The Solid State

The Solid State

Question

Calculate the number of unit cells in 8.1 g of aluminium if it crystallizes in a
f.c.c. structure. (Atomic mass of Al = 27 g mol–1)

Answer

Given
Mass of Al =8.1
Atomic mass of Al = 27 g mol-1
Number of atoms = Number of moles x 6.022 x1023space equals fraction numerator 8.1 over denominator 27 end fraction space straight x space 6.022 space straight x space 10 to the power of 23 space equals space 0.3 space straight x 6.022 space straight x space 10 to the power of 23
space equals space 1.8066 space straight x space 10 to the power of 23
As one fcc unit has 4 atoms
Hence number of unit cells having 1.8066 x1023 atoms
fraction numerator 1.8066 space straight x space 10 to the power of 23 over denominator 4 end fraction space equals space 4.51 space straight x 10 to the power of 22 space unit space cell

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