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QJEEAdv20Che07d: JEE Advanced 2020 Chemistry - Class 12 JEEAdv20Che07d Solution: The cubic unit cell structure of a compound containing cation M …

The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

JEE Advanced 2020 Paper 1 Offline Chemistry - Solid State Question 13 English

Multiple Choice Options

  • A The empirical formula of the compound is MX.
  • B The cation M and anion X have different coordination geometries.
  • C The ratio of M −- X bond length of the cubic unit cell edge length is 0.866.
  • D The ratio of the ionic radii of cation M to anion X is 0.414.

Step-by-Step Verified Solution

(a) The empirical formula of the compound :

Contribution of M and X :

M(2×12)X(4×14)⇒MX{M_{\left( {2 \times {1 \over 2}} \right)}}{X_{\left( {4 \times {1 \over 4}} \right)}} \Rightarrow MX

(b) Coordination number of both M and X is 8.

(c) Distance between M and X

=a24+a22=34a=32a= \sqrt {{{{a^2}} \over 4} + {{{a^2}} \over 2}} = \sqrt {{3 \over 4}} a = {{\sqrt 3 } \over 2}a

⇒\Rightarrow 0.866 a

(d) rM : rX=(3−1) : 1⇒0.732:1{r_M}\,:\,{r_X} = (\sqrt 3 - 1)\,:\,1 \Rightarrow 0.732:1 , thus statement (d) is incorrect.

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