A hypothetical metal M crystallizes in a BCC lattice. At a certain temperature, it undergoes a transition to an FCC lattice. Assuming the radius of the metal atom remains constant, what is the ratio o

Question

A hypothetical metal M crystallizes in a BCC lattice. At a certain temperature, it undergoes a transition to an FCC lattice. Assuming the radius of the metal atom remains constant, what is the ratio of the electrical conductivity ( σ FCC ​ / σ BCC ​ ) if conductivity is directly proportional to the packing efficiency?

TestHub · Accepted Answer

Question Explanation:

Calculating the ratio of conductivity based on packing efficiency.

Concept:

Packing Efficiency in BCC and FCC lattices. Detailed Step-by-Step

Solution:

1. Packing Efficiency (PE) for BCC = $\frac{3 π}{8} \approx 0.68$

2. Packing Efficiency (PE) for FCC = $\frac{2 π}{6} \approx 0.74$

3. Given σ∝PE:

$\frac{σ _{FCC}}{σ _{BCC}} = \frac{0..74}{0.68} = 1.088$

4. Note: While in real metals, conductivity also depends on the Mean Free Path, defines the proportionality strictly to PE.

Correct Answer: Option (B, D) 1.088 and 0.74 : 0.68

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