A certain element crystallises in a bcc lattice of unit cell edge length 27$\mathop A\limits^o$. If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cel in $\mathop A\limits^o$ 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]
Answer (integer)
33
Solution
For BCC unit cell, $\sqrt 3 a = 4R$<br><br>$a = {{4R} \over {\sqrt 3 }} = 27$<br><br>$R = {{27\sqrt 3 } \over 4}$<br><br>For FCC unit cell<br><br>$\sqrt 2 a = 4R$<br><br>$\Rightarrow$ $a = {4 \over {\sqrt 2 }}\left( {{{27\sqrt 3 } \over 4}} \right)$<br><br>$\Rightarrow$ $a = 27\sqrt {{3 \over 2}}$<br><br>$\Rightarrow$ $a = 33.12 \approx 33$
About this question
Subject: Chemistry · Chapter: States of Matter · Topic: Gas Laws
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