JEE Main 2017 · Chemistry · Solutions, Solid State and Surface Chemistry · medium

A metal with atomic radius r undergoes a transition from a body-centred cubic to a face-centred cubic structure with the atomic radius unchanged. The…

Single correct option

A metal with atomic radius

r

undergoes a transition from a body-centred cubic to a face-centred cubic structure with the atomic radius unchanged. The volume occupied per mole of the metal changes by nearly

A. decrease by $8.1\%$
B. increase by $8.1\%$
C. decrease by $6\%$
D. decrease by $12\%$

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Answer: (A) decrease by $8.1\%$

bcc:

a=4r/\sqrt3

, 2 atoms/cell, volume per atom

=a^3/2=\dfrac{32r^3}{3\sqrt3}=6.158r^3

. fcc:

a=2\sqrt2\,r

, 4 atoms/cell, volume per atom

=a^3/4=4\sqrt2\,r^3=5.657r^3

. Change

=(5.657-6.158)/6.158=-0.0814

, i.e. a decrease of

8.1\%

. (Equivalently packing fractions

0.68

and

0.74

: the ratio

0.68/0.74

gives

8.1\%

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