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. 1

Like light, electrons exhibit a dual wave-particle nature. 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) 2

The Heisenberg Uncertainty Principle The Heisenberg uncertainty principle states that it is impossible to know exactly both the velocity and the position of a particle at the same time. 3

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.

The electron cloud of an atom can be compared to a spinning fan blade. 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. The electron cloud of an atom is compared here to photographs of a spinning airplane propeller. a) The airplane propeller is somewhere in the blurry region it produces in this picture, but the picture does not tell you its exact position at any instant. b) Similarly, the electron cloud of an atom represents the locations where an electron is likely to be found.

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 electron cloud of an atom is compared here to photographs of a spinning airplane propeller. a) The airplane propeller is somewhere in the blurry region it produces in this picture, but the picture does not tell you its exact position at any instant. b) Similarly, the electron cloud of an atom represents the locations where an electron is likely to be found.

1st energy level = 1 orbital 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? 14