In a body-centred cubic lattice given below, what are the three distances $ \mathrm{AB}, \mathrm{AC} $ and $ \mathrm{AA} $ '?

Question

In a body-centred cubic lattice given below, what are the three distances $ \mathrm{AB}, \mathrm{AC} $ and $ \mathrm{AA} $ '?, $ a, \sqrt{2} a, \frac{\sqrt{3} a}{2} $, $ a, \frac{\sqrt{3} a}{2}, \sqrt{2} a $, $ \frac{\sqrt{3} \mathrm{a}}{2}, \sqrt{2} \mathrm{a}, \mathrm{a} $, $ a, \frac{a}{\sqrt{2}}, \frac{\sqrt{3} a}{2} $

MARKS App · Accepted Answer

Edge length = AB = AD = BC = CD = a ∴ AC = AB 2 + BC 2 = 2 a Now, AA ′ + A ′ G = 2 AA ′ = 3 a ∴ AA ′ = 3 a 2

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