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Questions
How many atoms constitute one unit cell of a face-centered cubic crystal?
How many atoms are present per unit cell in a face-centred cubic system?
In a face-centred arrangement of atoms of an element, what will be the numbers of atoms present in respective unit cells? Justify your answer with calculation.
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Solution
The cubic unit cell in face-centred cubic systems is made up of one atom at each of the cube’s eight corners and atoms at the centre of each of the cube’s six faces. Eight unit cells share each corner atom evenly, contributing 1/8 of the unit cell. Two unit cells share equally each atom located in the centre of the face, contributing half of the two unit cells.
∴ Number of atoms in a face-centred unit cell = `(8 xx 1/8) + (6 xx 1/2)`
= 1 + 3
= 4 atoms
Thus, the unit cell of a face-centred cubic system contains 4 atoms.
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