A metallic element has a cubic lattice. Each edge of the unit cell...

Edge length of the unit cell $= 2\overset{.}{A} = 2 \times {10}^{- 8}cm$

Volume of unit cell $= \left(2 \times {10}^{- 8}\right)^{3} = 8 \times {10}^{- 24}{cm}^{3}$

Mass of one unit cell = volume $\times$ density

$= 8 \times {10}^{- 24} \times 25$

Number of unit cell in $200g$ of metal

$= \dfrac{ mass of the metal }{ mass of one unit cell }$

$= \dfrac{200}{8 \times {10}^{- 24} \times 25} = 1 \times {10}^{24}$