Question

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

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

Answer 1

Answer: (D)

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

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

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

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

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

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

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