The edge length of the unit cell is 407 pm
Unit cell
A unit cell is the smallest representation of an entire crystal structure
Face centered cubic structure
A face centered cubic structure is one in which there is an atom on each face of the unit cell and one atom at each corner of the unit cell.
So, for a face centered unit cell of atomic radius, r and edge length, a, we have that
(4r)² = a² + a²
16r² = 2a²
8r² = a²
Taking square root of both sides, we have
The edge length
a = (2√2)r
So, for a silver atom with atomic radius 144 pm, the edge length a is
a = (2√2)r
a = (2√2)144 pm
a = 288√2 pm
a = 407.3 pm
a ≅ 407 pm
The edge length of the unit cell is 407 pm
Learn more about edge length of face centered cubic unit cell here:
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