JEE Advance - Chemistry (2020 - Paper 1 Offline - No. 12)
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).
The empirical formula of the compound is MX.
The cation M and anion X have different coordination geometries.
The ratio of M$$-$$X bond length of the cubic unit cell edge length is 0.866.
The ratio of the ionic radii of cation M to anion X is 0.414.
Explanation
(a) The empirical formula of the compound :
Contribution of M and X :
$${M_{\left( {2 \times {1 \over 2}} \right)}}{X_{\left( {4 \times {1 \over 4}} \right)}} \Rightarrow MX$$
(b) Coordination number of both M and X is 8.
(c) Distance between M and X
$$ = \sqrt {{{{a^2}} \over 4} + {{{a^2}} \over 2}} = \sqrt {{3 \over 4}} a = {{\sqrt 3 } \over 2}a$$
$$ \Rightarrow $$ 0.866 a
(d) $${r_M}\,:\,{r_X} = (\sqrt 3 - 1)\,:\,1 \Rightarrow 0.732:1$$, thus statement (d) is incorrect.
Contribution of M and X :
$${M_{\left( {2 \times {1 \over 2}} \right)}}{X_{\left( {4 \times {1 \over 4}} \right)}} \Rightarrow MX$$
(b) Coordination number of both M and X is 8.
(c) Distance between M and X
$$ = \sqrt {{{{a^2}} \over 4} + {{{a^2}} \over 2}} = \sqrt {{3 \over 4}} a = {{\sqrt 3 } \over 2}a$$
$$ \Rightarrow $$ 0.866 a
(d) $${r_M}\,:\,{r_X} = (\sqrt 3 - 1)\,:\,1 \Rightarrow 0.732:1$$, thus statement (d) is incorrect.
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