Quantum Mechanics

Unit 3, Part 2Quantum Mechanics

Chemistry Notes

Light & Wave Motion

• Waves carry energy from 1 place to another

• Light = Electromagnetic Radiation

–carries energy through space

–Behaves as a wave or as a stream of particles of energy

(wave-particle nature of light)

A Typical Wave

http://www.pas.rochester.edu/~afrank/A105/LectureV/FG03_003_PCT.gif

Wave Descriptions

• Wavelength: distance from crest to crest (or trough to trough); unit = m

• Wave speed: how fast the wave travels over time; unit = m/s

• Frequency: the # of waves that pass an area in a given amount of time; unit = 1/s = Hz

The Nature of Light

• The Photon – a bundle of a specific amount of electromagnetic energy

–Generally considered particle-like but also demonstrates wave-like properties

The Electromagnetic Spectrum

Gamma (shortest)

X-ray

Ultraviolet/UV

Visible

Infrared/IR

Microwave

Radio (longest)

The Electromagnetic Spectrum

http://www.yorku.ca/eye/spectrum.gif

Looking At Wavelength

Frequency

Short Wavelength

High Frequency

Energy

Short Wavelength

High Energy

Or

High Amplitude

High Energy

http://www2.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l2a2.gif

Visible Light Spectrum

Red

Orange

Yellow

Green

Blue

IndigoViolet http://cache.eb.com/eb/image?

id=73584&rendTypeId=35

Long Short

Absorption & Emission Spectra

Absorption

something is being “taken in”

Emission

something is being “given off”

--Atoms will release energy as photons of light; the energy of the photons corresponds to the energy changes experienced by the atom


The “fingerprint” of an element; unique Absorption – when an atom absorbs

energy; electrons jump to higher energy levels; dark line spectra

Emission – when an atom releases photons of energy; electrons return to lower energy levels; bright line spectra


http://www.astro.columbia.edu/~archung/labs/fall2001/images/spectrum_line.gif

Hydrogen Atom Example

Notice the spectral lines in the same positions? These represent specific energy level changes of the electrons in the atom.

http://www.solarobserving.com/pics/hydrogen-spectra.jpg

Dark Line

Bright Line

The Bohr Model

http://library.thinkquest.org/19662/images/eng/pages/model-bohr-2.jpg

Light Energy Released

Light Energy Taken In

Bohr Model of Atom

• Small nucleus with e- orbiting like planets around the sun

• Electrons occupy specific energy levels (orbits)

• Currently, atomic models suggest that e- occupy 3D regions called orbitals within an electron cloud

Ground State vs. Excited State

http://imagine.gsfc.nasa.gov/docs/teachers/lessons/xray_spectra/images/emit.gif

http://content.answers.com/main/content/wp/en/thumb/c/c4/180px-Energylevels.png

Ground State = lowest energy level

Excited State = a higher energy level

Higher energy levels are closer together…

Energy Levels Are Quantized

1. Atom absorbs energy, electrons jump from ground state to higher energy level

2. Electrons return to ground state, atom gives off photon of energy

The photon is quantized = carries a specific amount of energy that depends on the size of the “jump” from 1 energy level to the next

Chemical Behavior of Atom

• Determined by electron structure

• How the electrons are arranged determines how they will behave in a reaction

Locating Electrons in an Atom

• Impossible to predict the exact location

• The most probable location is described as the orbital within electron cloud

• Describe the locations of electrons (or its address) as the electron configuration

The Electron Configuration

• Pauli Exclusion Principle

–No 2 electrons can have the same electron figuration

–No 2 electrons can occupy the same location at the same time

–Remember - electrons are always moving!

Electrons & Energy Levels

• Energy levels are quantized = specific amounts of energy

• Energy levels are called the principle energy levels

• Each principle energy level can be divided into specific sublevels

The Hydrogen Example

• Atomic Number = 1

–1 proton

–1 electron

• Hydrogen has only 1 electron but more than 1 orbital. The electron can only occupy one orbital at a time.

