Unit 3

The Quantum

Model

The Quantum Mechanical Model

• Erwin Schrodinger (1887-1961) In 1926 Schrodenger proposed our modern model for the atom, the quantum

mechanical model, which

is based mathematical

calculations.

The Quantum Mechanical Model

• Like the Bohr model, electrons are restricted to certain energy levels.

• Unlike the Bohr model, electrons do NOT have to take an exact path around the nucleus.

The Quantum Mechanical Model

The importance of the quantum mechanical model is that it determines:

1. allowed energies an electron can have

2. how likely it is to find the electron in a particular location

The Quantum Mechanical Model

-We cannot know both the location and velocity of an electron (Heisenberg’s uncertainty principle), thus Schrodinger’s equation does not tell us the exact location of the electron, rather it describes the probability that an electron will be at a certain location in the atom.

The Quantum Mechanical Model

• Because it behaves as a particle, a baseball follows a well-defined path as it travels from the pitcher to the catcher. Because of their wave nature, an electron's path cannot be precisely known. The best we can do is to calculate the probability of the electron following a specific path.

• If the baseball displayed wave-particle duality, the path of the baseball could not be precisely determined. The best we could do would be to make a probability map of where a "pitched" electron will cross home plate.

The Quantum Mechanical Model

• Today we say that the electrons are located in a region outside the nucleus called the electron cloud.

The nucleus is not a little “planet”- rather the way we look at atoms is now like a probability map. Where the cloud makes up regions where electrons may be found.

A. Quantum

• To move from one energy level to another, an electron must gain or lose just the right amount of energy.

• The exact amount of energy required to move from one energy level to another is called a quantum of energy.

IV. Quantum Mechanics Model of the Atom and Quantum

Numbers

• Unlike the rungs of a ladder, the energy levels in an atom are NOT equally spaced. In fact, the energy levels become more closely spaced the farther they are from the nucleus.

B. Photon

• An electron falling from a higher energy level to a lower energy level gives off an exact amount of light (called a photon).

A. Energy Levels

• energy levels (represented by the letter n; also called the principal quantum number) are assigned values in order of increasing energy: n=1,2,3,4, and so forth.

• Which energy level is furthest away from the nucleus and has electrons with the highest energy - 1,2,3, or 4? _______4

B. Sublevels

• Within each energy level, the electrons are located in various sublevels – there are 4 different sublevels s, p, d, and f.

• s, p, d, and f describe the shapes of the orbitals.)

Remember we’re talking about what the probability map looks like!

C. Orbitals• Orbitals are regions of the electron cloud.

• Each orbital can only hold 2 electrons at a time.

• For example, within the s sublevel there is 1 orbital (which is spherical); it is called the s orbital.

Each s ortibal holds 2 electrons

1 orbital - 2 electrons

Within the p sublevel there are 3 orbitals (which are dumbbell shaped)

called the p orbitals.

3 orbitals – 6 total electrons

Within the d sublevel there are 5 orbitals (4 of which are

clover leaf shaped)

called the d orbitals.

5 orbitals -10 total electrons

Within the f sublevel there are 7 orbitals (that are flower-shaped)

called the f orbitals.

7 orbitals - 14 total electrons

The electron cloud

http://www.youtube.com/watch?v=K-jNgq16jEY

Sublevel Number of orbitals this

sublevel contains

Shape of orbitals

Total number of electron this sublevel can

hold

s

p

d

f

Electron Arrangement in Atoms

• Electron Configurations: the way in which electrons are arranged in various orbitals around the nucleus of the atom

Three rules of electron configurations

1. Aufbau Principle – electrons fill in order from lowest to highest energy.

2. The Pauli exclusion principle

– An orbital can only hold a maximum of two electrons. Two electrons in the same orbital must have opposite spins.

Three rules of electron configurations

3. Hund’s rule – the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons for a set of degenerate orbitals. By convention, all unpaired electrons are represented as having parallel spins with spin “up”.

Three rules of electron configurations

1. Orbital NotationExample: Hydrogen ____ Helium _ Lithium ___ ___

1s 1s 1s 2s

We Do: Potassium

You Do: Silicon

Remember to fill each orbital in the correct order

2. Electron Configuration Notation

The number of electrons in a sublevel is shown by adding a superscript to the sublevel designation. The superscript indicates the number of electrons present in that sublevel.

• Example:

We Do: Cobalt___________________________

You Do: Arsenic__________________________

3. Noble Gas Notation (Shorthand Notation)In order to write less, a noble gas can stand for

that element’s number of electrons

Example: Sodium [Ne] 3s1

The [Ne] stands for the first 10 electrons

because neon has 10 electrons 10 + 1 = 11 electrons

We Do: Cobalt ________________________

You Do: Arsenic _______________________

Elements in the same block of the periodic table have their final

electrons in the same sublevel.