# NEET Chemistry The Solid State Questions Solved

Spinel is an important class of oxides consisting of two types of metal ions with the oxide ions arranged inCCP pattern. The normal spinel has 1/ 8 of the tetrahedral holes occupied by one type of metal ion and 1/2 of the octahedral holes occupied by another type of metal ion. Such a spinel is formed by Zn2+, A13* and 02-with Zn2+ in the tetrahedral holes. If CCP arrangement of oxide ions remains undistorted in the presence of all the cations, formula of spinel and fraction of the packing fraction of crystal are respectively :

(1) ZnAl2O4 , 77%

(2) ZnAl2O4, 74%

(3) Zn2AlO4, 74%

(4) Zn3Al2O6,74%

(1) Formula  Zn Al2O4

Packing fraction =

= $\frac{\left(\frac{4}{3}{\text{\hspace{0.17em}πr}}_{{\text{Zn}}^{2+}}^{3}\right)\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\left(\frac{2\text{\hspace{0.17em}}×\text{\hspace{0.17em}}4}{3}{\text{\hspace{0.17em}πr}}_{{\text{A/}}^{\text{3\hspace{0.17em}+}}}^{3}\right)\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\left(\frac{4\text{\hspace{0.17em}}×\text{\hspace{0.17em}}4}{3}{\text{\hspace{0.17em}πr}}_{{\text{O}}^{2-}}^{3}\right)}{{\text{a}}^{\text{3}}}$

= $\frac{\left(\frac{4}{3} \pi \frac{{a}^{3} {\left(0.225\right)}^{3}}{{\left(2\sqrt{2}\right)}^{3}}\right) + \left(2 × \frac{4}{3} \pi \frac{{a}^{3} {\left(0.414\right)}^{3}}{{\left(2\sqrt{2}\right)}^{3}}\right) + \left(4 × \frac{4}{3} \pi \frac{{a}^{3}}{{\left(2\sqrt{2}\right)}^{3}}\right)}{{a}^{3}}$= 0.77

Difficulty Level:

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