Topic 2/12 Overview 2.2: Electron configuration 2.1: The Nuclear Atom 12.1: Electrons in Atoms

Why the QM model of the atom? Spectra of elements other than H are not adequately explained/calculated by Bohr (energy-level) model.

Quantum Mechanical Model of the Atom 1. Electrons are treated as waves (i.e. deBroglie equation). 2. The mathematical function that describes the electron wave is called a wave equation (ψ). (i.e. Schrodinger’s wave equation) 3. It is impossible to calculate the exact position and momentum of an e- simultaneously (i.e. Heinsenburg Uncertainty Principle)

Quantum Mechanical Model of the Atom Atomic orbital (def.) – a 3-D space where there is a high probability of finding an e-. (a.k.a. electron cloud).

Quantum Mechanical Model of the Atom 4. The probability of finding an electron in a given space can be determined and is related to the square of the wave function, |ψ|2. 5. When analyzed, the wave function gives us regions of space around the nucleus where there is a high probability of finding an e-. These are called atomic orbitals (a.k.a. electron clouds).

Quantum Mechanical Model of the Atom

Quantum Mechanical Model of the Atom 6. A greater number of characteristics of the electron are quantized in the QM model than in the Bohr model. Electrons and their orbitals are described by four quantum numbers. n = principal quantum # ℓ = angular momentum quantum # mℓ = magnetic quantum # ms = spin quantum number

Quantum Numbers a) Principal quantum number (n): describes energy level of the electron n = 1, 2, 3.... Physical interpretation: Size of the atomic orbital.

Quantum Numbers b) Angular momentum quantum number (ℓ) describes energy sublevel where electron is located ℓ = s, p, d, f,... Physical interpretation: shape of orbital

Quantum Numbers s sublevel = 1 orbital with 1 orientation

Quantum Numbers c) magnetic quantum # (mℓ) describes specific orbital within the sublevel that electron is located in. Physical interpretation: orientation of orbital p sublevel = 3 orbitals with different orientations

Quantum Numbers d sublevel = 5 orbitals with different orientations

3d orbitals

Quantum Numbers f sublevel = 7 orbitals with different orientations

Levels, sublevels, and orbitals

Quantum Numbers d) spin quantum # (ms) describes magnetic moment generated by the electron ms = +½(up), -½(down) Physical interpretation: self-rotation of electron on an axis

Communicating Electron Arrangement Orbital diagram: Lines/boxes = orbitals arrows = electrons direction of arrow = spin Electron configuration superscripts = # e-’s individual orbitals not shown

Rules for Writing Ground-State electron configurations Electrons will occupy the lowest energy orbital available (Aufbau principle). If a pair of electrons occupy the same orbital, they must have opposite spins (Pauli exclusion principle) In a set of equal-energy orbitals, electrons will occupy all vacant orbitals before pairing up with another electron (Hund’s rule).

Sublevel energies Energy: ns < np < nd < nf Ex. 4s < 4p < 4d < 4f

Sublevel energies Radial distribution function: describes probability of finding an electron at various distances from nucleus http://chemwiki.ucdavis.edu/Under_Construction/chem1/Atoms_and_the_Periodic_Table/The_Quantum_Atom

Sublevel energies http://chemwiki.ucdavis.edu/Under_Construction/chem1/Atoms_and_the_Periodic_Table/The_Quantum_Atom

Sublevel energies http://chemwiki.ucdavis.edu/Under_Construction/chem1/Atoms_and_the_Periodic_Table/The_Quantum_Atom

Relative energy of sublevels (Aufbau diagram)

Relative energy of sublevels (Aufbau diagram)

Relative energy of sublevels (Aufbau diagram) Can be found using the periodic table.

Shorthand electron config’s Noble gases can be used to shorten an e- config Ex = 1s22s22p63s1 becomes [Ne]3s1

Learning Check Write electron configurations for the following species using only your periodic table: Fluorine Ca Arsenic Al2+ P1-

Learning Check Write ECs for the following: Fluorine: [He]2s22p5 Ca [Ar]4s2 Arsenic [Ar]4s23d104p3 Al2+ [Ne] 3s1 P1- [Ne]3s23p4

Exceptions in the d block! Atoms naturally adopt lowest energy state. A half-filled (d5) and fully-filled d orbital (d10) are very stable (less e-e repulsion) and are therefore favored.

Exceptions in the d block: Cr Cr expected: [Ar] 4s23d4 Cr actual: [Ar] 4s13d5

Exceptions in the d block Cu expected [Ar] 4s2 3d9 Cu actual: [Ar] 4s13d10

Transition metal ions When any d-block elements form ions, the 4s electrons are ALWAYS lost first. Ex. Fe Fe2+ Fe3+

Transition Metal Ions The rule: Take the (n+1)s electrons off first, and then as many nd electrons as necessary to produce the correct positive charge.

Answers Sc3+ = [Ar] = [Ne]3s23p6 Cr3+ = [Ar] 3d3 Cr6+ = [Ar] Fe2+ = [Ar]3d6 Fe3+ = [Ar]3d5 Ni2+=[Ar]3d8 Cu2+=[Ar]3d9 Zn2+ = [Ar]3d10

2. Write the noble gas (shorthand) electron configuration for… Manganese Rb+ Strontium S+ Palladium I‒