Quantum Mechanical Model- Basic Definitions

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Quantum Mechanics?

A set of four numbers which help us to get the complete information about the electrons in an atom. It gives us information about its location, orientation, and type of orbital and its energy.

The four Quantum numbers are-

  1. Principal Quantum Number (n)

  • Provides information about the size of orbital, energy of shell, and maximum electrons a shell can contain
  • Notations are K, L, M, N, etc.

  1. Azimuthal Quantum Number (l)

  • Talks about sub-shells (s, p, d, f, etc.) and shape (spherical, dumbbell, etc.) of orbitals
  • For a given ‘n’; ‘l’ can have values ranging from ‘0’ to ‘n-1’

  1. Magnetic Orbital Quantum Number (ml)

  • Quantum Number describing the behavior of e¯ in the magnetic field
  • Describing the preferred orientations of orbitals in sub-shell
  • For a given ‘l’; ‘ml’ has 2n+1 possible values

  1. Electron Spin Quantum Number (ms)

  • Talks about it’s clockwise and anti-clockwise rotation about its own axis
  • Denoted by “+1/2” and “–1/2” or spin up (↑) and spin down (↓)
  • Only 2 electrons can occupy a single orbital

Principles to be followed for filling up of electrons in an orbital 

  1. Aufbau Principle

  • Electrons are filled one by one in order of increasing energy, i.e., starting from the orbital with lower energy.
  • Aufbau is basically a German word which means building up or construction

  1. Pauli’s Exclusion Principle

  • No 2 electrons can have the same set of 4 Quantum numbers
  • The 2 electrons (maximum possibility) in an orbital can not have the spin (↑ or ↓)

  1. Hund’s Rule of Maximum Multiplicity

  • The pairing of electrons in the same orbital will not start until each orbital in a given subshell is filled with 1 electron with the same spin.

Quantum Mechanical Model is basically based on the following developments-

  • Dual Behaviour of Matters
  • Heisenberg’s Uncertainty Principle

Dual Behaviour

  • Just like light, all the matters have dual behavior too i.e., particle nature and wave nature.

De-Broglie’s expression for the wavelength and momentum of all material particles is-

λ = h/mv

Here ‘h’ is plank’s constant = 6.626 *10-34 Js
v = velocity of particle
m = mass of the particle

  • De- Broglie equation is not significant to macroscopic objects because bodies having large mass have a very small wavelength. (Wavelength is inversely proportional to its mass).

Heisenberg’s Principle

  • One cannot determine the position and momentum of microscopic moving particles at the same time.

Δx  × Δp ≥ h/4Π

  • This principle led to the failure of Bohr’s Model. Bohr’s Model had well-defined paths but unlike Heisenberg’ Principle, for having a well-defined path a particle must be defined by velocity and position at a given instant.

Quantum Mechanics few terms

  • Quantum Mechanics is defined by an equation called the Schrodinger Equation. (ĤΨ = ΕΨ)
  • Schrodinger explains the probability of finding the electron (Ψ2) at a point instead of discrete paths.
  • Wave Function (Ψ) – It is basically a mathematical expression that has no physical meaning. Its value depends on the coordinate of the electron in the atom.

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