Atomic Orbitals

Weirdness: de Broglie’s Equation• De Broglie’s equation

predicts the wavelength (λ) of an electron of mass m that has a velocity v, where h is Planck’s Constant (6.626 x 10^-34 Js)

• What does this mean? It means that ANY moving object is described by, and acts as a wave.

• For everyday objects, the wavelengths are just too small to notice!!!

Heisenberg's Insight• Heisenberg added to

Schrödinger's insights by realizing that, by measuring the location of a small particle such as an electron, we necessarily affect its location and velocity.

• This means we can never know exactly where or how fast a small particle is moving.

• It’s like measuring the location and velocity of a moving car by smashing another car into it. It changes things!!!

Imagine that you're blind and over time you've developed a technique for determining how far away an object is by throwing a medicine ball at it. If you throw your medicine ball at a nearby stool, the ball will return quickly, and you'll know that it's close. If you throw the ball at something across the street from you, it'll take longer to return, and you'll know that the object is far away.

The problem is that when you throw a ball -- especially a heavy one like a medicine ball -- at something like a stool, the ball will knock the stool across the room and may even have enough momentum to bounce back. You can say where the stool was, but not where it is now. What's more, you could calculate the velocity of the stool after you hit it with the ball, but you have no idea what its velocity was before you hit it.

This is the problem revealed by Heisenberg's Uncertainty Principle. To know the velocity of a quark we must measure it, and to measure it, we are forced to affect it. The same goes for observing an object's position. Uncertainty about an object's position and velocity makes it difficult for a physicist to determine much about the object.

• -http://science.howstuffworks.com/innovation/science-questions/quantum-suicide2.htm

…And Schrödinger's Wave Equation

• Schrödinger put it all together and created the equation that tells us the probability of finding an electron in a certain space…because that is all we can accurately measure.

So what does all this mean?

• It means that when we talk about the structure of an atom, we talk about orbitals and probabilities…And we have a set of symbols that represent all of these characteristics of the electrons in an atom. They are called the quantum numbers.

The Quantum Mechanical Model of the Atom

• Bohr’s “orbit” or “running track” model of the atom only works for hydrogen, so it’s mostly wrong.

• Electron orbits are like waves on a string. – (This is super weird!)

There are 4 quantum numbers:

• n, l, ml, ms

– n = size/energy– l = shape– ml = orientation

• (up, down, forward, diagonal, etc. )

– ms = spin (up or down)

n = principle energy level

• n = the size and energy of the orbital– Like the floor of a

building– Higher numbers are

bigger and higher in energy.

– n = 1,2,3,4,5,6,7

l = sublevel

• l = shape• l = s, p, d, f

– s = 2 electrons– p = 6 electrons– d = 10 electrons– f= 14 electrons

• Sublevels are like wings on a floor in a building

• l = n-1– 0, 1, 2,…n-1

ml = magnetic quantum #

• Gives orientation in space– Up/down, front/back,

left/right, diagonal, etc.

• ml = -l to +l

Ms = e- spin

• ms = electron “spin”• +1/2 or -1/2 only

Electron Configuration

• An electron configuration is a list of the orbitals occupied by electrons in an element.

• It gives you all of the quantum numbers, and each electron has its own unique set of 4 numbers

Rules, rules, rules…

• There are 3 rules you need to remember in writing an electron configuration:

– Aufbau Principle– The Pauli Exclusion Principle– Hund’s Rule

Aufbau Principle

• Electrons like to be in the lowest energy state possible…their “ground state.”

Hund’s Rule• Electrons like to spread out• Every orbital in a subshell

must be occupied by one electron before doubling any up, and all of the electrons in the separate subshells must have the same spin.

• Everybody on the hotel floor wants their own room, and they all want to sleep facing the same direction.

Pauli Exclusion Principle

• “[N]o two electrons in a single atom can have the same four quantum numbers; if n, l, and ml are the same, ms must be different such that the electrons have opposite spins, and so on.” (Wkipedia, Pauli Exclusion Principle)

• Electrons in the same room of the hotel want to sleep facing different directions!!

Electron Configurations: The Easy Way

1. Determine the number of electrons in the atom or ion.

2. Count that many boxes along the periodic table showing the orbitals.

3. Each box is worth one electrons in an orbital.

4. Write down all the orbitals you passed.

5. Make sure the superscripts equal the number of electrons.

Remember:s = 2 electron maxp = 6 electrons maxd = 10 electrons maxF = 14 electrons max

Fe (26 electrons) =

Handout

• #4 – Diagonal Rule Handout• #4 – Electron Config. Help Handout

You can use the periodic table…

…or the electron configuration diagram

Practice

1. Neutral Sodium (Na)– 11 protons– 11 electrons– Count along the periodic table…– 1s2 2s2 2p6 3s1 (superscripts add up to 11!!)

Remember:s = 2 electron maxp = 6 electrons maxd = 10 electrons maxF = 14 electrons max

Practice

1. Sodium ion (Na+)– 11 protons– 10 electrons (1 less than protons!!)– Count along the periodic table…– 1s2 2s2 2p6 (superscripts add up to 10!!)

• Note: this is also the electron configuration for [Ne]!

Remember:s = 2 electron maxp = 6 electrons maxd = 10 electrons maxF = 14 electrons max

There is also a short cut using noble gases. Noble gases are the elements on the far right of

the periodic table…

The shortcut is called noble gas notation.

• Just take the last noble gas that you passed, write the symbol in brackets, and then complete the configuration that comes after that noble gas!

Example1. Noble Gas configuration for Ca

– 20 protons– 20 electrons– Count along the periodic table…– The last noble gas before Ca is Argon (Ar)– So the noble gas configuration is:

• [Ar] 4s2 -- Agon’s configuration + 4s2

Remember:s = 2 electron maxp = 6 electrons maxd = 10 electrons maxF = 14 electrons max

Irregular configurations of Cr and Cu

Chromium steals a 4s electron to half fill its 3d sublevel

Copper steals a 4s electron to FILL its 3d sublevel

Wait!! There are always exceptions…

Practice

• WS #5 – Basic Electron Configurations• WS #6 – Electron Config.• WS #7 – Electron Config.

Valence Electrons• Involved in chemical reactions. When 2 atoms

approach each other, they only see each other’s outer most electrons.

• Valence electrons are the s and p electrons from the highest energy level (outermost).

• You will never have more than 8 valence electrons.

• Ex: Ge atomic #321s2 2s2 2p6 3s2 3p6 4s2 3d10 4p2

1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p2

• Step 1: Find the highest energy level.

Step 2: Count the number of s and p electrons in that level. Those represent your valence electrons!

Did you say 4?

There are 2 “s” and 2 “p” electrons for a total of 4.

[Ar] 4s2 3d10 4p2OR

For Example: Electron Dot Structures

We determine electron dot structures by looking at the valence electrons ONLY. For example….

• Selenium (Se) has the following electron configuration: – 1s22s22p63s23p64s23d104p4

• The outermost energy level for selenium is the ____________ level.

• The valence electrons, therefore, are:– 4s24p4 (6 electrons total)– ONLY COUNT THE s AND p ELECTRONS!!!!

• Thus, the electron dot structure is:

4th

Back to Germanium

• 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p2

Ge

Practice

• WS #9 – Electron Dot Practice