Wed June 29, 2011 By: Neha Sharma

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?

Expert Reply
Thu June 30, 2011

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/No

Mass of unit cell=Z x M/No

So, Density=Z X M/a3 x No   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

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