Quantum Mechanics & Electron Configuration Chapter 5: Electrons in Atoms

Part 1: Models of the Atom 1897: Thompson Model (Plum Pudding) 1911: Rutherford Model – Small, dense, + charged nucleus Electrons orbit around 1913: Bohr Model 1926: Quantum Mechanical Model – Erwin Schrodinger & his math equations

Bohr Model (aka the versions you’ve learned before)  Electrons move around the nucleus in fixed spherical orbits with fixed energies  Fixed energies = orbits / energy levels  Aka rungs of a ladder  Electrons can go to a higher or lower energy level  Either gain or lose energy to move levels  Electrons CANNOT be between levels

Atomic Emission Spectra ** When atoms absorb energy (i.e. electric current), they move to a higher energy level … … these electrons emit light when they return back to a lower energy level  Emission spectra is unique for each element - The light emitted consists of only a mixture to specific frequencies…  If you pass the light through a slit and then a prism, you can separate the resulting light into its frequencies (aka colors) Barium

Light  Has properties of both:  a Particle ( ____________)  a Wave Light Waves: Amplitude: crest of the wave (height from 0) Wavelength: distance between crests (λ) Frequency: # of waves per unit time (ν) Units: Hertz (Hz) aka s -1

Math Time!!! c = λν C = speed of light (constant) = x 10 8 m/s λ = Wavelength (m) ν = Frequency (Hz or s -1 )

More Math…  The energy (E) of a photon is directly proportional to its frequency. Higher freq = More Energy Lower Freq = Less Energy E = h x v E = energy (joules – J) H = Plank’s constant = 6.626E-34 Js v = Frequency (Hz or s -1 )

Example: What is the energy of a quantum of light with a frequency of 7.39 x Hz?

Think about this…  E = h x v  c = λν What would you do if you were asked to solve for the frequency of light if you are given a wavelength of 700nm?

Emission Spectra Lab Look at the gas tubes and follow directions provided.

Continuous Spectrum v. Line Spectrum  What did you observe in the Emission Lab?

Light has Wave-Particle Duality (& so do electrons)  Particle & Wave-like Nature  Depends on experiment / what we try to observe  Throws a wrench in Bohr Model…  New method of describing the motion of subatomic particles = foundation of quantum mechanics = movement/organization of subatomic particles

The Quantum Mechanical Model  This is what we use today  Describes: LOCATION & ENERGY of electrons  Electrons do not have a direct orbit around nucleus  Based on probability  Electron clouds  Electrons do have energy levels

Hog Hilton Sample Problem  Book 15 hogs into their rooms  6 th floor ____ ____ ____ _____ _____  6 th floor ______  5 th floor ______ ______ ______  4 th floor ______  3 rd floor ______ ______ ______  2 nd floor ______  1 st floor ______

Hog Hilton Sample Problem Place 15 electrons into their spaces  3d_____ _____ _____ _____ ____  4s _____  3p ______ ______ ______  3s ______  2p ______ ______ ______  2s ______  1s ______

But…all of these electrons are not organized into hotel rooms, but ATOMIC ORBITALS

So, what exactly is an ATOMIC ORBITAL ? Atomic Orbital = region of space in which there is a high probability of finding an electron  They come in different SHAPES, SIZES & ENERGY LEVELS!!  These are described by Quantum Numbers…

Part 2 Quantum Numbers Get ready…here we go…

Quantum Numbers Used to describe the location of electrons Electrons in an atom CANNOT have the same quantum numbers  Unique for each electron  Like an address

Principle Quantum Number (think…Energy Level)  n  Allowable values = 1, 2, 3 … n ( positive, integer values )  Describes energy level  Position of the electron w/ respect to nucleus  As n increases = further from nucleus

Angular Momentum Quantum Number (Azimuthal Quantum Number) (think…energy sublevel) Pay attention…this is where it starts to get complicated  l  Allowed values: 0, 1, 2, … (n-1)  Describes the sublevel  SHAPE of the orbital  SHAPES:  l = 0 = s orbital = spherical cloud  l = 1 = p orbital = dumbbell cloud  l = 2 = d orbital = clover cloud  l = 3 = f orbital = … too complicated

Example  If I had a principal quantum number of 2, what are my possible angular momentum quantum numbers? n = 2 l =

Angular Momentum Quantum Number: Orbital Shapes

Magnetic Quantum Number (m l )  Determines spatial orientation (x, y, z, plane)  Possible Values: - l to + l  Examples: if it is a d orbital d orbital: l = m l =

