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Meaway and Maidstone co lege OI Technology Chatham, United Kingdom
I I
Effettive Magnetic Moment
The measurement of the magnetic susceptibility of a chemical compound is a widely used physical method particularly relevant in the study of transition metal complexes.' In such studies the quantity of most interest is the "effective magnetic moment" of the paramagnetic center in the complex (pall) which is calculated from the experimentally determined susceptibility. This is generally expressed in terms of the Bohr magneton (pe, B.M.). The purpose here is to emphasize that, as defined, pall is a numher and does not have the "unit" fi,. This is true irrespective of whether magnetochemistry is dealt with in terms of the traditional three-quantity system of equations written in the nonrationalized form (the CGS approach) or in terms of the four-quantity system of equations written in the rationalized form (the SI apprbach).2 The dimensionless nature of pelf in both the CGS approach and in the S I approach is demonstrated below using the relevant eauations. In order to em~hasize units, these are used in preference to dimensions. Base units rather than derived units are used throughout.
The S I equation for xnrcorresponding to eqn. (1) is
where p,, the permeability of a vacuum, appears as a physical quantity having dimensionss (fro = 4 s X lo-' kg m S - ~ A - ~i.e., ) it isnot unity asin theGCS approach. The SI units (given in parentheses) for the other physical quantities are m ( m amole-'), k(J OK-' = kg mas-' OK-' ), T ( W
e(C
-
A s), h(J s = kgmz S-I),
m(kg)
and hence from eqn. (4) Units of PB = A s X kgmass-' kg
CGS
(The units of the physical quantities are given in From eqn. (3) parentheses.) The paramagnetic molar susceptibility xn is related to the "effective magnetic moment" by the e q u a t i ~ n ~ . ~ and where xa is the molar susceptibility (ema mole-'); k, the Boltzmann constant (erg OK-' = g ern2 OK-'); L, the Avogadro constant (mole-'); T, the thermodynamic temperature (OK); and pa the Bohr magneton.
where e is the electronic charge (esu = cm* g% s-I); h , the Planck constant (ergs = g cm2s-I); m, the electron mass (g); c, the velocity of light (cm s-'). Hence from eqn. (2)
=
From eqn. (1)
gvl s-1
pefl is a numher. Although the present symbol could be retained, the current name given to pelf is not satisfactory. The Bohr magneton numbe? would be a preferable name.
FIGGIS, B. N., AND LEWIS,J., "Modern Coordination Chemistry," (Edilw: LEWIS,J., AND WILXINS, R. G.), Interscience, New York, 1960, p. 400. MCGLASHAN, M. L.,"Physico-chemical Qwntities and Units" (2nd ed.), Royal Institute of Chemistry Monographs for Teachers, No. 15, London, 1971, p. 82. AND LEWIS,op. cit., p. 404. FIGGIS A., "Introduction to Magnetochemistry," Aca'IEAIWSHAW, demic Press, London and New York, 1968, p. 4. 6 P ~ s s G., , AND SUTCLIFFE, H., J. CHEM.EDUC.,48, 180 11971\. ~ - --, 6 K ~ S. ~F. A,, ~ ''Coordination ~ , Compounds," Nelson, London, 1969, p. 129.
Volume 49, Number
7,July 1972
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505
