Chapter 6 Section 2

Sec 6.5 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

Orbitals and Quantum Numbers Orbitals – specific distribution of electron density in space (given by probability density); quantum mechanical model

Orbitals and Quantum Numbers 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) There is no n= 0 value. The ground state is n = 1 Excited states are n = 2, 3, 4 etc

Quantum Numbers Azimuthal quantum number, l, * defines shape of the orbital * designated by letters s, p, d, and f s = 0 p = 1 d = 2 f = 3

Quantum Numbers Magnetic quantum number, m l, * describes orientation of orbital in space * ranges from l and –l Ex: if l = 3 then m l could be -3, -2, -1, 0, 1, 2, 3 Take a look at an orbital diagram. Compare the number of m l options with the number of boxes per sublevel.

Quantum Numbers Spin quantum number, m s, * describes the direction of electron spin There are 2 options for the m s value + ½ or - ½ The first electron in the orbital is spin up and the second electron is spin down.

Electron shells – a 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 The shell with the principal quantum number n, will have exactly n subshells Each subshell has a specific number of orbitals. For a given l, there are 2l + 1 allowed values of m 1 The total number of orbitals in a shell is n 2

Ground State – when the electron is in the lowest energy orbital Excited State – when the electron is in any other orbital

Representations of Orbitals

S- orbital Appears to be spherical Size increases as n increases All s-orbitals are spherically symmetrical –Nodes = the intermediate regions where ψ 2 goes to zero; the number of nodes increases with increasing values of n

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

D - orbitals

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

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

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 Z eff = Z-S Screening effect – the effect of inner electrons in decreasing the nuclear charge experienced by outer electrons

Energies of Orbitals In a many-electron atom, for a given value of n, Z eff decreases with increasing value of l The energy of an electron depends on the effective nuclear charge, Z eff 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

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, m s = a quantum number associated with the electron spin; two possible values + ½ or -1/2

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

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

6.8 Electron Configuration

Electron Configuration for Ions Write the electron configuration for the Li +1 ion. Write the electron configuration for the O -2 ion. Write the electron configuration for the Al +3 ion.

Abbreviated electron configurations Look for the nearest noble gas with a lower atomic #. Write the chemical symbol for the noble gas in brackets. Add the remaining part of the electron configuration to the noble gas.

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

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

6.9 Electron Configurations and the Periodic Table