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Question

(A) The $HCP$ unit cell consists of $6$ atoms per unit cell.The base of the $HCP$ unit cell is a regular hexagon with side length $a = 2r$.The area of

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$24\sqrt{2} r^3$

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(A) The $HCP$ unit cell consists of $6$ atoms per unit cell.The base of the $HCP$ unit cell is a regular hexagon with side length $a = 2r$.The area of the base is $6 	imes \frac{\sqrt{3}}{4} a^2 = 6 	imes \frac{\sqrt{3}}{4} (2r)^2 = 6\sqrt{3} r^2$.The height of the $HCP$ unit cell is $h = 4r \sqrt{\frac{2}{3}}$.Volume $=$ Area of base $	imes$ Height $= (6\sqrt{3} r^2) 	imes (4r \sqrt{\frac{2}{3}}) = 24\sqrt{3} 	imes \sqrt{\frac{2}{3}} r^3 = 24\sqrt{2} r^3$.

The volume of the $HCP$ unit cell is

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