Shapes or boundary surfaces of Orbitals

Shapes or boundary surfaces of Orbitals

s-orbitals: For s-orbital l = 0 and hence, m can have only one value, i.e., m = 0. This means that the probability of finding the electron in s-orbital is the same in all directions at a particular distance. In other words s-orbitals are spherically symmetrical.

The electron cloud picture of 1s-orbital is spherical. The s-orbitals of higher energy levels are also spherically symmetrical. However, they are more diffused and have spherical shells within them where probability of finding the electron is zero. These are called nodes. In 2s-orbital there is one spherical node. In the ns orbital, number of nodes are (n-1).

p-orbitals: For p-orbitals l = 1 and hence 'm' can have three possible values +1, 0, -1. This means that there are three possible orientations of electron cloud in a p-sub-shell. The three orbitals of a p-sub-shell are designated as p_x, p_y and p_z respectively along x-axis, y-axis and z-axis respectively. Each p-orbital has two lobes, which are separated by a point of zero probability called node. Each p-orbital is thus dumb bell shaped.

In the absence of magnetic field these three p-orbitals are equivalent in energy and are, therefore, said to be three-fold degenerate or triply degenerate. In the presence of an external magnetic field, the relative energies of the three p orbitals vary and depend on their orientation or magnetic quantum number. This probably accounts for the splitting of a single spectral line into a number of closely spaced lines in presence of a magnetic field (fine structure).

d-orbitals: For d-orbitals l = 2 , m = 0, ±1, ±2 indicating that d-orbitals have five orientations, i.e., there are five d-orbitals which are

named as d_xy, d_yz, d_zx, d_z² and d_x²_-y². All these five orbitals, in the absence of magnetic field, are equivalent in energy and are, therefore, said to be five-fold degenerate

The three orbitals namely d_xy, d_yz and d_zx have their lobes lying symmetrically between the coordinate axes indicated in the subscript to d, e.g. the lobes of d_xy orbital are lying between the x-and y-axes. This set of three orbitals is known as t_2g set. d_x²_-y² and d_z² orbitals have their lobes along the axes (i.e. along the axial directions), e.g., the lobes of d orbital lie along the x and y-axes, while those of d_z² orbital lie along the z-axis. This set is known as e_g set.