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Question
Calculate the number of atoms present in 2 gram of crystal which has face-centred cubic
(FCC) crystal lattice having edge length of 100 pm and density 10 gcm−3
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Solution
Given: Density (d) = 10 g cm−3
Edge length (a) = 100 pm = 100 × 10−10 cm.
Mass of crystal = 2 g
To find: Number of atoms
Formula: Density = Mass/Volume
Calculation: Density = Mass/Volume
∴ Volume = Mass/Density
∴ Volume = `"2g"/(10gcm^(−3))` = 0.2 cm3
Volume of unti cell = a3 = (100 × 10–10 cm)3 = 1 × 10−24 cm3
Number of unit cells in 2 g of crystal = total volume/volume of unit cell
`(0.2cm)^3/(1×10^(−24) cm^4)`
The given unit cell is of fcc type, therefore, it contains 4 atoms.
0.2 × 1024 unit cells will contain 4 × 0.2 × 1024 = 0.8 × 1024 atoms
= 8 × 1023 atoms
Number of atoms present in 2g of crystal is 8 × 1023 atoms
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