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Study Guide

An atom needs to have 8 electrons in its outer shell in order to feel complete. This need is what drives atoms to bond with each other. That's why it's important to understand exactly what's going on in the electron cloud. This cloud is different from the electron "pool" which is reserved solely for metallic crystals and **metallic bonding**.

The electron cloud we're talking about is the place where electrons move around outside of the nucleus. Think of it as one big electron disco where all of the outer electrons are moving about and shaking their groove things. Electrons, however, have their own way of 'dancing' within the cloud.

The old way of thinking about electron movement in fixed orbits around the nucleus is incorrect. In other words, electrons are not like roller coasters moving along a stationary track. That is an old-fashioned idea we should throw out the window. Let's think of electron movement in terms of probability, or where the electrons are most likely to be found—it's like finding the odds of rolling a particular number with two dice. Unlike the old planetary model of the atom, this new quantum-mechanic model describes a less certain electron orientation.

To begin to understand how electrons *really* behave, we need to learn about **quantum** **numbers**. These are the numbers assigned to each particular electron in an atom. Think of it as an electron's cell phone number. Each electron in an atom has his own distinct set of four quantum numbers; just like your phone number is different from everyone else's.

This may get a little wordy, but trust us. It will make sense.

The first quantum number, also called the **principal quantum number**, determines the energy level or shell that the electron is in. The symbol used to describe the first quantum number is *n*. The value of *n* will be always be a whole number that represents how far away the electron is from the nucleus. The higher the number the further away from the nucleus the electron will be. Let's clear this up with an example. If an electron has a value of 4 for *n*, it is likely that it will be located further away from the nucleus than an electron with a value of 2 for *n*.

It's also important to note that each energy level is divided into sublevels, and the number of sublevels is equal to the quantity of *n* and can have values of 0 all the way to n — 1. For instance, the second energy level (*n* = 2) has two sublevels with values of 0 and 1 and the fourth energy level (*n* = 4) has four sublevels with values of 0, 1, 2, and 3.

Okay, so what's the deal with these sublevels? They are described by the second quantum number, also called the **angular momentum quantum number**. This number is used to determine the type of sublevel or subshell that that each electron occupies. The symbol used to describe the second quantum number is *l*, and the value of *l* can be 0, 1, 2, or 3. These numerical values correspond to the letters s, p, d, or f, respectively.

We sense some confusion. Fear not. Let's clear it all up with an example.

If an electron has a value of 4 for *n* (the first quantum number) and a value of 0 for *l* (the second quantum number), then the electron would be located in the 4^{th} energy level in an "s" sublevel because s = 0.

Hopefully that helps.

Each sublevel contains a certain number of orbitals. An orbital is a three-dimensional space that can hold up to two electrons. These orbitals are described by the third quantum number, also called the **magnetic quantum number**. The symbol used to describe the third quantum number is *m _{l}*.

Keep reading. If you're confused, we promise you'll get it. There is a chart below to help ease the information once you've absorbed it all.

The possible values of *m _{l}* depend upon the value of the electron's second quantum number

We can see the finish line on the horizon—one last quantum number to go. The fourth and final quantum number, also called the **spin quantum number**, is used to determine the "spin" direction of each electron in a particular orbital. We're not talking about records, baby. (Maybe that's why the Beatles were confused.) It is described by the symbol *m _{s}* and can have a designated value of +1/2 or -1/2.

As stated by the **Pauli exclusion principle**, no two electrons in a single atom can have the same exact set of four quantum numbers—just like no one else has your same cell phone number. The first three quantum numbers can certainly be the same, but if so, the fourth must be different. The quantum numbers can be used as a road map to determine the exact location of each particular electron.

Pat yourself on the back; we just got through quantum numbers. Don't worry; anything with the word "quantum" in it gets our brains aching, too. Feel free to re-read this section. People take entire college courses to try to understand this stuff.

**Summary of Quantum Numbers**

AKA | Symbol Used | Possible Numbers | Determines | |

1st Quantum Number | Principal Quantum Number | n | 1 – n | Energy Level (Shell) |

2nd Quantum Number | Angular Momentum Quantum Number | l | 0, 1, 2, 3, …, n-1 (s, p, d, f) | Type of Sublevel (Subshell) |

3rd Quantum Number | Magnetic Quantum Number | m_{l} | +l, … , 0, … , -l | Orbital |

4th Quantum Number | Spin Quantum Number | m_{s} | +1/2 and -1/2 | Spin |

Now that we know all about quantum numbers, we'll be using this information to help us use shorthand to describe the arrangement of the electrons in an atom.

