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276 CHAPTER 3
and inserting the expression for from Eq. (3.29), one obtains
Thus, by combining Eqs. (3.36) and (3.106)
The total charge in the ion cloud is, on the one hand, equal to [Eq. (3.39)]
as required by the electroneutrality condition and, on the other hand, the result of
integrating dq. Thus,
What lower limit should be used for the integration? In the point-charge model,
one used a lower limit of zero, meaning that the ion cloud commences from zero (i.e.,
from the surface of a zero-radius ion) and extends to infinity. However, now the ions
are taken to be of finite size, and a lower limit of zero is obviously wrong. The lower
limit should be a distance corresponding to the distance from the ion center at which
the ionic atmosphere starts (Fig. 3.30).
Fig. 3.30. For a finite-sized ion, the ion atmos-
phere starts at a distance a from the center of the
reference ion.