(Chemistry Ch-2) 8. Shapes of Atomic Orbitals; Energies of Atomic Orbitals

• 
  Ψ² (i.e, square of the wave function) at a point gives the probability density of the electron at that point.
• The variations of Ψ²and Ψ with r for 1s and 2s orbitals are shown in the figure below.

• For 1s orbital, the probability density is maximum at the nucleus and it decreases sharply as we move away from it.
• For 2s orbital, the probability density first decreases sharply to zero and then again starts increasing.
• The region where the probability density function reduces to zero is called nodal surface or node.
• For ns-orbital, there are (n -1) nodes.

For 2s-orbital, there is one node; and for 3s-orbitals, there are two nodes.

Boundary Surface Diagrams

• Give a fairly good representation of the shape of the orbitals
• Boundary surface diagrams for 1s and 2s orbitals are:

• 1s and 2s are spherical in shape.

• Boundary surface diagram for three 2p orbitals (l = 1) are shown in the figure below.

• Boundary diagrams for the five 3d orbitals are shown in the figure below.

• The total number of nodes is given by (n-1) i.e, sum of l angular nodes and (n-l-1) radial nodes.

Energy of Orbitals:

• The energy of the orbitals increases as follows:

1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f < ….

• Lower the value of (n + l) for an orbital, lower is its energy.
• When two orbitals have the same value of (n + l), the orbital with lower value of n will have lower energy.
• Energy level diagram:

       

• Effective nuclear charge (Z_eff e): Net positive charge experienced by the electrons from the nucleus
• Energies of the orbitals in the same subshell decrease with the increase in the atomic number (Z).