Core Concept

1. Principal Quantum Number (n):

• Imagine electron shells around the nucleus. n tells you the shell number, with n = 1 being the closest (lowest energy) and n increasing as you move further out.

• Allowed values: Positive integers (1, 2, 3, ...)

2. Azimuthal Quantum Number (l):

• This number defines the suborbital within a shell. It relates to the electron's angular momentum and the shape of the orbital.

• Allowed values: 0 to (n-1). For example, if n = 3, possible l values are 0, 1, and 2.

• Suborbital types:

  • l = 0: s orbital (spherical)

  • l = 1: p orbitals (3 dumbbell shapes)

  • l = 2: d orbitals (5 complex shapes)

  • l = 3: f orbitals (7 even more complex shapes)

3. Magnetic Quantum Number (ml):

• This number describes the orientation of the suborbital within a specific shell and suborbital type (defined by l).

• Allowed values: -l to +l (including 0). For example, if l = 2 (d orbital), ml can be -2, -1, 0, 1, or 2.

• Essentially, ml tells you how many different orientations a particular suborbital can have.

4. Electron Spin Quantum Number (ms):

• This number reflects the intrinsic spin of the electron, which can be either +1/2 or -1/2.

• Electrons come in "pairs" within an orbital, but they can have opposite spins, following the Pauli Exclusion Principle.

Key Points to Remember:

• Each electron has a unique set of all four quantum numbers.

• Quantum numbers help us predict the order in which electrons fill orbitals based on their energy levels (Aufbau Principle).

• The combination of n and l determines the main energy level of an electron.

• Electrons in orbitals with higher n or higher l values are generally farther from the nucleus and have higher energy.