The Quantum Model

Energy as wave and particle

Bohr Model

Electrons are a HUGE deal in chemistry

Responsible for chem rxns

Today: How many are there Where do they reside

Periodic Table

Electron Configurations Electron configurations are...

Electron Configuration Vocab Principle Energy Level

correlates to the period (1-7), periods go from left to right across the periodic table

Sublevel are located in the principle energy level. There are 4 that we

will talk about s, p, d and f.

Orbital located in the sublevel. Where electrons are most likely to be

found 1 ORBITAL HOLDS 2 ELECTRONS

Writing Electron Configurations Principle Energy Level[sublevel]number of electrons

OR a[b]c

Get your periodic table! Start from left to right!

Orbital Diagrams Tool for creating electron

configurations

2 dimensional representation of where electrons are in an atom

Aufbau Principle electrons are added to the lowest available

energy level. Hydrogen as an example:

Pauli Exclusion Principle each orbital can hold two electrons those electrons must have opposite spins

spin is represented by the arrow facing up or down.

Hund’s Rule Orbitals of equal energy are occupied by one

electron before 2 electrons occupy 1 orbital. The second electron is added after all orbitals have one electron

Aufbau Diagram

Noble Gas Configuration – Short cut Locate the element on the PT

Trace backward to the nearest noble gas

Put that noble gas in [] (brackets)

Fill in remaining electrons

Principle Quantum Numbers Quantum numbers define the characteristics of a

particular electron.

Work as an address for the electron

electrons repel each other, no two electrons can have the same address. Pauli Exclusion principle

Quantum Numbers – electron Address State

City

Street

Number of

your home

n - principle energy level

1, 2, 3, 4 . . .

l – sublevel

“shape” of the region of space (s, p, d, f)

m - orbital orientation

axes of the magnetic moment.

s – spin

Can be +1/2 or –1/2 for electrons

Valence Electrons Electrons in the HIGHEST energy level (n)

Electrons that interact during chem rxns

Always in the s & p sublevels

Finding Valence Electrons Locate the highest

energy level Count the electrons

present Orbital diagrams

SUPER helpful

Example: Sulfur How many valence e’s?

Shapes of s orbitals

s orbital

s orbitals

Shapes p orbitals

Nodal plane

P orbitals in more detail p sublevel

3 orbitals x, y & z

Work like a coordinate plane Atoms are 3-D

Shapes of d orbitals

Heisenberg Uncertainty Principle An electron’s location and speed cannot be

determined at the same time. If we cause change to find one variable, we are no

longer looking at the actual e- situation. If we need to slow or stop it to locate it or if we need to

locate it to find its speed, then we allow the chance of change.

So quantum mechanics can tell us the probability that an electron is somewhere, but it does not tell us how it got there.

Nodal Surfaces A nodal surface is a region that defines the border of an

orbital. This is where the probability function equals zero. Electrons CAN NOT exist in this area.

Nodal surfaces are spherical for the “s” orbitals.

3s orbital

Nodal surfaces are NOT spherical for other orbitals.

2p orbital

The Electromagnetic Spectrum

What is light? Wave

Particle

Red Light

Violet Light

• Low frequency

• Long wavelength

• High frequency

•Short wavelength

Wave Comparisonnm = 1 x 10-9 m

Waves & Wavelength

How many wavelengths are represented in each figure below?

C=

It stands to reason that if energy is constant then (wavelength) is inversely proportional to (frequency).

OR

As wavelength increases frequency decreases

Max Planck• Max Planck mathematically determined “h” that could

be multiplied by to solve for energy (E) every time an electron gave off light as it fell. (This simply means that all wavelengths are proportional)

E = h

• Thus E will tell us the relative distance apart of each energy level in a given atom based upon the spectral lines.

C= Remember that Einstein told us that matter and energy

are the same thing. Matter is simply frozen energy.

From Einstein we were able to come up with several more equations to understand quantum mechanics.

C= = wavelength

Ex: yellow orange = 580 nanometers So as in the lab, using a spectroscope we can determine

the wavelength of the color of light (). We can solve for frequency () mathematically.

De Broglie De Broglie argued that as particles (i.e.electrons) drop back to

lower energies, photons of energy are given off in “packets” or specific amounts called quanta. His doctoral board scoffed and was ready to deny his degree but changed their minds when Einstein supported him fully.

His model changed the Bohr model so that all elements could be explained according to their frequencies of energy.

Remember that energy is constant and that standing waves are quantized as well (they only increase by multiples of ½)

De Broglie

Essentially the model went from

Bohr

to

de Broglie

Spectra With the de Broglie

Model, it became possible to explain the spectral lines of all models.

Each wavelength would allow electrons to fall back to lower energy levels emitting various energies which translate to

frequencies thus defining a wavelength

Hydrogen Emission Spectrum

Some Atomic Emission Spectra Hydrogen

Mercury

Argon

Helium

de Broglie and Wave Model An electron in its path

is associated with a wavelength.

The wavelength depends on the mass:

Example ProblemWhat is the characteristic wavelength of an electron with a velocity of 5.97 x 106 m/s? (Use 9.11 x 10-31 kg for the mass of an e-)

Bright-line Spectra Atoms are quantized, existing only in definite energy

states so an atom absorbs a specific quanta of energy pushing electrons to higher energy levels. An “EXCITED” electron jumps from its ground state to a higher energy level. The energy cannot be maintained so it falls back to where it came from losing exactly the same amount of energy that it absorbed.

Energy of Electrons We can calculate the energy the electrons of a hydrogen atom emit

when they fall by using the Balmer equation

So if an electron falls from the 6th energy level to the 2nd energy level then –

Note: energy levels are not actually distances between electrons and the nucleus.

22

121

n

kEn = 3,4,5 . . .

k = constant = 2.179x10-18

36

810179.2

36

1

36

910179.2

36

1

4

110179.2

6

1

2

110179.2

1818

1822

18E

Excited atoms

Schrodinger applied idea of e- behaving as Schrodinger applied idea of e- behaving as a wave to the problem of electrons in a wave to the problem of electrons in atoms.atoms.

He developed the He developed the WAVE EQUATIONWAVE EQUATION

Solution gives set of math expressions Solution gives set of math expressions called called WAVE FUNCTIONS, WAVE FUNCTIONS,

Each describes an allowed energy state of Each describes an allowed energy state of an e-an e-

E. SchrodingerE. Schrodinger1887-19611887-1961

Quantum or Wave MechanicsQuantum or Wave MechanicsQuantum or Wave MechanicsQuantum or Wave Mechanics

Waves: standing, travellingQ1 - A standing wave is the combination of

two waves (travelling in opposite directions). It has nodes, where a portion of the wave remains stationary (spring demonstration)

Notice that a standing wave (which is what an electron is) can only have certain wavelengths

(0.5, 1, etc.) because the ends are fixed as nodes

W = 0.5

W = 1

W = 1.5

W = 2