Explain the significance of three quantum numbers in predicting the position of an electron in an electron in an atom .

Explanation

Each electron quantum number (n ) : The prinicipal quantum number is used to described by a set of three quantum numbers n. L and `m_(1) ` .
1. Prinicipal quantum number (n ) : The principal quantum number is used to describe th size and energy of the main shell . It is denoted by 'n ' .'n' has positive integer values of 1,2,3,.......... It is used to know the number of orbitals `(n^(2) )` and electrons in an orbit . `(2n ^(2))` .

As . 'n' increases the shells becomes larger and the electrons in shells are farther from the nucleus and their energys increaes .
2. The angular - momentum quantum number (l ) : 'l' has integer values from '0' to n-1 for each value of 'n' Each 'l' value reqresents one sub- shell . It is used to describe the shape of an orbit

3. The magnetic quantum number `(m_(1))` : The magnetic quantum number `(m_(1))` has integer values between -l and +l including zero .

If l=0 the possible `m_(t ) ` value is 1.
l= 1, the possible `m_(l) ` value is `-1 ,0 and 1`.
thus for a certain value of l . there are `(2l +1)` integer values of `m_(f ) ` orbitals with different orientations along x,y,z axes labelled as `P_(x ) .P_(y) and P_(X ) ` orbitals .
predicting the position the position of an elecrton in an atom : If the values of n ,l and `m_(l) ` 2,-1,1 respectively the electron is present in `2p_(x ) ` orbital in L- shell .