Question

A body centred cubic arrangement is shown: $O$ is the body centre; $A, B, C, D, \ldots \ldots, H$ are the corners. What is the magnitude of the angle $AOB$ ?

• A. $120^{\circ}$
• B. $109^{\circ} 28'$
• C. $104^{\circ} 31'$
• D. $70^{\circ} 32'$

Answer 1

Answer: (D)

$AO = OB =\frac{\sqrt{3}}{2} a=\ell$

$\therefore a^{2}=2 \ell^{2}-2 \ell^{2} \cos \theta$

$a^{2}=2 \ell^{2}(1-\cos \theta)$

$a^{2}=\frac{3}{2} a^{2}(1-\cos \theta)$

$\therefore 1-\cos \theta=\frac{2}{3}$

$\cos \theta=\frac{1}{3},$

$\therefore \theta=70^{\circ} 32'$