Chemistry · Ch 4 — The d- and f-Block Elements

Magnetic Properties

4.3.9

Magnetic Properties

Two kinds of magnetic response

When a sample is placed in a magnetic field, it responds in one of a few characteristic ways. A diamagnetic substance is weakly repelled by the applied field, while a paramagnetic substance is attracted to it. A substance attracted very strongly to the field is called ferromagnetic — ferromagnetism is best understood as an extreme, cooperative form of paramagnetism rather than as a wholly separate phenomenon. A large fraction of transition-metal ions are paramagnetic.

Origin of paramagnetism: unpaired electrons

Paramagnetism originates in unpaired electrons. Each unpaired electron carries its own magnetic moment, contributed both by its spin angular momentum and by its orbital angular momentum. For compounds of the first-row transition series specifically, the orbital contribution is effectively "quenched" by the surrounding chemical environment and makes no significant contribution to the overall moment — so, for these ions, the magnetic moment is governed almost entirely by how many unpaired electrons are present.

The spin-only formula

The magnetic moment arising from electron spin alone is given by the spin-only formula:

\mu = \sqrt{n(n+2)}

where:

$n$ is the number of unpaired electrons in the ion, and
$\mu$ is the resulting magnetic moment, expressed in units of the Bohr magneton (BM).

A single unpaired electron on its own contributes a magnetic moment of 1.73 BM. As the number of unpaired electrons rises, the magnetic moment predicted by this formula rises correspondingly — so an experimentally observed magnetic moment can be read "backwards" as a practical indicator of how many unpaired electrons a given atom, molecule or ion actually carries.

Comparing calculated and observed values across the series …

Table 4.7Calculated and Observed Magnetic Moments (BM)

Ion	Configuration	Unpaired electron(s)	Calculated	Observed
$Sc^{3+}$	$3d^0$	0	0	0
$Ti^{3+}$	$3d^1$	1	1.73	1.75
$Tl^{2+}$	$3d^2$	2	2.84	2.76
$V^{2+}$	$3d^3$	3	3.87	3.86
$Cr^{2+}$	$3d^4$	4	4.90	4.80
$Mn^{2+}$	$3d^5$	5	5.92	5.96
$Fe^{2+}$	$3d^6$	4	4.90	5.3–5.5
$Co^{2+}$	$3d^7$	3	3.87	4.4–5.2
$Ni^{2+}$	$3d^8$	2	2.84	2.9–3,4
$Cu^{2+}$	$3d^9$	1	1.73	1.8–2.2
$Zn^{2+}$	$3d^{10}$	0	0

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