Summary of "Quantum Numbers | Atomic Structure - BSc 1st Year Inorganic Chemistry"

This lecture explains the concept of Quantum Numbers, which are integral values used to describe the position and properties of electrons within an atom. Quantum Numbers serve as an "address" for electrons, identifying their energy levels, subshells, orbitals, and spin orientations. The lecture covers all four Quantum Numbers in detail:

Main Ideas and Concepts:

Quantum Numbers Overview
- Quantum Numbers are integral values derived from the mathematical solution of the Schrödinger wave equation.
- They describe the position and motion of electrons in three-dimensional space.
- There are four Quantum Numbers in total, which act as identification numbers or addresses for electrons inside an atom.
The Four Quantum Numbers:
- Principal Quantum Number (n)
- Azimuthal (or Subsidiary/Orbital Angular Momentum) Quantum Number (l)
- Magnetic Quantum Number (m)
- Spin Quantum Number (s)

Detailed Explanation and Key Points:

1. Principal Quantum Number (n)

Denoted by n.
Represents the shell or main energy level of an electron.
Determines the distance of the electron from the nucleus (radius of the shell).
Energy of the electron depends on n: closer to nucleus → lower energy; farther → higher energy.
Maximum number of electrons in a shell = 2n².
Shells are labeled as K (n=1), L (n=2), M (n=3), N (n=4), etc.

2. Azimuthal Quantum Number (l)

Denoted by l.
Also called subsidiary or orbital angular momentum quantum number.
Defines the subshell within a shell and the shape of the orbital.
Values range from 0 to (n-1) for each Principal Quantum Number n.
Each value corresponds to a specific subshell type:
- l = 0 → s subshell (sharp)
- l = 1 → p subshell (principal)
- l = 2 → d subshell (diffuse)
- l = 3 → f subshell (fundamental)
Maximum electrons in a subshell = 2(2l + 1):
- s subshell: 2 electrons
- p subshell: 6 electrons
- d subshell: 10 electrons
- f subshell: 14 electrons

3. Magnetic Quantum Number (m)

Denoted by m.
Describes the orientation of the orbital within a subshell in space.
Values range from -l to +l, including zero.
Number of possible values = number of orbitals in the subshell.
- For s (l=0): m = 0 → 1 orbital
- For p (l=1): m = -1, 0, +1 → 3 orbitals
- For d (l=2): m = -2, -1, 0, +1, +2 → 5 orbitals
- For f (l=3): m = -3 to +3 → 7 orbitals

4. Spin Quantum Number (s)

Denoted by s.
Represents the spin direction of the electron about its own axis.
Two possible values: +1/2 (alpha spin, clockwise) or -1/2 (beta spin, anticlockwise).
Spin causes a magnetic moment due to electron motion.
Spin Quantum Number does not affect the energy, shape, size, or orientation of the orbital.
It only indicates how electrons are arranged within an orbital (Pauli exclusion principle).

Summary of Quantum Numbers and Their Roles:

Quantum Number Symbol Values Represents Maximum Electrons / Orbitals Principal Quantum Number n 1, 2, 3, ... Shell / main energy level Max electrons = 2n² Azimuthal Quantum Number l 0 to n-1 Subshell / orbital shape Max electrons = 2(2l + 1) Magnetic Quantum Number m -l to +l Orbital orientation within subshell Number of orbitals = 2l + 1 Spin Quantum Number s +1/2 or -1/2 Electron spin direction 2 electrons per orbital (with opposite spins)

Summary of "Quantum Numbers | Atomic Structure - BSc 1st Year Inorganic Chemistry"