Quantum Numbers
This is our final way to describe the location of an electron. It consists of four numbers that act as coordinates to
locate the electron’s position. These numbers will refers only to the element’s highest energy electron because the
other fall into the same locations that have been described in the elements preceding it.
1. Principle Quantum Number (n):
a. ENERGY LEVEL
b. Indicate distance from the nucleus
c. How to figure it out:
d. Options available:
2. Second Quantum Number (ℓ):
a. SUBLEVELS
b. Indicates the shape of the region.
i. Spherical - ______
ii. Dumbbell - ______
iii. Double dumbbell donut - ______
iv. Fancy - ______
c. How to figure it out:
d. Options available:
3. Magnetic Quantum Number (mℓ):
a. ORBITALS
b. Indicate the orientation of the region in space
c. How to figure it out:
d. Options available:
4. Spin Quantum Number (ms):
a. When two electrons are in a magnetic field, they will align opposite of one another. This is called the
“spin”.
b. The electrons within an orbital must have opposite spins to overcome their repulsion.
c. How to figure it out:
d. Options available:
Quantum Numbers Practice Problems
Write the four quantum numbers which describe the location of the highest energy electron of the following:
1. N #7 ____________________________________________________
2. Ni #28___________________________________________________
3. Xe #54___________________________________________________
4. Re #75___________________________________________________
5. Pu #94___________________________________________________
6. Br #35___________________________________________________
7. P #15___________________________________________________
8. At #85___________________________________________________
9. H #1 ___________________________________________________
10.Rb #37__________________________________________________
Identify the element whose highest energy electron would have the following four quantum numbers:
11. 3, 1, -1, +1/2___________________________________________________
12. 4, 2, +1, +1/2___________________________________________________
13. 6, 1, 0, -1/2____________________________________________________
14. 4, 3, +3, -1/2___________________________________________________
15. 2, 1, +1, -1/2___________________________________________________
Which of the following represents a permissible set of quantum numbers? (answer “yes” if permissible and “no” if
no permissible)
16. 2, 2, +1, -1/2___________________________________________________
17. 5, 1, 0, +1/2____________________________________________________
18. 6, 3,-2, +1/2____________________________________________________
19. 7, 0, 0, -1/2____________________________________________________
20. 4, 1, 8, +1/2____________________________________________________