Magnetic dipole moment of the nucleus arises due to the motion of charged particles. Orbitals and spin angular momentum of protons produce magnetic field within the nucleus. This field can be described in terms of resultant magnetic dipole moment located at the center of the nucleus.**In a covalent bond present between two different atoms (hetero atomic molecule) the bond pair of electrons are attracted towards atom with higher electronegativity.**

Hence it acquires partial negative charge and the other atom acquires partial positive charge. Such a molecule with two different poles (one with partial positive charge and the other with partial negative charge) is called polar molecule. Such bonds are called polar bonds and behaves as a **dipole **with positive and negative charges separated by a distance (**bond length**).

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Basically the magnetic materials are classified on the basis of presence of magnetic dipole moments in the materials. A charged particle with angular momentum always contributes to the permanent magnetic dipole moments. In general there are three important contributions to the angular moment of an atom.

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**1. Triatomic molecules (AB**_{2}**)**

**2. Tetra atomic molecules (AB**_{3}**) **

**3. ****Penta atomic molecules (AB**_{4})

### Solved Examples

**Question 1: **A paramagnetic substance is composed of atoms with a magnetic dipole moment of 3.3$\mu$_{B}. It is placed in a magnetic field of strength 5.2T. To what temperature must the substance be cooled so that the magnetic energy of each atom would be as large as the mean translational kinetic energy per atom?

** Solution: **

The magnetic energy of a dipole in an external field is U = -$\mu$.B, and the mean translational kinetic energy per atom is (3/2)kT.

These are equal in magnitude when the temperature is

T = $\frac{\mu B}{3/2\ k}$

= $\frac{3.3\ X\ 9.27\ X\ 10^{-24}J/T\ X\ 5.2T}{1.5\ X\ 1.38\ X\ 10^{-23}j/k}$

**= 7.7K**

**Question 2: **Calculate M for a material in which

** Solution: **

1. Given $\mu$_{R} = 1.4 and H = 350a_{x} A/m

The magnetic susceptibility,

x_{m} = $\mu$_{R} = 1.4-1 = 0.4

The magnetization vector for the material,

M = x_{m} H = 0.4 x 350a_{x} = 140A/m

2. Here $\mu$_{R} = 6, n = 2.5 x 10^{29} atoms/m^{3} magnetic dipole moment is m= 2.8 x 10^{-30} a_{x} Am^{2}

The magnetization, M = n x m = 2.5 x 10^{29} x 2.8 x 10^{-30}ax = 0.7a_{x} A/m

- Orbital magnetic dipole moment
- Electron spin magnetic moment and
- Nuclear spin magnetic moment

The angular momentum of an electron is called spin of the electrons. As electron is a charged particle, the spin of the electron produces magnetic dipole moment. In an atom with completely filled orbitals the contribution in spin magnetic moment is zero. In other words the spins of the electrons in in completely filled shells contribute more in the resultant spin magnetic moment.

The total magnetic dipole moment of an atom can be calculated by summing up all the above mentioned magnetic dipole moments in appropriate manner.

Dipole moment is a vector quantity and is represented by an arrow pointing towards more electronegative atom. In hetero diatomic molecules the dipole moment is never equal to zero. Greater the electronegative difference between the bonded atoms greater will be the dipole moment.

H - F | H - Cl | H - Br | HI |

1.78D | 1.07D | 0.79D | 0.38 |

In triatomic molecules if $\mu$= 0, it will possess linear structure and $\mu$ not equal to zero, then it will have V shape.

Example: Molecules like CO_{2}, BeF_{2} have zero dipole moment hence they have linear shape. In molecules like H_{2}O, H_{2}S the $\mu$ $\neq$ 0 hence they have V shape.

Tetra atomic molecules with planar shape have $\mu$ = 0 and those with pyramidal shape do not have zero dipole moment ii.e. molecules with a lone pair of electrons. Example NH_{3}, NF_{3}.The dipole moment in ammonia is 1.47D while NF_{3} has 0.24D.This is because in NH_{3} the bond moments are in same direction as that of lone pair,in NF_{3} the bond moments are in different direction with that of lone pair of electron.

Penta atomic molecules with tetrahedral shape ,with similar atoms bonded to central atom have zero dipole moment.

Example: CH_{4}, CCl_{4} etc.If one of the atom is replaced by a different atom the dipole moment is not zero.

Example:CHCl_{3 }

- Polar and non-polar molecules can be distinguished .Non polar molecules have zero dipole moment.
- Shapes of molecules can be predicted
- Ionic character in the molecule can be known

The magnetic energy of a dipole in an external field is U = -$\mu$.B, and the mean translational kinetic energy per atom is (3/2)kT.

These are equal in magnitude when the temperature is

T = $\frac{\mu B}{3/2\ k}$

= $\frac{3.3\ X\ 9.27\ X\ 10^{-24}J/T\ X\ 5.2T}{1.5\ X\ 1.38\ X\ 10^{-23}j/k}$

- $\mu$
_{R}= 1.4 and H = 350a_{x}A/M - $\mu$
_{R}= 6 and there are 2.5 x 10^{29}atoms/m^{3}, each having a magnetic dipole moment of 2.8 x 10^{-30}a_{x}A.m^{2}

1. Given $\mu$

The magnetic susceptibility,

x

The magnetization vector for the material,

M = x

2. Here $\mu$

The magnetization, M = n x m = 2.5 x 10

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