An element crystallises in an fcc lattice with unit cell edge 4.00x10^-8 cm and density 10.0 g cm^-3. The number of atoms in 100 g of the element is

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An element crystallises in an fcc lattice with unit cell edge $4.00 \times 1 0^{- 8} cm$ and density $10.0 g c m^{- 3}$ . The number of atoms in $100 g$ of the element is

Volume of

100

= 100/10.0 = 10.0 c m^{3}

. Unit cell volume

= (4.00 \times 1 0^{- 8})^{3} = 6.4 \times 1 0^{- 23} c m^{3}

, so number of cells

= 1.5625 \times 1 0^{23}

. With 4 atoms per fcc cell, atoms

= 4 \times 1.5625 \times 1 0^{23} = 6.25 \times 1 0^{23}