Quantum Numbers

• 4 quantum numbers make up the electron configuration–(n) = principle energy level

–(l) = energy sublevel

–(m) = actual orbital

–(s) = spin

Quantum Number Analogy

• Hospital Complex Analogy–(n) = building

–(l) = floor

–(m) = room

–(s) = bed

(assuming 2 beds per room)

Electron Configurations Written

• Example = 2p3

2 = principle energy level

p = sublevel

3 = # of electrons in sublevel

Quantum Number (n)

• Principle energy level

• n = 1, 2, 3, 4, 5, 6, or 7

• n = corresponds to the row (period) on the periodic table

• As n increases, energy increases

• n refers to orbital size; as n increases, the orbital size increases

• 1 = close to nucleus, 7 = far away

Quantum Number (l)

• Energy sublevel

• Not all e- in an energy level have the exact energy

• l= s, p, d, or f

• Sublevels may overlap

• A filled sublevel is spherical in shape

• Orbital shapes can be complex

Quantum Number (m)

• The actual orbital of the electron

• Each orbital holds 2 electrons

• s sublevel – 1 orbital, spherical shape

• p sublevel – 3 orbitals, dumbell shape

• d sublevel – 5 orbitals, weird shape

• f sublevel – 7 orbitals, complex shape

Orbital Shapes

http://lincoln.pps.k12.or.us/lscheffler/OrbitalShapesOverheads_files/image002.jpg

Quantum Number (s)

• Spin of the electron

• Clockwise (+½) or Counterclockwise (-½)

• Electrons in the same orbital have opposite spins

3d ___ ___ ___ ___ ___

4s ___

3p ___ ___ ___

Principle Energy Level (n)

Energy Sublevel (l)

Orbital (m) holds 2 electrons total

Example Orbital Diagrams

1s 1s2s 1s2s2p

http://www.uwgb.edu/dutchs/PETROLGY/WhatElmsLookLike.HTM

Electron Configuration Guidelines

• Elec. configuration lists ALL e- in the atom, giving the principle energy level, sublevel, and e- per sublevel

• An atom is neutral: the # of protons equals the # of electrons, described by the atomic number

• The period (row) describes the number of energy levels present


• 2n2 = the maximum number of electrons in an energy level

–n = the energy level

n = 1, then 2 electrons




• The nth energy level has n sublevels present

–n = 1, then 1 sublevel

–n – 2, then 2 sublevels• Any element is “put into” the energy

level (period) of its highest energy level electrons, even if these electrons are not filled in last


• Lower energy levels fill in first; then higher energy electrons are filled in

• Hund’s Rule: in any sublevel, one electron is placed in each orbital before pairing begins– Some exceptions (discussed later)

• Degenerate: orbitals have the same energy & appear at same “level” on an orbital filling diagram


Place one electron in each

orbital before pairing!

Degenerate Orbitals: All 3 have the same energy and appear at the same level

Hund’s Rule


• Order of Orbital Filling

You will use the Periodic Table to help remember this!

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d…

Orbital Filling Clues

http://pegasus.cc.ucf.edu/~jparadis/chem2045/chapter06.html


Reminder!

Each Orbital Holds 2 Electrons

s 1 orbital 2 electrons

p 3 orbitals 6 electrons

d 5 orbitals 10 electrons

f 7 orbitals 14 electrons

Orbital Filling Diagrams

• See notes packet for diagram template

• Aufbau Principle (to build up)–Electrons fill lowest energy states

first–If multiple orbitals, electrons fill all

unoccupied orbitals first before pairing electrons with opposite spins (Hund’s Rule)

Exceptions You Need to Know

• Copper (Cu) & Chromium (Cr)–Electrons are found in unexpected

places; there is extra stability in having half-filled d orbitals

–The completion of a d sublevel is desired, so an electron will fill the d sublevel before the next s

–1 electron in each d5

Technology

Quantum Mechanics