What are magnetic properties and magnetic moment?, Chemistry

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The transition metal complexes are known to be paramagnetic in character. CFT helps us to understand the magnetic properties in terms of magnetic susceptibility measurements. The magnetic property of a substance depends upon the oxidation state, electronic configuration, co-ordination number of central metal and the nature of ligand field. An unpaired electron because of its spin is equivalent to an electric current flowing in a circular conductor. Hence, it behaves as a magnet. The magnetic moment will thus be expressed as

1865_magnetic property.png

Here, e = charge of an electron,

m = mass of electron, h = planck's constant

and c = velocity of light.

The value of 599_magnetic property1.png   obtained from the above expression is 9.274 × 10^-21 ergs gauss-1. This is taken as a unit of magnetic moment called Bohr magneton (B.M.)

A substance containing one or more unpaired electrons has a definite value of magnetic moment and is attracted in external magnetic field. Such substances are called paramagnetic substances. On the other hand those substances having paired electrons will have zero magnetic moment and hence do not possess magnetic properties. These are known as diamagnetic substances.

The magnetic moment of a substance depends upon the number of unpaired electrons i.e. greater is the number of unpaired electrons more is the magnetic moment. It has been shown that the magnetic moment of a substance containing 'n' unpaired electrons is approximately given by the expression below:

Magnetic moment, 1789_magnetic property2.png   Bohr magnetons.

Magnetic moment is also given mathematically as,

2128_magnetic property3.png   (here S = sum of spins of electrons)

Or 1830_magnetic property4.png   (? value of gyromagnetic ratio = 2.0)

This relationship is used to calculate the number of unpaired electrons in an ion.

From the knowledge of a number of unpaired electrons and the value of magnetic moment ( 105_magnetic property5.png ) it is possible to find

Valence state of the metal ion is a given complex.

Natures of bonding in the complex i.e. spin free or spin-paired type.

The values of n calculated by this expression for different magnetic moments are given in the table below:

Magnetic moment (Bohr magneton)	Number of unpaired electrons (n)
0	0
1.73	1
2.83	2
3.87	3
4.90	4
5.92	5

A critical study of the magnetic data of co-ordination compounds of metals of the first transition series reveals some complications. For metal ions with upto three electrons in the d-orbitals, like Ti³⁺ (d₁); V³⁺(d₂); Cr³⁺ (d₃); two vacant d-orbitals are available for octahedral hybridization with 4s- and 4p- orbitals. The magnetic behaviour of these free ions and their co-ordination entities is similar. When more than three 3d electrons are present, the required pair of 3d-orbitals for octahedral hybridization is not directly available (as a consequence of Hund's rule). Thus for (Cr²⁺, Mn³⁺), d5 (Mn²⁺, Fe³⁺), d₆ (Fe²⁺, Co³⁺) cases, a vacant pair of d orbitals results only by pairing of 3d electrons which leaves two, one and zero unpaired electrons respectively.

The magnetic data agree with maximum spin pairing in many cases, especially with co-ordination compounds containing d6 ions. However, with species containing d4 and d5 ions there are complications.

[Mn(CN)₆]^3- has magnetic moment of two unpaired electrons while [MnCl₆]^3- has a paramagnetic moment of four unpaired electrons.

[Fe(CN)₆]^3- has magnetic moment of a single unpaired electron while [FeF₆]^3-has a paramagnetic moment of five unpaired electrons.

[CoF₆]^-3 is paramagnetic with four unpaired electrons while [Co(C₂O₄)₃]^3- is diamagnetic.

This apparent anomaly is explained by valence bond theory in terms of formation of inner orbital and outer orbital co-ordination entities.[Mn(CN)₆]^3- [Fe(CN)₆]^3- and [Co(C₂O₄)₃]^3-are inner orbital complexes are paramagnetic and the latter diamagnetic. On the other hand,[MnCl₆]^3-, [FeF₆]^3-and [CoF₆]^3-are outer orbital complexes involving sp3d2-hybridisation and are paramagnetic corresponding to four, five and four unpaired electrons.

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