This notation is called **electron configuration** and will allow us to predict how an atom will react with other atoms and what types of compounds will be formed as a result. This condensed way of representing the pattern of electrons in an atom uses a sort of build-up pattern. The pattern starts by drawing out an energy level diagram (see below).

Each circle represents a subshell (*l*) in a given energy level. Notice that each energy level is color-coded. This is just to help orient you when filling out the energy level diagram. Aren't we just so helpful?

The above diagram simplifies how to fill in the electron configuration from lowest to highest. Notice the arrows first point to the little guy named 1s. Remember this corresponds to the *n *= 1, *l *= 1 state. It also happens to be the lowest energy configuration; that's why we fill it first. If we continue to follow the arrows we'll get a proper arrangement of states from low to high energy.

If you ever get stuck on an exam, feel free to draw out the above diagram. It's a quick and easy way to get a correct electron configuration.

We also have to know how many electrons can fit into each state. There is only one s-orbital per shell, and it can hold a total of 2 electrons. There are three total p-orbitals (*m _{l }*= -1,0,1) that can hold a total of 6 electrons (because each

Here's an example to help put this in context. We need to write the electron configuration for an oxygen atom. First, go to the periodic table and find how many electrons oxygen has. The atomic number (or proton number) is 8. Because it is a neutral atom, the number of protons equals the number of electrons. Since the atomic number is 8, the number of electrons must be 8. No problems so far.

Now with this information we can represent the pattern of electrons in the oxygen atom using the **electron configuration**. All we need to do is consecutively write the number of the energy level, the type of orbital (s, p, d, etc) and then the number of electrons in that orbital, as a superscript. All of the superscript numbers in the electron configuration will add up to the number of electrons—in this case 8. If we follow the arrows we get a configuration of 1s^{2} 2s^{2} 2p^{4}.

Here is the electron configuration of hydrogen:

Since hydrogen only has one electron we only have to look at the first row to fill it in. The larger the number of electrons, the more rows we will need to use to fill out the electron configuration.

We can also draw an energy level diagram like the one below, where the lowest energy states are on the bottom, and the highest energy states are on the top. The main difference between this diagram and the one we showed before is that now the individual orbitals are shown as lines.

To do this, we must follow some rules when filling electron energy level diagrams. First of all, be sure to fill the lowest energy levels first as stated by the **Aufbau prinicple**. Also, remember to fill each orbital with a single electron before you start adding pairs as stated in **Hund's rule**.

In other words, every electron configuration will begin with 1s since it is the lowest energy level.

Just like siblings, electrons would much prefer a single room before they have to share a space with their little brother or sister. In other words, as in the case of oxygen with four 2p electrons, put the first three electrons into their own p orbital. Finally, you'll then have no choice but to pair up the fourth and final electron with a partner.

Energy Level Diagram

Use that directional path (dashed arrows) to help guide you as you fill the energy level diagram

Let's fill out the energy level diagram for sulfur based on all these rules. Thankfully you won't have to use your nose. First, let's go to the periodic table and find how many electrons sulfur has. Again, it's a neutral atom so it will have the same number of electrons as protons. Since the atomic number is 16, the number of electrons is 16. That gives us sixteen arrows to place in the blank lines starting with the bottom row.

After looking at the energy level diagram, the electron configuration for sulfur would be written as:

1s^{2}2s^{2}2p^{6}3s^{2}3p^{4}

Note: If we add up all the superscripts, we get the number of electrons in the atom (atomic number, Z, number of protons). For sulfur this would be 16. We can also tell from this notation and from the energy level diagram that sulfur needs 2 more electrons to complete its outer shell.

Use the following table to help remember how many subshells, orbitals, and total electrons there can be in each energy level (shell). A quick way to determine what the maximum number of electrons each energy level (*n*) can hold is the following formula: 2*n*^{2}.

If the atom has an energy level of 4, *n* = 4, then the total number of electrons the energy level can hold is 2(4)^{2} = 32 electrons.

Energy Level n (Shell) | Type of Sublevel (Subshell) | Number of Orbitals | Electron Capacity |

1 | s | 1 | 2 (2 total) |

2 | s p | 1 3 | 2 6 (8 total) |

3 | s p d | 1 3 5 | 2 6 10 (18 total) |

4 | s p d f | 1 3 5 7 | 2 6 10 14 (32 total) |

Can't get enough of this orbital madness? Dying to know what these orbitals really look like? Check out 3D representations of all the orbitals here or watch a video about orbitals here.

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