most current view) A mathematical “wave equation” describes the probable locations of electrons. Quantum mechanical model (most current view) A mathematical “wave equation” describes the probable locations of electrons. 1. electrons may be found anywhere outside nucleus. There are regions of high probability called orbitals. 2. Electron orbitals correspond to 3-D regions in space with different shapes.

3. Certainty of the Bohr model is replaced with the region in space where an electron may be found 90% of the time. 4. Radii of the orbits predicted by Bohr correspond to distances from the nucleus where electrons are likely to be found. Schrödinger model of the atom identifies the probable locations where electrons will be found using four quantum numbers. Each set of 4 quantum numbers results in a unique “address” for locating an electron.

n = Principle Quantum Number Values allowed: n = 1,2,3, …. Values allowed: n = 1,2,3, …. Gives the main energy level occupied by the electron / distance from nucleus Gives the main energy level occupied by the electron / distance from nucleus Lowest energy level is n = 1, as in Bohr Lowest energy level is n = 1, as in Bohr

l = angular momentum quantum number Values allowed: l = integers from 0 to ( n -1) Values allowed: l = integers from 0 to ( n -1) Gives the sublevel within the energy level Gives the sublevel within the energy level Sublevel gives the shape of the orbital Sublevel gives the shape of the orbital Sublevel described by letters: s p d f ( l = 0,1, 2, 3) Sublevel described by letters: s p d f ( l = 0,1, 2, 3)

m = magnetic quantum number Values allowed: m = integers from – l to + l Values allowed: m = integers from – l to + l Gives the orientation of the orbital in space (along the x, y, z axis) Gives the orientation of the orbital in space (along the x, y, z axis) Tells how many orbitals there are in each sublevel Tells how many orbitals there are in each sublevel Example if l = 0 there is only one position, if l = 1 then magnetic numbers = -1, 0, 1. indicate there are 3 orbital positions Example if l = 0 there is only one position, if l = 1 then magnetic numbers = -1, 0, 1. indicate there are 3 orbital positions spdf 1357

s = spin quantum number Gives direction of spin of electrons in an orbital Gives direction of spin of electrons in an orbital Values allowed: s = +½ or –½ Values allowed: s = +½ or –½

Electron Filling Order Chart 1s 2s2p 3s3p3d 4s4p4d4f 5s5p5d5f 6s6p6d6f6g 7s7p7d7f 8s8p8d

Electron Configuration of Oxygen Oxygen, Z = 8 1s 2 2s 2 2p 4 1s 2 2s 2 2p 4

Orbital Filling Diagrams Show how electrons are distributed in orbitals. Show how electrons are distributed in orbitals. Each box or horizontal line represents the unoccupied orbital. Each box or horizontal line represents the unoccupied orbital. Each arrow represents an electron Each arrow represents an electron

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

Pauli Exclusion Principle: No 2 electrons in the same atom can have the same set of 4 quantum numbers No 2 electrons in the same atom can have the same set of 4 quantum numbers

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

Example: write the orbital diagram for carbon, Z= ___ and fluorine, Z= ___ Carbon, Z = 6 ___ ___ ___ ___ ___ 1s 2s 2p ↑↓ ↑↓ ↑ ↑ ___ ↑↓ ↑↓ ↑ ↑ ___ 1s 2s 2p 1s 2s 2p

Fluorine, Z = 9 Fluorine, Z = 9 ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 1s 2s 2p 1s 2s 2p ↑↓ ↑↓ ↑↓ ↑↓ ↑ ↑↓ ↑↓ ↑↓ ↑↓ ↑ 1s 2s 2p 1s 2s 2p