Quantum Numbers

Q: What are quantum numbers?

A: Quantum numbers are integers arising from the solutions to the wave equation that describe specific properties of electrons in atoms.

Q: What does the first quantum number (n) describe?

A: It describes the orbital’s energy level and size.

Q: What does the second quantum number (l) describe?

A: It describes the orbital’s shape.

Q: What does the third quantum number (ml) describe?

A: It describes the orbital’s orientation in space.

Q: What does the fourth quantum number (ms) describe?

A: It describes if the orbital spins.

Q: What is the principal quantum number?

A: A positive whole number (integer) that indicates the energy level and relative size of an atomic orbital.

Q: What is the range of the principal quantum number (n)?

A: It can range from one to infinity.

Q: What is the smallest value of n?

A: n = 1 is the smallest value (closest to the nucleus).

Q: What does every energy level (shell) have?

A: Every energy level (shell) is occupied by an n value.

Q: Is the size the same for all atoms?

A: Yes, the size is the same for all atoms.

🔷 SECOND QUANTUM NUMBER (l)

Q: What is the orbital shape quantum number?

A: An integer that describes the shape of an atomic orbital within each principal energy level.

Q: What does the orbital shape quantum number represent?

A: It represents the sublevels of each level.

Q: What is the relationship between l and n?

A: The value of l depends on n. Whatever n is, l is 0 to (n−1).
Example: if n = 3, l can be 0, 1, or 2.

Q: What letters represent each l value?

A:
l = 0 → s
l = 1 → p
l = 2 → d
l = 3 → f

Q: How is each value of l identified?

A: Each value of l is identified by a specific letter.

🔸 THIRD QUANTUM NUMBER (ml)

Q: What is the magnetic quantum number?

A: An integer that indicates the orientation of an orbital in the space around the nucleus.

Q: What does the value of ml depend on?

A: The value of ml depends on the value of l.

Q: What is the range of ml values?

A: For any given value of l, ml ranges from −l to +l.
Example: if l = 2, ml can be −2, −1, 0, 1, 2.

Q: How many orbital positions are in the p type when l = 1?

A: There are three orbital positions in the p type.

Q: What letters describe the p orbital positions?

A: The letters x, y, and z describe each position.

Q: What formula is used to determine the maximum number of electrons?

A: 2n²

🔹 FOURTH QUANTUM NUMBER (ms)

Q: What is the spin quantum number?

A: It specifies the orientation of the axis on which the electron is spinning.

Q: What are the two possible values of ms?

A: +½ and −½.

Q: How is the sign of ms denoted?

A: By arrows (which will be discussed later).

Q: What does the Pauli Exclusion Principle state?

A: A maximum of two electrons can occupy an orbital, and the electrons must have opposite spins.