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Copper crystallizes in a face-centred cubic lattice with a unit cell length of 361 pm. What is the radius of copper atom in pm?
A
108
B
128
C
157
D
181
Detailed Solution
In a face-centred cubic unit cell the atoms touch along the face diagonal.
Face diagonal = $\sqrt{2}a$, and it contains corner atom radius + diameter of the face-centre atom + corner atom radius = 4r
$4r = \sqrt{2}a$, so $r = \frac{\sqrt{2}a}{4} = \frac{a}{2\sqrt{2}}$
$r = \frac{1.414\times361}{4}$
r = 127.6 pm $\approx$ 128 pm
Face diagonal = $\sqrt{2}a$, and it contains corner atom radius + diameter of the face-centre atom + corner atom radius = 4r
$4r = \sqrt{2}a$, so $r = \frac{\sqrt{2}a}{4} = \frac{a}{2\sqrt{2}}$
$r = \frac{1.414\times361}{4}$
r = 127.6 pm $\approx$ 128 pm