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The number of atom in 100g of an FCC crystal with density d=10g/cm3 and cell edge equal to 100 pm is equal to


Solution

d = Z x M/a3 x NA
 where, a is edge of unit cell 
 NA = Avogadro number (6.022 × 1023) 
 M = Molar mass 
 Z = number of atoms per unit cell 
 For fcc, Z = 4 
From the given data we can calculate the Molar mass of given substance as:
M = d x a3 x NA /z
​Number of atoms = givan mass / molar mass(M) x NA
Putting the vaue of M in above equation we get
Number of moles = given mass x z x NA / d x a3 x NA
Number of atoms = given mass x z​ / d x a3
​putting the values we get:
Number of atoms = ( 100 g x  4) /( ​10 gcm^-3  x (100 x 10-10 cm)^3 )= ​400 / 10 x 10^-24 = 4 x 10^25 atoms

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