An element crystallizes in the simple cubic structure. its density is 8g/ml.if 200g of the element contain 2.4*10^24 atoms , calculate its unit cell edge?

Density=Mass of unit cell/volume of unit cell

Mass of unit cell=Number of atoms in unit cell x Mass of each atom=Z x m

Mass of an atom present in unit cell=Atomic mass/Avogadro number=M/N_o

Mass of unit cell=Z x M/N_o

So, Density=Z X M/a³ x N_o   g cm^-3

Z=Number of atoms in unit cell,

m=Mass of each atom

a=Edge length, a³= Volume

Density=8=2.4 x 10²⁴ x 200/a³ x 6.023 x 10²³;

a³=2.4 x 10²⁴ x 200/8 x 6.023 x 10²³=4800/48.184=99.61 cm³;

Unit cell edge(a)=(99.61)^1/3cm=4.63 cm