Chemistry Solids NUMS 2024
PMDC Verified Question 17 of 54
Predict the shape of \( \text{CsCl} \) having radius ratio of 0.93
A
Tetrahedral
B
Octahedral
C
Body centered cubic
D
Hexagonal
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: Body centered cubic
Concept:
The radius ratio (\( \frac{r_{\text{cation}}}{r_{\text{anion}}} \)) of an ionic compound allows us to predict the coordination number and the resulting 3D geometric shape of its crystal lattice.

Solution:
  • Crystallographic rules map specific radius ratio ranges to specific geometries:
  • Ratio \( 0.225 - 0.414 \) \( \rightarrow \) Tetrahedral (Coordination = 4)
  • Ratio \( 0.414 - 0.732 \) \( \rightarrow \) Octahedral (Coordination = 6)
  • Ratio \( 0.732 - 1.000 \) \( \rightarrow \) Cubic (Coordination = 8)
  • The given radius ratio for Cesium Chloride (\( \text{CsCl} \)) is 0.93, which is greater than 0.732.
  • This high ratio indicates that the large \( \text{Cs}^+ \) ion can comfortably fit 8 \( \text{Cl}^- \) ions around it, resulting in a coordination number of 8.
  • A coordination number of 8 corresponds to a body-centered cubic (BCC) structural shape (often specifically termed a simple cubic lattice with a body-centered interstitial, but commonly accepted as BCC in multiple-choice formats).


Why other options are incorrect:
  • A: Tetrahedral requires a much smaller ratio (< 0.414).
  • B: Octahedral requires a ratio between 0.414 and 0.732 (like \( \text{NaCl} \)).

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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