## Quiz of the Week - Chemistry 221 Quantum Numbers

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### A Quick Review of Quantum Numbers

 Quantum Number Quantum Name Values n shell 1, 2, 3, 4, ... (infinity) l subshell 0, 1, 2, ... (n - 1) ml orbital -l ... 0 ... +l ms electron spin +1/2 or -1/2

Each electron in an atom can have its own unique "address" or set of four quantum numbers.

Example: Consider a Beryllium atom with four electrons. Beryllium is in the second period, so possible n values are 1 and 2. Electrons are filled using the lowest value of n (or n + l), so the electrons will be placed into the n=1 shell before they enter the n=2 shell.

When n = 1, the only allowed value of l is 0; likewise, the only allowed value of ml = 0. We will place the first two electrons in a 1s orbital. Each electron can have either a "spin up" (ms = +1/2) or "spin down" (ms = -1/2) configuration.

The first electron's set of quantum numbers (or address) will be: n = 1, l = 0, ml = 0, ms = +1/2 The second electron's set of quantum numbers (or address) will be: n = 1, l = 0, ml = 0, ms = -1/2

When n = 2, allowed values of l are 0 and 1. Lowest (n + l) values are filled first; hence, a (n + l) value of (2 +0) = 2 will be filled before a (n + l) value of (2 + 1) = 3. When l = 0, the only allowed value of ml = 0. We will place the next two electrons in a 2s orbital. Each electron can have either a "spin up" (ms = +1/2) or "spin down" (ms = -1/2) configuration.

The third electron's set of quantum numbers (or address) will be: n = 2, l = 0, ml = 0, ms = +1/2The fourth electron's set of quantum numbers (or address) will be: n = 2, l = 0, ml = 0, ms = -1/2

The nlx notation is used to describe the subshell and/or orbital in which the electrons are assigned in an atom or ion. The electron filling order is found by using the n + l rule or an Aufbau diagram. To avoid number duplicity, l values are assigned a letter value as follows:

 Value of l Letter Notes 0 s Stupid 1 p People 2 d Drink 3 f Freakin' 4 g Gasoline

Example: Considering Beryllium again, we would place the first two electrons in the 1s subshell (n + l = 1 + 0 = 1), and the second two electrons in the 2s subshell (n + l = 2 + 0 = 2, so 2s is filled after 1s due to a lower (n + l) value.) The complete electron configuration for neutral Beryllium with its four electrons in the ground state would be:

1s2 2s2

Example: Considering Aluminum with its 13 electrons in the neutral ground state, we would place the electrons in successively higher subshells using the (n + l) values (or by consulting an Aufbau diagram.) The complete electron configuration for neutral Aluminum with its 13 electrons in the ground state would be:

1s2 2s2 2p6 3s2 3p1

### Chemistry 221 - Quantum Numbers

1. When n = 3, possible values of l are:
• 0, 1 and 2
• 1, 2, 3
• 2 only

2. When l = 2, possible values of ml are:
• 0 and 1
• -2, -1, 0, +1, +2
• 0, 1, 2

3. When ml = 1, possible values of ms are:
• 0 only
• -1, 0 and +1
• +1/2 and -1/2

4. Is 3d a correct combination of n and l quantum numbers?
• yes
• no

5. Is 2f a correct combination of n and l quantum numbers?
• yes
• no

6. The values of n and l in a 5p subshell are:
• n = 5 and l = 1
• n = 1 and l = 5
• n = 5 and l = 5

7. The correct electron configuration for carbon is:
• 1s2 2s2 2p6
• 1s2 2s2 2p2
• 1s2 2s2

8. What neutral element has the following electron configuration: 1s2 2s2 2p6 3s2
• fluorine
• calcium
• magnesium

9. What neutral element has the following electron configuration: 1s2 2s2 2p6 3s2 3p5
• oxygen
• sulfur
• chlorine

10. What neutral element has the following electron configuration: 1s2 2s2 2p6 3s2 3p6 4s2 3d3
• titanium