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JEE Advanced levelSingle correct optionDifficulty 3 of 3ss068

An element exists in an fcc form and in a bcc form. Assume the atomic radius is the same in both forms. Taking $2 = 1.414$ and $3 = 1.732$ , the ratio $ρ_{fcc} / ρ_{bcc}$ is

A1.09
B0.92
C2.00
D1.33

Answer: A

ρ \propto Z / a^{3}

. fcc:

Z = 4

,

a = 22 r = 2.828 r

. bcc:

Z = 2

,

a = 4 r / 3 = 2.309 r

. Ratio

= \frac{4/2.82 8 ^{3}}{2/2.30 9 ^{3}} = 1.089 \approx 1.09

.

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