Ionic diamagnetic susceptibilities

Abstract

Abstract Various attempts have been made to evaluate ionic diamagnetic susceptibili­ties. The two chief methods of attack have been (1) by the evaluation of formulæ connecting the diamagnetic susceptibility with the charge distribution of a symmetrical atom or ion, and (2) from a consideration of experimental data. In this paper ionic diamagnetic susceptibilities are calculated from Slater’s formula^ introducing a slight modification in the method of evaluating the effective nuclear charge. 2. Methods of Calculating Diamagnetic Susceptibility. The classical formula for the diamagnetic susceptibility of a symmetrical atom or ion is x = - e2/6mc2Ʃr-2, where r-2 is the time average of r2, the distance of the electron from the nucleus. The summation is extended over all the circumnuclear electrons. In quantum mechanics this formula also holds, but the value of r-2 is different. Van Vleck and Pauling,11 independently, have calculated the value of r-2 as r-2 = a02n4/(z-s)2[1+3/2{1-l(l+1)-⅓/n2}], where (Z —s) is the effective nuclear charge, a0 the radius of the one quantum orbit of hydrogen (a0 = 0·532 X10-8 cm.), and n and l the total and serial quantum numbers. Substituting this value of r-2 in equation (1) and introducing numerical values for the physical constants the diamagnetic susceptibility of a gram atom is given by x = -2·010 x 10-6Ʃn4/(z-s)2{1-3l(l+1)-1/5n2}.