Node and Nodal planes in orbitals

Node: It is point/ line/ plane/ surface in which probability of finding electron is zero.

Total number of nodes = n-1

There are of 2 types.

(1) Radial nodes/ spherical nodes number of radial nodes =

(2) Angular nodes/ number of nodal planes number of angular nodes/ nodal planes = 

*Nucleus and are not considered as node.

Types of orbitals:

Case-I : If =0 and m = 0 it implies that s subshell has only one orbital called as s orbital.

Shapes of s-orbitals: The s-orbitals are spherically symmetrical about the nucleus

It implies that, p subshell have three orbitals called as p_x, p_y and p_z.

Shape  of p-orbitals :

We have three p-orbitals, commonly known as p_x, p_y and p_z. These three p-orbitals, possesses equivalent energy and therefore, have same relation with thenucleus. They, however , differ in their direction & distribution of the charge.

These three p-orbitals are situated at right angle to another and are directed along x, y and z axes (figure)

1. Each p orbital has dumb bell shape (2 lobes which are separated from each other by a point of zero probability called nodal point or node or nucleus).

2. The two lobes of each orbital are separated by a plane of zero electron density called nodal plane.

3. Each p orbital of higher energy level are also dumb bell shape but they have nodal surface.

Nodal plane:

Orbital                       Nodal plane

p_x                                            yz plane

p_y                                            xz plane             

p_z                                            xy plane

Case III          When = 2, ‘m’ has five values -2, -1, 0, +1, +2. It implies that d subshell of any energy shell has five orbitals. The shapes of all d- orbital is not identical. Shapes of these Four d orbitals are same

d_xy, d_yz, d_xz, 

Shape of d-orbitals:

It implies that d subshell has 5 orbitals i.e. five electron cloud and can be represent as follows:

Each d-orbital of higher energy level are also double dumbell shaped but they have nodal surface.

In d orbital :

(i)  Nodal Point  1

(ii) Nodal Surface 3 d_xy 0 Nodal surface

4 d_xy  1 Nodal surface

5 d_xy 2 Nodal surface

nd_xy  (n-3)

Number of nodal surface = 

(iii) ) Nodal Plane d_xy xz&yz nodal plane

d_xz xy&zy nodal plane

d_zy zx&yx nodal plane

2, nodal plane

0, nodal plane

Number of nodal surface =  

Note: Orbitals of d subshell are Equivalent in energy.