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Question

An element having atomic mass 65.1g/mol has face centred cubic unit cell with edge length 3.608×108cm. Calculate the density of the element. [Given NA=6.022×1023atoms/mol]

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Solution

Unit-cell edge length =360.8pm
Volume of unit cell =(360.8×1012cm)3=4.7×1023cm3
Mass of the unit cell =Number of atoms in the unit cell × Mass of each atom
Number of atoms in the fcc unit cell =8×18+6×12=4
Mass of one atom =Atomic mass/Avogadro number
=61.5/6.023×1023
Mass of the unit cell =4×606.023×1023
Density of unit cell =Mass of unit cell/Volume of unit cell
=4×65.16.023×1023×14.7×1023
=9.2gcm3


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