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Question:

Calculate the number of unit cells in 8.1 g of aluminium if it crystallizes in a face-centred cubic (f.c.c.) structure?

Solution:

Given that, Mass of aluminium, w = 8.1 g
Number of atoms of Al, NAl = (Mass / Molar mass) × NA = (w/M) × NA = (8.1/27) × NA
There are 4 atoms present per unit cell as it crystallizes in a face-centred cubic (f.c.c) structure.
Therefore, number of unit cells = (8.1 × 6.023 × 1023) / (27 × 4) = 4.52 × 1022 unit cells