Quantum Mechanical Model of the Atom Quantum Numbers & Electron Configurations

Name This Element

Building on Bohr  The simple Bohr model was unable to explain properties of complex atoms  Only worked for hydrogen  A more complex model was needed…

Quantum Numbers  Four numbers used to describe a specific electron in an atom  Each electron has its own specific set of quantum numbers  Recall: Describes orbitals (probability clouds)

The Principal Quantum Number “n”  Indicates the average distance (size) of the orbital from the nucleus (same as Bohr’s energy levels)  Higher n = greater distance from nucleus = greater energy  n = integers > 1 (1,2,3…)  The greatest number of electrons possible in each energy level is 2n 2

Electron Energy Level (Shell) Generally symbolized by n, it denotes the probable distance of the electron from the nucleus. Number of electrons that can fit in a shell: 2n 2

Principle Quantum Number n = 1 n=2 n=3 n=4 n=5 n=6 Energy

The Secondary Quantum Number “l”  Describes the shape of the orbital  Atoms with many electrons showed spectrum with many lines, some close together and others spaced apart  Subshells within the main energy levels  Each subshell has a different shape with the highest probability of finding an electron

The Secondary Quantum Number “l”  Positive integers ranging from 0-3  Maximum value of n-1  l = 0 (s orbital)  l = 1 (p orbital)  l = 2 (d orbital)  l = 3 (f orbital)  Total number of sublevels = n

Orbitals of the same shape (s, for instance) grow larger as n increases… Nodes are regions of low probability within an orbital. Sizes of s Orbitals

The s orbital has a spherical shape centered around the origin of the three axes in space. s orbital shape

There are three dumbbell-shaped p orbitals in each energy level above n = 1, each assigned to its own axis (x, y and z) in space. p orbital shape

Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbells ” …and a “dumbell with a donut”! d orbital shapes d orbital shape

f orbital shape

Energy Level and Orbitals  n=1, only s orbitals  n=2, s and p orbitals  n=3, s, p, and d orbitals  n=4, s,p,d and f orbitals Remember: l = n-1

The Magnetic Quantum Number “m l ”  Describes orientation of the orbital  m l = integers from -l to +l  Maximum number of orientations = n 2

The First Three Quantum Numbers

The Spin Quantum Number “m s ”  Describes the direction an electron is spinning in a magnetic field (up or down)  Only two electrons per orbital  m s = + 1/2 or - 1/2

Quantum Numbers Summary Chart NameSymbolAllowed ValuesProperty Principaln positive integers 1,2,3… Orbital size and energy level Secondary (Angular momentum) l Integers from 0 to (n-1) Orbital shape (sublevels/subshells) Magneticmlml Integers –l to +lOrbital orientation Spinmsms +½ or –½ Electron spin Direction

 The distribution of electrons among the energy levels, sublevels, orientations, and spins of an atom is known as the electron configuration.  Having a basic understanding of how the electrons are configured helps us determine the interaction of atoms of elements to other elements  When they come into contact it’s the outer electrons that do the chemistry. Electron Configurations

Pauli Exclusion Principle  No 2 e- in an atom can have the same set of four quantum numbers (n, l, m l, m s ). Therefore, no atomic orbital can contain more than 2 e-.orbitalorbital 2 electrons

Theoretically electrons would fill orbitals numerically. However, experimental evidence shows us that there are overlaps that affects the order of fill. Energy Overlaps

Aufbau Principle  Aufbau Principle: an e- occupies the lowest energy orbital that can receive it.  Aufbau order:

Hund’s Rule  Hund’s Rule: orbitals of equal energy are each occupied by one e- before any orbital is occupied by a second e-, and all e- in singly occupied orbitals must have the same spin 1s 2s 2p

Orbital Diagram Rules 1. Represent each electron by an arrow 2. The direction of the arrow represents the electron spin 3. Draw an up arrow to show the first electron in each orbital. 4. Hund’s Rule: Distribute the electrons among the orbitals within sublevels so as to give the most unshared pairs. Put one electron in each orbital of a sublevel before the second electron appears. Half filled sublevels are more stable than partially full sublevels.