Example: p-orbital n = 2 l = m l = This means, there are _______ p-orbitals and that they are in three directions (x, y, z axes):

What orbital corresponds to : n = 2 l = 1 m l = 0 Energy level = Sublevel = _____ - orbital Orientation: Orbital:

 Number of orbitals within an energy level: n 2 Examples: How many orbitals are in energy level 2? n = l = m l = Orbitals =  Each orbital holds 2 electrons: So, how many electrons can energy level 2 hold? # Electrons = 2n 2

Spin Quantum Number  m s  Describes the direction of the electrons spin within an orbital (remember, each orbital only holds 2 electrons)  Possible Values: ½ or -½ (spin up, spin down)  Think back to hogs…

Ahhh…it’s too much information…HELP!!!  Solution: STUDY and PRACTICE!!! Quantum #SymbolPossible ValuesDescription Principle Quantum Number n1, 2, 3, etcEnergy level Angular Momentum Quantum Number l0 … n-1Sublevel & shape Magnetic Quantum Number mlml -l … +lSpatial Orientation of orbital (x,y,z) Spin Quantum Number msms +½ or -½Direction of Spin

Examples 1. n = 3 (what are the possible quantum numbers?) 2. What orbital corresponds to n = 4 & l = 2?

 What orbital corresponds to n = 4, l = 1, m l = -1 Energy Level = Sublevel = Orbital orientation = Orbital =

Re-iterate: OrbitalHow Many Types of Orbitals (orientations) How Many Electrons in Shape s1 p3 d5 f7

Principle Quantum Number (n) Angular Momentum Quantum Number (sublevels) (l) Shapes of Sublevels # electrons (2n 2 )

Principle Quantum Number (n) Angular Momentum Quantum Number (sublevels) (l) Shapes of Sublevels# electrons (2n 2 ) 10s2 20, 1s p8 30, 1, 2s p d18 40, 1, 2, 3s p d f32 50, 1, 2, 3, 4s p d f (g)50 60, 1, 2, 3, 4, 5s p d f (g h)72 70, 1, 2, 3, 4, 5, 6s p d f (g h i)98

STOP Do You Have Any Questions?

PART 3 Rules of Electron Configuration

Aufbau Principle  Electrons enter orbitals of lowest energy first  Orbitals within a sublevel have equal energy (3px, 3py, 3pz)  Exceptions: Cr, Cu  Which hog rules is this?

Pauli Exclusion Principle  An atomic orbital may only hold two electrons  Electrons must have opposite spin  Clockwise or counterclockwise spin  Denoted with arrows  Prevents two electrons from having same quantum numbers  Which hog rule is this?

Hund’s Rule  Every orbital of the same energy is singly occupied before any orbital is doubly occupied  Electrons have the same spin  Second electrons added have opposite spins  Which hog rule is this?

PART 4 Writing Electron Configurations

Electron Configuration Diagonal Rule  Starting with the top arrow, follow the arrows one by one in the direction they point, listing the sublevels as you pass through them.  Stop when you get to the sublevel you need.

Electron Orbital Diagram 3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 1s ___

Example: Fill Orbitals w/ 7 electrons 3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 1s ___

Review: 1. How many electrons fill an s orbital? 2. How many electrons fill a p orbital ?(remember subshells…) 3. How many electrons fill a d orbital? 4. How many electrons fill an f orbital?

Example: Cl 3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 1s ___ Give the final E.C:

With a partner: Examples: Give the E.C  H  He  Li  Be  B  C  N  F

No more…Make it  Write the electron configuration for Barium:  Ahhhhhhhhhh!!! Too many electrons!!  But wait…there’s a shortcut…  Noble gas / shorthand configuration:  Find the nearest noble gas that came before the element you are interested in  Write the symbol of that noble gas in [brackets]  Write the configuration as normal from there…

Examples: Sb

Stop & Practice  E.C. Worksheet

All Together Now…  Mendeleev didn’t know quantum numbers  BUT…our periodic table is related to HOW electrons fill the levels in the different shells  Blocks  s block  Groups 1 & 2  p Block  Groups 3 – 8  d block  Transition Elements  f Block  Rare earth metals

It ends w/…

Another Example: Ba (shorthand)

Stop & Practice  Patterns in Electron Configuration Worksheet

Columns  Elements have similar properties  Why?  Similar ground state electron configurations  Examples  Noble gases  Complete sublevel  Favorable - do not react  Halogens  One electron short of completely filled sublevel  Readily react with elements who have a single electron