Crystal Defects

Step 1: Crystal Field Stabilization Energy (CFSE)
The crystal field stabilization energy (CFSE) is a measure of the energy stability in coordination complexes, resulting from the splitting of d-orbitals in a metal ion due to the ligand field.
A zero CFSE means that the d-orbitals do not split significantly, or the metal ion is in a high-spin state where the energy difference between orbitals is negligible.
Step 2: Analyzing the Options
In option (a) [Co(H O) ] , the d-orbitals experience significant splitting, resulting in non-zero CFSE.

In option (b) [Fe(H O) ] , the metal is also high-spin, with non-zero CFSE.

In option (c) [Co(H O) ] , there is splitting of the d-orbitals and non-zero CFSE.
In option (d) [Mn(H O) ] , the ion has a electron configuration, which does not result in significant d-orbital splitting, giving a CFSE of zero.

Step 3: Conclusion \ \ Thus, the complex [Mn(H O) ] shows zero crystal field stabilization energy.

Step 1: Understanding Schottky Defect
A Schottky defect occurs in a crystal when equal numbers of cations and anions are missing from the lattice sites, creating vacancies.
This type of defect maintains the overall electrical neutrality of the crystal.
Step 2: Explanation of Other Options
Option (a) describes an interstitial defect, where an ion occupies an interstitial space, which is not a Schottky defect.

Option (b) is incorrect because a Schottky defect involves equal numbers of cations and anions being missing, not unequal numbers.
Option (c) is incorrect because the density of the crystal decreases due to the vacancies created in Schottky defects.

Step 3: Conclusion Thus, a Schottky defect in a crystal occurs when an equal number of cations and anions are missing from the lattice.

Step 1: Understanding the Efficiency of Packing
In crystal structures, the packing efficiency refers to the fraction of the volume occupied by atoms in a unit cell.

Step 2: Explanation of BCC Structure
In a Body-Centered Cubic (BCC) structure, the packing efficiency is 68%.
This means that 68% of the volume of the unit cell is occupied by atoms.
Step 3: Why Other Options are Incorrect
Option (b) CCP structure (also called FCC) has a packing efficiency of 74%, which is greater than that of BCC.

Option (c) FEC structure is not a standard name for a crystal structure.
Option (d) HEP structure does not refer to any standard crystal packing arrangement.

Step 4: Conclusion
Thus, the efficiency of packing in a BCC structure is 68%.