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Total Volume of atoms present in a face centerid cubic unit cell of a metal is (r is atomic radius)

$(a)\;\large\frac{16}{3}\pi r^3\qquad(b)\;\large\frac{20}{3}\pi r^3\qquad(c)\;\large\frac{24}{3}\pi r^3\qquad(d)\;\large\frac{12}{3}\pi r^3$

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In f.c.c n = 4
$\therefore Occupied\; Volume = 4\times V$
$\Rightarrow\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = 4\times \large\frac{4}{3}\pi r^3$
$\Rightarrow\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; = \large\frac{16}{3}\pi r^3$
Hence answer is (a)
answered Feb 17, 2014 by sharmaaparna1

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