Scientific Understanding

**What sections should I know before attempting to learn this section?**

—> Complete Electron Configuration **Part 3**

—> Electron Configuration Diagram **Part 5**

—> Quantum Numbers **Part 3 (m _{L })**

—> Quantum Numbers **Part 4 (m _{s} ) **

—> Quantum Numbers **Part 5 (All Together)**

**What are the possible quantum numbers?**

The other common type of problem with quantum numbers is, what are the possible quantum numbers given in each of the quantum categories? For these questions I usually turn to a formula because it is easier to understand that way. You can also think about it conceptually if you want and I will explain this way as I go. In these problems they usually propose or give you one quantum category, like the energy level (n), and then ask you for the possibilities of another quantum category like the orbital types (L). The formulas I use to help me out are below.

n = number

L = n – 1 (and all integers to zero)

m_{L} = L + the negative integers of L

m_{s} = +1/2 or -1/2

How do you use these formulas? Pick a number for your energy level. For an example I am going to pick 3. (You can take a look at this periodic table if you don’t remember where your energy levels are) Take your energy level and minus 1 from it to get your possible L.

3 – 1 = 2….So L can equal 2, 1, 0. That means you can have an electron in the d, p, or s orbitals.

Now take your L possibilities add the negative integers to get m_{l}.

2, 1, 0, (-1, -2)….So your m_{l} can equal 2, 1, 0, -1, -2. That means in your d type orbitals you can have up to 5 orbitals labeled 2, 1, 0, -1, or -2. (Take a look at this periodic table if you don’t remember where your orbitals are.)

The last one, as always, is the easiest. No matter what the other quantum numbers are m_{s} can only be either +1/2 or -1/2.

**VIDEO Quantum Number Demonstrated Example 3****:** What are the possible quantum numbers if your n = 2?

**Step 1:**

If your n = 2 then what are your possible L?

n – 1 = L ….. 2 – 1 = 1

Answer: L = 1 or 0

**Step ****2****:**

If your L = 1 or 0 what are your possible m_{L}?

Answer: m_{L} = 1 or 0 or -1

**Step ****3****:**

What are your possible m_{s}?

Answer: +1/2 or -1/2

COMPLETE ANSWER: L = 1,0, m_{L} = 1,0,-1, m_{s} = +1/2, -1/2

**VIDEO Quantum Number Demonstrated Example 4****:** What are the possible quantum numbers if your m_{L} = -3

**Step 1:**

If your m_{l} = -3 what are your possible L?

We are dealing with the f orbitals here so the L for the f orbitals is 3

Answer: L = 3 or higher

**Step ****2****:**

If your L = 3 what are your possible n?

The first energy level that contains f orbitals is the 4^{th} but energy levels beyond the 4^{th} also have f orbitals.

Answer: n = 4 or higher.

**Step ****3****:**

What are your possible m_{s}?

Answer: +1/2 or -1/2

COMPLETE ANSWER: n = 4 or higher, L = 3 or higher, m_{s} = +1/2, -1/2

Notice, depending on which quantum number was picked for the question it can severely limit or open up the possibilities of the other quantum numbers.

**PRACTICE PROBLEMS**: What are the possible quantum numbers for the following problems? Remember to have your regular periodic table handy. Also if you need it have the quantum periodic table and the energy level periodic table ready.

L = 2 | n = 3,4,5… m_{L} = 2,1,0,-1,-2 m_{s} = +1/2, -1/2 |

n = 4 | L = 3,2,1,0 m_{L} = 3,2,1,0,-1,-2,-3 m_{s} = +1/2, -1/2 |

m_{L}= 1 |
n = 2,3,4… m_{L} = 1,0,-1 m_{s} = +1/2, -1/2 |