1 s 3 s 2 p 2 s 4 s 3 p 4 p 3 d 5 s 4 d Energy O xygen 8O 2 unpaired electrons

1 s 3 s 2 p 2 s 4 s 3 p 4 p 3 d 5 s 4 d Energy Nickel 28Ni 2 unpaired electrons

Orbital Diagram Examples  H  _ 1s  Li   _ 1s 2s  B    __ __ 1s 2s 2p  N      _ 1s 2s 2p

Electron Configuration  Electron configuration is a shorthand notation that shows electron arrangement within orbitals.  Electron configuration can be written in one of 3 methods: 1. Energy-Level Diagrams (orbital diagram) 2. Complete electron configuration 3. Condensed electron configuration (AKA noble gas configuration)

Electron Configuration Principal quantum number “n” Secondary quantum number “l”

Electron Configuration  The total of the superscripts must equal the atomic number (number of electrons) of that atom  The differentiating electron is the electron that is added which makes the configuration different from that of the preceding element.  The “last” electron.  H1s 1 He1s 2 Li1s 2, 2s 1 Be1s 2, 2s 2 B1s 2, 2s 2, 2p 1

 Fe (Atomic Number = 26) 1s 2 2s 2 3s 2 4s 2 2p 6 3d 6 3p 6 1s 2 2s 2 3s 2 2p 6 Mg (Atomic Number = 12) Ne (Atomic Number = 10) Ti (Atomic Number = 22) Zr (Atomic Number=40) 1s 2 2s 2 2p 6 1s 2 2s 2 3s 2 4s 2 2p 6 3d 2 3p 6 1s 2 2s 2 3s 2 4s 2 2p 6 3d 10 3p 6 4p 6 5s 2 4d 2 Electron Configuration

 Don’t have to write out the entire electron configuration.  There is a short-cut:  Keeps focus on valence electrons  An atom’s inner electrons are represented by the symbol for the nearest noble gas with a lower atomic number. K: [Ar]4s 1 Electron Configurations Electron Configuration

For the element Phosphorus electrons 1s 2 2s 2 2p 6 3s 2 3p 3 [Ne]P: Must be a Noble gas (One just before Element) Electron Configurations 3s 2 3p 3 Electron Configuration

Let’s do a couple more: Ba:[Xe] 6s 2 Hg:[Xe] V:[Ar] 4s 2 4f 14 5d 10 3d 3 Electron Configuration

Exceptions to the order of filling

Electron Configuration for Ions  For anions: add extra electrons  For cations: draw the neutral atom, then subtract the required number of electrons from the orbital with the highest principal quantum number “n”  Examples S 2-, Na +, Zn 2+

Ion Configurations P [Ne] 3s 2 3p 3 - 3e-  P 3+ [Ne] 3s 2 3p 0 To form cations from elements : remove 1 e- (or more) from subshell of highest n [or highest (n +  )].

Transition metals ions: remove ns electrons and then (n - 1)d electrons. E 4s ~ E 3d - exact energy of orbitals depend on whole configuration Fe [Ar] 4s 2 3d 6 loses 2 electrons  Fe 2+ [Ar] 4s 0 3d 6 Ion Configurations 2

 The chemistry of an atom occurs at the set of electrons called valence electrons  The valence electrons are electrons in an atom’s highest energy level.  For the Group – A elements, it is the outermost s & p e - of the atom.  Specifically the 2 s electrons + 6 p electrons (octet electrons)  The arrangement of the valence e - lead to the element’s properties. And this leads to… properties

Mendeleev’s Periodic Table Dmitri Mendeleev

Modern Russian Table

Stowe Periodic Table

A Spiral Periodic Table

“Mayan” Periodic Table

The Periodic Table Period Group or Family