Quantum numbers (principal, azimuthal, magnetic and spin)
A set of four numbers that describe the state of an electron in an atom, defining its energy, shape, orientation, and spin.
What is Quantum numbers (principal, azimuthal, magnetic and spin)?
Indicates the main energy level or shell of an electron. Higher 'n' means higher energy and larger distance from the nucleus.
Key formula / rule: Range of Azimuthal Quantum Number (l)
Key points
- Define and differentiate between the four quantum numbers.
- Determine the possible values of quantum numbers for a given electron.
- Explain the significance of each quantum number in describing an electron's state.
- Apply the Pauli Exclusion Principle using quantum numbers.
Common exam trap
Confusing the ranges of l and ml.
Definitions
- Term
Principal Quantum Number (n)
- Meaning
Indicates the main energy level or shell of an electron. Higher 'n' means higher energy and larger distance from the nucleus.
- Term
Azimuthal Quantum Number (l)
- Meaning
Defines the shape of an electron's orbital and the subshell it belongs to. Also known as the angular momentum quantum number.
- Term
Magnetic Quantum Number (ml)
- Meaning
Specifies the orientation of an orbital in three-dimensional space relative to an external magnetic field.
- Term
Spin Quantum Number (ms)
- Meaning
Describes the intrinsic angular momentum of an electron, often visualized as its 'spin' in either a clockwise or counter-clockwise direction.
- Term
Pauli Exclusion Principle
- Meaning
No two electrons in an atom can have the exact same set of all four quantum numbers (n, l, ml, ms).
Learning objectives
Define and differentiate between the four quantum numbers.
Determine the possible values of quantum numbers for a given electron.
Explain the significance of each quantum number in describing an electron's state.
Apply the Pauli Exclusion Principle using quantum numbers.
Formulae
- Name
Range of Azimuthal Quantum Number (l)
- Note
For a given principal quantum number 'n'.
- Expression
l = 0, 1, 2, ..., n-1
- Name
Range of Magnetic Quantum Number (ml)
- Note
For a given azimuthal quantum number 'l'.
- Expression
ml = -l, -l+1, ..., 0, ..., l-1, l
- Name
Number of orbitals in a subshell
- Note
This is equal to the number of possible values for ml.
- Expression
Number of orbitals = 2l + 1
- Name
Maximum number of electrons in a subshell
- Note
Each orbital can hold a maximum of 2 electrons (with opposite spins).
- Expression
Maximum electrons = 2 * (2l + 1)
- Name
Maximum number of electrons in a shell
- Note
Sum of electrons in all subshells for a given 'n'.
- Expression
Maximum electrons = 2n²
Prerequisites
Atomic Structure
Bohr's Model of Atom
Electron Shells and Subshells
Common mistakes
Confusing the ranges of l and ml.
Assuming l can be equal to n.
Forgetting that ml can be zero.
Not understanding the physical significance of each quantum number.
Incorrectly applying the Pauli Exclusion Principle.
Keywords
Quantum Numbers
Principal Quantum Number
Azimuthal Quantum Number
Magnetic Quantum Number
Spin Quantum Number
Electron Shell
Subshell
Orbital
Pauli Exclusion Principle
Atomic Structure
Schrödinger Equation
Practice preview
Which of the following sets of quantum numbers is not possible for an electron in an atom?…
easy
What is the maximum number of electrons that can be accommodated in an atom with the principal quantum number n=3?…
easy
An electron has the quantum numbers n=3, l=1, m_l=0, m_s=-1/2. Which subshell does this electron belong to?…
medium