A certain element crystallises in a bcc lattice of unit cell edge...

A certain element crystallises in a bcc lattice of unit cell edge length 27 $\overset{o}{A}$ . If the same element under the same conditions crystallises in the $fcc$ lattice, the edge length of the unit cell in $\overset{o}{A}$ will be __________. (Round off to the Nearest Integer).

[Assume each lattice point has a single atom]

[Assume $\sqrt{3} = 1 . 73, \sqrt{2} = 1 . 41$ ]

Correct answer

Step-by-step solution

For $BCC\sqrt{3}a = 4r$

so $r = \dfrac{\sqrt{3}}{4} \times 27$

for $FCCa = 2\sqrt{2}r$

$= 2 \times \sqrt{2} \times \dfrac{\sqrt{3}}{4} \times 27$

$= \dfrac{\sqrt{3}}{\sqrt{2}} \times 27$

$= 33$

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