Quantum Mechanical Model•Certain properties of matter can only be explained using a wave model.

Example - diffraction of electrons (electron microscope)

•In 1924, Louis de Broglie developed an equation that predicts that all moving objects have wave-like behavior.

•These wave properties are significant when particles are extremely small (such as electrons).

•Like light, electrons exhibit a dual wave-particle nature.

•Quantum mechanics describes the motions of subatomic particles and atoms as waves.

•Later, Werner Heisenberg concluded that it is impossible to know exactly both the velocity and the position of an electron or any other particle at the same time. (Heisenberg uncertainty principle)

The Heisenberg Uncertainty Principle

• In 1926, Erwin Schrödinger devised a mathematical equation that treated electrons in atoms as waves.

• The modern description of the electrons in atoms, the quantum mechanical model, comes from the mathematical solutions to the Schrödinger equation.

• The quantum mechanical model determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus.

• These regions of space in which there is a high probability of finding an electron are known as orbitals or electron clouds.

• A fan blade has the same probability of being anywhere in the blurry region, but you cannot tell its location at any instant.

• The electron cloud of an atom can be compared to a spinning fan blade.

• In the quantum mechanical model, the probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloud. The cloud is more dense where the probability of finding the electron is high.

• The total number of orbitals that exist in a given energy level or shell is equal to the energy level number squared.

1st energy level = 1 orbital

2nd energy level = 4 oribitals

3rd energy level = 9 orbitals

4th energy level = 16 orbitals

• Orbitals can have different shapes.

• Number of different shapes in each energy level is equal to the energy level number.

– 1st energy level 1 shape– 2nd energy level 2 shapes– 3rd energy level 3 shapes– 4th energy level 4 shapes

• Different shaped orbitals occupy their own specific region within an energy level.

• These are known as sublevels.– 1st energy level 1 sublevel– 2nd energy level 2 sublevels– 3rd energy level 3 sublevels– 4th energy level 4 sublevels

• Letters are used to describe the shape of different orbitals.

• First energy level – only one type of orbital

• “s” orbital

• Spherical shaped orbital

• The first energy level composed of one sublevel – called the 1s sublevel.

• Second energy level – 2 types of orbitals

• s orbital– In what way is the s-orbital in the second energy similar to

the s-orbital in the first energy level?

– In what way is the s-orbital in the second energy different from the s-orbital in the first energy level?

• The second type of orbital is called a p-orbital.• p-orbitals look like dumbbells (two lobes)

– The second energy level composed of two

sublevels – 2s and the 2p.

• Third energy level – three shapes – three sublevels– s-orbital – sphere – p-orbital – “dumbell”– d-orbital – “four leaf clover” (four lobes)

– The third energy level composed of three sublevels – 3s, 3p, and the 3d.

• Fourth energy level – four shapes – four sublevels

– s-orbital – p-orbital– d-orbital– f-orbital – complex shape

– The fourth energy level composed of four sublevels – 4s, 4p, 4d, and the 4f.

One Minute Paper• You have one minute to answer these two

questions concerning today’s lesson.

– What was the most important thing you learned?

– What is still muddy?