. The principal quantum number ‘ n ’ is a positive integer with value of n = , , ....... The principal quantum number determines the size and to large extent the energy of the orbital. For hydrogen atom and hydrogen like species (He + , Li + , ....
etc.) energy and size of the orbital depends only on ‘ n ’. The principal quantum number also identifies the shell . With the increase in the value of ‘ n ’, the number of allowed orbital increases and are given by ‘ n ’ All the orbitals of a given value of ‘n’ constitute a single shell of atom and are represented by the following letters n = ............ Shell = K L M N ............
Size of an orbital increases with increase of principal quantum number ‘ n ’. In other words the electron will be located away from the nucleus. Since energy is required in shifting away the negatively charged electron from the positively charged nucleus, the energy of the orbital will increase with increase of n . Azimuthal quantum number.
‘ l ’ is also known as orbital angular momentum or subsidiary quantum number. It defines the three-dimensional shape of the orbital. For a given value of n , l can have n values ranging from to n – , that is, for a given value of n , the possible value of l are : l = , , , .......... ( n – ) For example, when n = , value of l is only .
For n = , the possible value of l can be and . For n = , the possible l values are , and . Each shell consists of one or more sub-shells or sub-levels . The number of sub-shells in a principal shell is equal to the value of n .
For example in the first shell ( n = ), there is only one sub-shell which corresponds to l = . There are two sub-shells ( l = , ) in