Question: An ionic compound AB has ZnS type structure. If the radius of \[{A^ + }\;\] is 22.5 pm, then the ide...

Question

An ionic compound AB has ZnS type structure. If the radius of ${A^ + }\;$ is 22.5 pm, then the ideal radius (in pm) of ${B^ - }\;$ would be -
(a).54.35 pm
(b) 100 pm
(c) 145.16 pm
(d) none

Answer 1

Solution

Zinc sulphide has the chemical formula ZnS and is an inorganic substance. This is the most common form of zinc found in nature, which is found mostly in the mineral sphalerite. The pure substance is white, and it is extensively used as a pigment, despite the fact that it is generally black due to different impurities. Zinc sulphide may be transparent in its thick synthetic form, and it is utilised as a window for visual and infrared optics.

Complete answer:
There are two major crystalline forms of ZnS, and this dualism is a good illustration of polymorphism. The coordination geometry at Zn and S is tetrahedral in each form. Zinc blende or sphalerite is another name for the more stable cubic form
The sphere in the depression will create a vacuum between itself and the sphere above it in the layer. The Tetrahedral Emptiness is the name given to this void. The number of Tetrahedral Voids in a lattice may be easily calculated. The number of voids will be twice as numerous as the number of spheres (i.e. unit cells) in this case. As a result, there will be “2n” tetrahedral voids. The volume of the vacuum is significantly smaller than that of the sphere. Because the void occurs at the centre of four spheres, the coordination number of a tetrahedral void is four.
Anions are significantly bigger than cations. Large anions are located in lattice sites, whereas tiny cations are found in voids. The radius ratio is the ratio of cation to anion radius. The cation-anion radius ratio (also known as the radius ratio rule) is the ratio of the cation's ionic radius to the anion's ionic radius in a cation-anion complex in condensed matter physics and inorganic chemistry. This is simply stated as $\dfrac{{{r_C}}}{{{r_A}}}$
$\dfrac{{{r_C}}}{{{r_A}}} = 0.225$
Given ${r_c} = 22.5$
So ${r_A} = \dfrac{{22.5}}{{0.225}}$
${r_A} = 100$

Hence option a is correct.

Note:
Wurtzite is the mineral name for the hexagonal form, which may also be made synthetically. At about $1020{\text{ }}^\circ C$ , the shift from sphalerite to wurtzite takes place. A tetragonal form is also known as polhemus site, an extremely uncommon mineral having the formula (Zn,Hg)S.