From the Bohr Model to the Quantum

Mechanical ModelAdvanced Chemistry

Ms. Grobsky

Shortcomings of the Bohr Model

Bohr’s model was too simpleo Worked well with only hydrogen because H only has one

electrono Could only approximate spectra of other elements with

more than one electron Electrons do not move in circular orbits So there is more to the atomic puzzle…

de Broglie and the Dual Nature of Light

As a result of Planck’s and Einstein’s work, light was found to have certain characteristics of particulate mattero No longer purely wavelikeo Waveicle

But is the opposite also true? A physicist named de Broglie asked the question:

Does matter exhibit wave properties? The answer is Yes!

o As shown through X-ray diffraction patterns

Quantum Mechanical Model of the Atom

Things that are very small behave differently from things big enough to see

Come to find out, electrons bound to the nucleus are similar to standing waveso Standing waves do not propagate through spaceo Standing waves are fixed at both ends

• Think of a guitar or violin• A string is attached to both ends and vibrates to produce

a musical tone• Waves are “standing” because they are stationary – the

wave does not travel along the length of the string

Standing Wave Video

The Quantum Mechanical Model

Remember, energy is quantized (i.e. it comes in chunks)o Since the energy of an atom

is never “in between”, there must be a quantum leap in energy

Also, a physicist named Heisenberg stated that “[t]here is a fundamental limitation on how precisely we can know both the position and momentum of a particle at a given time”o It is impossible to know both

the velocity and location of an electron at the same time

The Quantum Mechanical Model

Erwin Schrodinger derived a mathematical equation that described the energy and position of electrons in an atom that became known as the “Quantum Mechanical Model”

An overview of the model:o Electrons are found in energy levels and ORBITALS

Atomic Orbitals Within each energy level, the complex math of

Schrodinger’s equation describes several shapeso These are called atomic orbitals

• Orbitals are NOT circular orbits for electrons• Orbitals ARE areas of probability for locating electrons

• Electron density maps (probability distribution) indicates the most probable distance from the nucleus• These DO NOT describe:

• How an electron arrived at its location• Where the electron will go next• When the electron will be in a particular location

• Orbitals of the same shape grow larger as number of energy levels increases• # of nodes (areas in which there is zero electron probability) increase as

well

Electron Density Maps??? WHAT?????

With a partner, complete page 204 - “Locating an ‘s’ Electron in an Atom by Analogy”o Be sure the marbles are caught after their first bounceo Be sure marbles are dropped from a consistent height

Change in procedure and data analysiso No carbon paper – you must mark each landing spot

with an “X” using a pencil!o Y-axis in graph is (# of dots/cm2)*10

Before you begin, do you expect each group to get the same pattern?

Do you expect a marble to land exactly in the middle?

Sample Marble Drop Probability

0 1 2 3 4 5 6 7 8 90

5

10

15

20

25

Maximum Radial Distance

Rad

ial D

istr

ibu

tion

(P

rob

-ab

ilit

y)

(Dots

/cm

2)*

10

So What do These Probability Distributions (Atomic Orbitals) Look

Like?

Atomic Orbitals Simulation

Follow along on page 205!Atomic Orbitals Java Applet

The s-Orbital

• Spherical shape• Single orbital• Seen in all energy levels• Can hold up to 2 electrons

The p-Orbital

p (z)

p (y)

p (x)

x-axis

y-axis

z-axis

• Dumbbell-shaped• Seen in 2nd energy level and above• Can hold up to 2 electrons PER SUBORBITAL (6 electrons

total)

The d-Orbital

• Five clover-shaped orbitals• Can hold up to 2 electrons per suborbital (10 electrons total)• Seen in 3rd energy level and above

The f-Orbital

• Seven equal energy orbitals• Each suborbital can hold up to 2 electrons (14 electrons total)• Shape is not well-defined• Seen in 4th energy level and above

Summary of Atomic Orbital Shapes

Arrangement of Atomic Orbitals

The orbitals of an atom are LAYERED!