Quantum numbers-

Those u numbers which are required to specify the position, energy momentum and spin of an electron in an atom. These numbers are

(1)  Principle Quantum no.

(2)  Azimuthal Quantum no.

(3)  Magnetic Quantum no.

(4)  Spin Quantum no.

(1)  Principle Quantum number-

a)Represented by n

b)It gives main energy shell or orbit

c)it gives an idea of the size of shell

d)It have any integral value except zero.

n= 1, electron belong to ‘K’ shell

n= 2, electron belong to ‘L’ shell

n= 3, electron belong to ‘M’ shell

n= 4, electron belong to ‘N’ shell

e)Energy of an electron for hydrogen or hydrogen like a shell is cal. By En

f)As value of n, increases energy of principal Quantum number increases. Thus it give an idea abort energy of electron.

g)Maximum number of electron present in any principle shell is 2n².

1. Azimuthal or angular momentum Quantum number  

1. It is represented by ‘l’.
2. It gives no. of subshell present in a shell.
3. It gives shape of orbital.
4. The value of ‘l’ depend upon the value of ‘n’.
5. For a given value of ‘n’ l can have values from o to (n-1). Each value of l represents are subshell.
6. It helps to explain the five lines of the spectrum.
7. If        n=1 , l=0              n=2,    l=0 and 1 (two subshell)

n=3  ,  l=0,1,2                n=4,    l=0,1,2,3, (four subshell)

8. l =0,1,2,3,4 of different subshell are designated  as s,p,d,f and g respectively.
9. The word s,p,d and f derived from sharp, principal, different and fundamental.The number of subshells present is any principal shell is equal to the number of principal quantum number.
10. The number of subshells present is any principal shell is equal to the number of principal quantum number.
11. The energies of different subshell in same principal shell are s>p>d>f.
12. Maximum number of electron in s,p,d and f subshell are 2,6,10&14 resp.
13. Angular momentum of the electron in an orbital

Angular momentum =

(Angular momentum depend on the value of l, does not depend upon the value of n.

eq. 18,25,35 (l=0), e- possess same angular momentum.

3)  Magnetic Quantum number – (m)

1. It gives number of orientations of electron present in a subshell.

2) It is represented by m  (for a given value of Quantum number)

3)For a given value of l, the value of m is –l to +l includes i.e. (2l+1) value.

4)If  l=0     m=0 or ‘s’ subshell has only one orbital

If  l=1     m=1, 0,+1 or ‘p’ subshell has 3 orbital

If  l=2     m=2,-1,0,+1,+2 or ‘d’ subshell has 5 orbital

If  l=3     m=3,-2,-1,0,+1,+2,+3 or ‘f’ subshell has 7 orbital

All 3 p orbital, 5 d orbital & 7 f orbital for a particular principal shell have the same energy in the absence of M.F. called degenerate orbital.

5. It explain when live spectrum is placed in a magnetic field each spectral live splits up into a number of lives (i.e. Zeeman effect )

4) Spin Quantum Number (s) or (m_s)

1. It gives direction of spinning of the electron in any orbital.
2. Direction of spin may be clockwise, spinning electron.
3. It may be represented as + ½ or – ½  or ↑or↓
4. It explain magnetic proof of a substance, spinning electron behave like micro magnet with definite magnetic moment.

5. If orbital contained paired electron, substance is diamagnetic and magnetic moment is zero. If it has unpaired electron it is paramagnetic.