1. Chapter 6
Section 2

2. Quantum Mechanics and Atomic Orbitals
Wave functions – describes the behavior of the electron, denoted with the Greek letter, ψ
The wave function has a known energy, but the electron location is unknown, so the probability of its position in space is given by probability density, ψ2
Electron density – distribution map of the probability of finding the electrons at the points of space (probability density); high probability density=high electron density

3. Orbitals and Quantum Numbers
Orbitals – specific distribution of electron density in space (given by probability density); quantum mechanical model
1. principal quantum number, n, relates to the size and energy of the orbital: integral values of 1,2,3, etc. an increase in n would mean a larger orbital, farther from the nuclear, and more energy (less tightly bound to nucleus)
2. azimuthal quantum number, l, defines shape of the orbital (designated by letters s, p, d, and f)
3. magnetic quantum number, m, describes orientation of orbital in space; range from l and -l

4. Subshell – set or orbitals that have the same n and l values
Electron shells – set of orbitals with the same value of n, such as 3s, 3p, 3d
Subshell – set or orbitals that have the same n and l values
1. The shell with the principal quantum number n, will have exactly n subshells
2. Each subshell has a specific number of orbitals. For a given l, there are 2l+1 allowed values of m1
3. the total number of orbitals in a shell is n2
Ground State – when the electron is in the lowest energy orbital
Excited State – when the electron is in any other orbital

5. Representations of Orbitals

6. S- orbital Appears to be spherical Size increases as n increases
All s-orbitals are spherically symmetrical
Nodes = the intermediate regions where ψ2 goes to zero; the number of nodes increases with increasing values of n

7. P - orbitals

8. P- orbitals
Concentrated on two sides of the nucleus, separated by a node at the nucleus, “two lobes”
the orbitals of a given subshell have the same size and shape but differ in spatial orientation

9. D - orbitals

10. d- and f- orbitals
The different d orbitals in a given shell have different shapes and orientations in space
When n is equal to or greater than 3, the d-orbitals are present. There are 5 d orbitals
When n is equal to or greater than 4, there are 7 equal f-orbitals present

11. Orbitals in Many-Electron Atoms
The presence of more than one electron greatly changes the energies of the orbitals
The electron-electron repulsions cause different subshells to be at different energies

12. Effective Nuclear Charge
Each electron is simultaneously attracted to the nucleus and repelled by the other electrons
Energy of the electron can be estimated by how it interacts with the average environment (created by the nucleus and other electrons)
Effective nuclear charge – the net positive charge attracting the electron
Zeff = Z-S
Screening effect – the effect of inner electrons in decreasing the nuclear charge experienced by outer electrons

13. Energies of Orbitals
In a many-electron atom, for a given value of n, Zeff decreases with increasing value of l
The energy of an electron depends on the effective nuclear charge, Zeff
In a many-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l
Degenerate - orbitals with the same energy

15. Electron Spin and the Pauli Exclusion Principle
Electron spin = a property of the electron that makes it behave as though it were a tiny magnet. The electron behaves as if it were spinning on its axis, electron spin is quantized
Electron spin quantum number, ms = a quantum number associated with the electron spin; two possible values + ½ or -1/2

16. Pauli exclusion principle states that no two electrons in an atom can have the same values for n, l, ml, and ms
Places a limit of two on number of electrons that can occupy any one atomic orbital

17. 6.8 Electron Configurations
Electron configuration – way in which the electrons are distributed among the various orbitals of an atom
Represent electron configuration through an orbital diagram – each orbital represented by a box and each electron by a half arrow

18. 6.8 Electron Configuration

19. 6.8 Electron Configuration
Paired – electrons in the same orbital
Unpaired – electron alone in an orbital
Hund’s rule – for degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin in maximized
Valence electrons-- outer-shell electrons
Core electrons- electrons in inner shells

21. Period 4 and Beyond Elements known as:
Transition Elements (and Metals)-Elements in which the D orbitals are filled
Lanthanide Elements- Elements in which the 4s sub shell is partly occupied
Actinide Elements- Elements in which the 5f orbitals are partly occupied

22. 6.9 Electron Configurations and the Periodic Table

23. THE END…finally