1. Tardigrade
  2. Question
  3. Chemistry
  4. 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 ?

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Q. 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 $AOB$ ?Chemistry Question Image

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Solution:

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

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

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

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

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

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

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