Quantum Numbers | Four Types of Quantum Numbers

What are Quantum Numbers?

Atoms have many shells and subshells, each with different sizes, shapes, and directions in space. These differences are described using numbers called quantum numbers.

Quantum numbers are a set of four numbers that give us all the information about an electron in an atom. They tell us where the electron is, its energy level, the type of orbital it occupies, and the direction of that orbital. It's like an address for the electron.

Types of Quantum Numbers

There are four quantum numbers that describe where electrons are in an atom. These are:

1. Principal Quantum Number (n)

• What it tells us: The main shell where the electron is found and its distance from the nucleus.

• Energy level: It indicates the energy of the orbital.

• Maximum electrons: The formula to find the maximum number of electrons in a shell is 2n22n 22n2, where nnn is the principal quantum number.

  Shell	Principal Quantum Number (n)	Maximum Number of Electrons
  K	1	2
  L	2	8
  M	3	18
  N	4	32

2. Azimuthal (or Angular Momentum) Quantum Number

• What it tells us: The number of subshells in a main shell and the shape of these subshells.
• Shapes: Subshells are labeled as s, p, d, f, etc.
• Formula for orbital angular momentum:

3. Magnetic Quantum Number (m)

• What it tells us: The orientation of the subshells in space.
• Magnetic influence: Electrons in a subshell can orient in different ways when in a magnetic field.

4. Spin Quantum Number (s)

• What it tells us: The direction of the electron's spin (like how the Earth spins on its axis).

These quantum numbers help explain the arrangement of electrons in atoms and their magnetic properties.

Example on Quantum Numbers:

Which quantum number cannot be determined from Schrödinger's wave equation?

(A) n (B) l (C) m (D) s

Answer: Quantum numbers n, l, and m are derived from the Schrödinger equation. Quantum number s is determined from spectral evidence. Therefore, the correct answer is (D).

Which of the following sets of quantum numbers is not allowed?

(A) n = 3, l = 1, m = +2 (B) n = 3, l = 1, m = +1 (C) n = 3, l = 0, m = 0 (D) n = 3, l = 2, m = ±2

Answer: For n = 3, possible values of l are 0, 1, and 2.

• For l = 0, possible values of m are 0.
• For l = 1, possible values of m are -1, 0, +1.
• For l = 2, possible values of m are -2, -1, 0, +1, +2.

Since l = 1 cannot have m = +2, the correct answer is (A).