Orbital Magnetic moment

## source : thepolywellblog.blogspot.com

## Magnetic moment-

#### The net magnetic moment of an atom is the vector sum of its orbital and spin magnetic moments.

The magnetic moment produced due to the spin of the electrons may be calculated by the formula-

μ = √ n ( n + 2)  BM

n = number of unpaired electrons present in an atom or ion

BM ( Bohr Magneton ) is the unit of magnetic moment

#### ” Greater is the number of unpaired electrons greater is the magnetic moment .” It is represented by ‘μ’

Note – This formula is not applicable to f- block elements.

### Orbital magnetic moment –

This magnetic moment is due to the orbital motion .It may be calculated by the formula –

#### Orbital magnetic moment = √ [l ( l + 1)] h / 2π

l = azimuthal quantum number of orbital

For s – orbital ,

l=0 ,

#### Orbital magnetic moment = 0

For p – orbital ,

l=1 ,

#### Orbital magnetic moment =√ [l ( l + 1)] h / 2π = √ [1 ( 1 + 1)] h / 2π

= √ 3. h / 2π = 1.41 h / 2π

For d – orbital ,

l=2 ,

#### Orb. magnetic moment =√ [l ( l + 1)] h / 2π = √ [2 ( 2 + 1)] h / 2π

= √ 6. h / 2π = 2.45 h / 2π

### Spin magnetic moment-

If magnetic moment arise due to the spin of unpaired electrons then,

μs = 4s (s+1) BM

s = total spin quantum number

This formula is related to the number of unpaired electrons ‘n’ by the equation,

μs = √n (n+2) BM

no. of unpaired electrons     magnetic moment ‘μs’          total spin quantum number ‘S’

1                                                 1.73                                           1 x 1/2 = 1/2

2                                                 2.83                                           2 x 1/2 = 1

3                                                 3.87                                           3 x 1/2 = 3/2

4                                                 4.90                                          4 x 1/2 = 2

5                                                 5.92                                          5 x 1/2 = 5/2

### Diamagnetic and Paramagnetic –

When a substance is placed in a magnetic field of strength ‘H’ then the intensity of the magnetic field in the substance may be greater than or smaller than ‘H’.

If the  magnetic field in the substance is  greater than  ‘H’, then the substance is paramagnetic. Paramagnetic material attracts the lines of force . Paramagnetism arises due to unpaired electron spins in the atom. Atoms or ions contain unpaired electrons , are paramagnetic in nature .

Ex – Cu++ , Fe++ , Ti++ , Cr3+ etc.

If the  magnetic field in the substance is  less than  ‘H’, then the substance is diamagnetic. Diamagnetic material repels the lines  of force . Atoms or ions do not have  unpaired electrons ( means all the electrons are paired) , are diamagnetic in nature .Their magnetic moment is zero.

Ex – Cu+ , Sc3+ , Ti 4+ , Cl  etc.