An ideal crystal, AB, has rock salt structure in which is occupying octahedral voids. The crystal is — Solid State Chemistry Question
Question
An ideal crystal, AB, has rock salt structure in which $\text{A}^+$ is occupying octahedral voids. The crystal is doped with atoms of 'C' which occupy all the tetrahedral voids without distorting the lattice. If the crystal shows defect such that the body-centred atom is missing, then the percentage of body diagonal covered by ions/atoms in the defective crystal is (Given: $\sqrt{1.5} = 29/24$)
💡 Solution & Explanation
In an ideal rock salt, anions touch along face diagonal ($a = 2\sqrt{2}r_B$). The body diagonal is $\sqrt{3}a$. Undistorted TVs mean $r_C = 0.225 r_B$. With body center missing, the diagonal covers 2 corner B ions ($2r_B$) and 2 C atoms ($4r_C = 0.9r_B$). Total covered = $2.9r_B$. Percentage covered = $\frac{2.9r_B}{\sqrt{3} \times 2\sqrt{2}r_B} = \frac{2.9}{2\sqrt{6}}$. Using $\sqrt{6} = 2 \sqrt{1.5} = 2(29/24) = 29/12$. Percentage = $\frac{2.9}{2 \times (29/12)} = \frac{2.9 \times 6}{29} = 0.6 = 60\%$. Therefore, correct answer is 0060.