QB_PH_SEC7_011: Crystal Structure & Lattice Dynamics

In a simple cubic lattice with lattice parameter $a = 2.50\text{ Å}$, what is the perpendicular interplanar distance $d_{210}$ (in Å)? (Round off to two decimal places)

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Cubic Interplanar Spacing Relation**: $d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$ 2. **Parameter Substitution**: - Lattice parameter: $a = 2.50\text{ Å}$ - Miller indices: $(hkl) = (210)$ $\sqrt{h^2 + k^2 + l^2} = \sqrt{2^2 + 1^2 + 0^2} = \sqrt{4 + 1 + 0} = \sqrt{5} \approx 2.23607$ 3. **Evaluation**: $d_{210} = \frac{2.50\text{ Å}}{2.23607} = 1.11803\text{ Å} \approx 1.12\text{ Å}$ 4. **Official Value**: 1.12 Å.