Verified Solution • 2025–26 Session moderate

QJEEM21Ch04ac: JEE Main 2021 Chemistry - Class 12 JEEM21Ch04ac Solution: A certain element crystallises in a bcc lattice of unit cell…

A certain element crystallises in a bcc lattice of unit cell edge length 27 Ao\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 Ao\mathop A\limits^o will be ____________. (Round off to the Nearest Integer).

[Assume each lattice point has a single atom]

[Assume 3\sqrt 3 = 1.73, 2\sqrt 2 = 1.41]

Step-by-Step Verified Solution

For BCC unit cell, 3a=4R\sqrt 3 a = 4R

a=4R3=27a = {{4R} \over {\sqrt 3 }} = 27

R=2734R = {{27\sqrt 3 } \over 4}

For FCC unit cell

2a=4R\sqrt 2 a = 4R

⇒\Rightarrow a=42(2734)a = {4 \over {\sqrt 2 }}\left( {{{27\sqrt 3 } \over 4}} \right)

⇒\Rightarrow a=2732a = 27\sqrt {{3 \over 2}}

⇒\Rightarrow a=33.12≈33a = 33.12 \approx 33

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