Quantum Mechanics

Wavefuctions 

• Wavefunction (Ψ) - describes the movement of a particle 

• Probability density (Ψ²) - probability of finding the particle in a region 

  • Node - where the probability of finding an electron is zero 

    • Wavefunctions have (n-1) nodes

Nodes

• Can occur whenever a wavefunction, and probability density, is 0 

• An electron can never be at a node

• Can “cross” nodes, because they are delocalized/standing waves

S orbitals 

• Exists for all energy levels n ≥ 1 

• L = 0 

P orbitals

• Exists for n ≥ 2 

• L = 1

D orbitals 

• Exists for n ≥ 3 

• L = 2

Shielding and Penetration

• Orbitals are a delocalized cloud of electron density 

• Penetrating - orbitals with radial probability closer to the nucleus 

  • The closer, more penetrating orbitals are shielding the further orbitals from the nucleus 

Diamagnetism vs Paramagnetism

• Paramagnetic - has unpaired electrons

  • Drawn towards magnets

• Diamagnetism - has paired electrons

  • Slightly repelled by magnets

Principle quantum number (n) 

• Principle quantum number - defines the size of and energy of the orbital

• Must be positive whole numbers

Number of orbitals in a shell

• n²

Angular momentum (l)

• Angular momentum - defines the 3D shape of the orbital 

• Can be any integer from 0 to (n-1)

Number of different shapes of orbitals per shell

• n

Magnetic quantum number (m_l)

• Magnetic quantum number - defines the spatial orientation of the orbital

• Allowed values are from -l, …, 0,... +l

Number of spatial orientations of orbitals in a subshell

• 2l + 1

  • s sublevel = 2 electrons.

  • p sublevel = 6 electrons.

  • d sublevel = 10 electrons.

  • f sublevel = 14 electrons

Spin quantum numbers (m_s)

• Spin quantum number - defines spin axis of electron 

• Allowed values for each orbital are +½ or -½ 

  • Only two electrons allowed per orbital