Ionic diamagnetic susceptibilities

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 = - e 2 /6 mc 2 Ʃ r -2 , where r -2 is the time average of r 2 , 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 = a 0 2 n 4 /(z- s ) 2 [1+3/2{1- l ( l +1)-⅓/ n 2 }], where (Z — s ) is the effective nuclear charge, a 0 the radius of the one quantum orbit of hydrogen ( a 0 = 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 -6 Ʃ n 4/(z- s ) 2 {1-3 l ( l +1)-1/5 n 2 }.