B.sc 1st year Book
(Page 6)

Shapes of orbitals

s-shape of orbital:

There is one s-orbital in every principal shell. Each s-orbitals is spherically symmetrical because its electron density is not concentrated in any particular direction.

This orbital has the following characteristic properties:

(i) It can have only one possible orientation:
(ii) All s – orbitals are similar in shape but become larger in size with the higher value of Π.
(ii) 1 s orbital is surrounded by 2 s – orbital, 2 s – orbital is surrounded by 3 s – orbital, and 90 on.
(iv) There is a region between two adjacent s – orbitals where the probability of finding an electron is zero. This is called the ‘nodal plane’ or ‘nodal surface’. The s-orbitals other than 15 are more complicated as they contain nodal surfaces. The number of nodal surfaces is. If the nodal surface is (n-1) at infinity excluded

p-shapes of orbitals:

Each principal shell has a set of three p-orbitals (except the K-shell), In p-orbitals, the probability of finding an electron is more in some particular directions from the nucleus. The probability distribution diagram of the p-orbital shows that this orbital consists of two lobes one on each side of the nucleus i.e. it is dumbbell in shape.

The p-orbitals have the following characteristic properties:

(i) The probability of finding an electron is equal on both sides of the nucleus in the lobes.
(ii) Depending upon the orientation, p-orbitals have been denoted as px, py, and pz because their lobes of maximum electron density lie along x, y, and z axes in space respectively.
(iii) All these orbitals have identical energies but different identities as individuals.
In other words, in the absence of an applied magnetic field, the p orbitals are equivalent in energies and said to be triply or three-fold degenerate.
(iv) When these orbitals visualize collectively they appear concentrically spherical around the origin of the cartesian axes.
(v) The p-orbitals have a plane of zero electron density referred to as the nodal plane which separates the two lobes e.g. xy plane is the nodal plane of the Pz-orbital.

d-shapes of orbitals :

Each principal shell (except K and L shells) has a sell of five d-orbitals which have the same radial function but differ in angular distribution. Shapes of orbitals

Structurally d-orbitals are of two types:

(a) The orbitals with double dumb-bell shaped for example dxy, dyz, dxz, and dx²-y² orbitals.
(b) The orbital of a dumbbell shape with a collar for example; dz² orbital.
Depending upon the orientation of orbitals in three-dimensional space d-orbitals are further divided into two groups e.g.
(i) The orbitals which have their lobes in between two adjacent axes, making 45° with the axes. For example, dxy, dyz, and dxz orbitals because they lie in xy, yz and xz planes respectively. A set of these orbitals is called a ‘triply’ degenerate ‘  ‘ set.
(ii) The orbitals have their lobes along the axis/axes for example dx²-y² orbitals have their lobes along x and y cartesian axes and dz² orbital has their lobes along z. axis. Both these orbitals are collectively known as ‘doubly’ degenerate ‘eg’ set.

The characteristic properties of d-orbitals are :

1.  Al_2g set of orbitals has two nodal planes each.
2. The dz² orbital contains two cone-shaped nodal surfaces. Thus, this orbital is different from the other four d-orbitals viz. dxy, dyz, dxz and dx²-y² orbitals. It is because most of its density is concentrated around the z-axis.
3. In absence of a magnetic field, all the five d-orbitals are equivalent in energies and are called “five-fold degenerate’, but in the presence of a magnetic field d-orbitals split into two sets of orbitals 4t_2g‘ and ‘eg’  sets: