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一、化学与数学的综合试题例1 求证离子半径比(r_+/r_-)的最小值为0.732时,AB型离子化合物的晶格才属CsCI型。解析:为求r_+/r_-的离子半径,需建立数学模型。模型的建立是根据CsCI的晶体结构,并作如下考虑:①阴、阳离子的配位数为8;②阴、阳离子(假定是刚性球)尽量接近(假定刚性球彼此相切,才可将阴、阳离子的距离看成是两离子半径之和),使引力最大;③相同电荷离子间尽量离开,使斥力最小。这样按图取一截面,即可建立起如图所示的数学模型,并按此模型进行数学证明。
First, comprehensive test of chemistry and mathematics Example 1 When the minimum ion radius ratio (r_+/r_-) is 0.732, the crystal lattice of the AB ion compound is CsCI type. Analysis: In order to find the ion radius of r_+/r_-, a mathematical model needs to be established. The model is based on the crystal structure of CsCI and is considered as follows: 1 The coordination number of yin and cations is 8; 2 The yin and cations (assumed to be rigid spheres) are as close as possible (assuming that the rigid spheres are tangent to each other, the yin can be The distance between the cation and the cation is considered to be the sum of the radii of the two ions, so that the gravitational force is maximized; 3 The same charged ions are left as far as possible so that the repulsive force is minimized. In this way, take a cross-section according to the figure, you can establish a mathematical model as shown in the figure, and according to this model for mathematical proof.