Quantum Mechanics

Quantum Mechanics • Better than any previous model, quantum mechanics does explain how the atom behaves. • Quantum mechanics treats electrons not as particles, but more as waves (like light waves) which can gain or lose energy. • But they can’t gain or lose just any amount of energy. They gain or lose a “quantum” of energy. A quantum is just an amount of energy that the electron needs to gain (or lose) to move to the next energy level. In this case it is losing the energy and dropping a level.

Atomic Orbitals • Much like the Bohr model, the energy levels in quantum mechanics describe locations where you are likely to find an electron. • Remember that orbitals are “geometric shapes” around the nucleus where electrons are found. • Quantum mechanics calculates the probabilities where you are “likely” to find electrons.

Atomic Orbitals • Of course, you could find an electron anywhere if you looked hard enough. • So scientists agreed to limit these calculations to locations where there was at least a 90% chance of finding an electron. • Think of orbitals as sort of a "border” for spaces around the nucleus inside which electrons are allowed. No more than 2 electrons can ever be in 1 orbital. The orbital just defines an “area” where you can find an electron. • What is the chance of finding an electron in the nucleus? Yes, of course, it’s zero. There aren’t any electrons in the nucleus.

Energy Levels • Quantum mechanics has a principal quantum number. It is represented by a little n. It represents the “energy level” similar to Bohr’s model. • n=1 describes the first energy level • n=2 describes the second energy level • Etc. • Each energy level represents a period or row on the periodic table. It’s amazing how all this stuff just “fits” together. Red n = 1 Orange n = 2 Yellow n = 3 Green n = 4 Blue n = 5 Indigo n = 6 Violet n = 7

Sub-levels = Specific Atomic Orbitals • Each energy level has 1 or more “sub-levels” which describe the specific “atomic orbitals” for that level. • n = 1 has 1 sub-level (the “s” orbital) • n = 2 has 2 sub-levels (“s” and “p”) • n = 3 has 3 sub-levels (“s”, “p” and “d”) • n = 4 has 4 sub-levels (“s”, “p”, “d” and “f”) • There are 4 types of atomic orbitals: • s, p, d and f • Each of these sub-levels represent the blocks on the periodic table. Blue = s block Yellow = p block Red = d block Green = f block

Orbitals d p • In the s block, electrons are going into s orbitals. • In the p block, the s orbitals are full. New electrons are going into the p orbitals. • In the d block, the s and p orbitals are full. New electrons are going into the d orbitals. • What about the f block? s

Objective C • Complete the chart in your notes as we discuss this. • The first level (n=1) has an s orbital. It has only 1. There are no other orbitals in the first energy level. • We call this orbital the 1s orbital.

Electron Configurations • What do I mean by “electron configuration?” • The electron configuration is the specific way in which the atomic orbitals are filled. • Think of it as being similar to your address. The electron configuration tells me where all the electrons “live.”

Rules for Electron Configurations • In order to write an electron configuration, we need to know the RULES. • 3 rules govern electron configurations. • Aufbau Principle • Pauli Exclusion Principle • Hund’s Rule • Using the orbital filling diagram at the right will help you figure out HOW to write them • Start with the 1s orbital. Fill each orbital completely and then go to the next one, until all of the elements have been acounted for.

Fill Lower Energy Orbitals FIRST Each line represents an orbital. 1 (s), 3 (p), 5 (d), 7 (f) • The Aufbau Principle states that electrons enter the lowest energy orbitals first. • The lower the principal quantum number (n) the lower the energy. • Within an energy level, s orbitals are the lowest energy, followed by p, d and then f. f orbitals are the highest energy for that level. High Energy Low Energy

No more than 2 Electrons in Any Orbital…ever. • The next rule is the Pauli Exclusion Principal. • The Pauli Exclusion Principle states that an atomic orbital may have up to 2 electrons and then it is full. • The spins have to be paired. • We usually represent this with an up arrow and a down arrow. • Since there is only 1 s orbital per energy level, only 2 electrons fill that orbital. Wolfgang Pauli, yet another German Nobel Prize winner Quantum numbers describe an electrons position, and no 2 electrons can have the exact same quantum numbers. Because of that, electrons must have opposite spins from each other in order to “share” the same orbital.

Hund’s Rule • Hund’s Rule states that when you get to degenerate orbitals, you fill them all half way first, and then you start pairing up the electrons. • What are degenerate orbitals? • Degenerate means they have the same energy. • So, the 3 p orbitals on each level are degenerate, because they all have the same energy. • Similarly, the d and f orbitals are degenerate too. Don’t pair up the 2p electrons until all 3 orbitals are half full.

Objective D • NOW that we know the rules, we can try to write some electron configurations. • Remember to use your orbital filling guide to determine WHICH orbital comes next. • Lets write some electron configurations for the first few elements, and let’s start with hydrogen.

Electron Configurations Note that all the numbers in the electron configuration add up to the atomic number for that element. Ex: for Ne (Z=10), 2+2+6 = 10

Objective D • One last thing. Look at the previous slide and look at just hydrogen, lithium, sodium and potassium. • Notice their electron configurations. Do you see any similarities? • Since H and Li and Na and K are all in Group 1A, they all have a similar ending. (s1)

Electron Configurations • This similar configuration causes them to behave the same chemically. • It’s for that reason they are in the same family or group on the periodic table. • Each group will have the same ending configuration, in this case something that ends in s1.

The End

Quantum Mechanics