An element crystallizes in fcc unit cell at room temperature but changes to HCP at high temperature. If edge length of fcc unit cell is 3 A ˚ , then find the height of HCP unit cell (in A ˚ ) (Use :

Question

An element crystallizes in fcc unit cell at room temperature but changes to HCP at high temperature. If edge length of fcc unit cell is 3 ​ A ˚ , then find the height of HCP unit cell (in A ˚ ) (Use : 3 ​ = 1.73 )

TestHub · Accepted Answer

The height of the HCP unit cell is given by:

$a = \frac{1}{2} \frac{3}{2} \overset{˚}{A}$

$2 a = 4 r$

$R = \frac{a}{2 2} = \frac{1}{2} \frac{3}{2} \overset{˚}{A}$

The height of the HCP unit cell is also:

$4 \frac{2}{3} R = 4 \frac{2}{3} \times \frac{3}{2 2} = 2 \overset{˚}{A}$

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