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Chemistry Question on Solid State

The Cu metal crystallises into fcc lattice with a unit cell edge length of 361 pm. The radius of Cu atom is:

A

127 pm

B

181 pm

C

157 pm

D

108 pm

Answer

157 pm

Explanation

Solution

In a face-centered cubic (fcc) lattice, the relation between the unit cell edge length a and the atomic radius r is: r=a22 Substituting a=361 pm: r=36122≈127 pm\text{In a face-centered cubic (fcc) lattice, the relation between the unit cell edge length } a \text{ and the atomic radius } r \text{ is:} \\\ r = \frac{a}{2\sqrt{2}} \\\ \text{Substituting } a = 361 \, \text{pm:} \\\ r = \frac{361}{2\sqrt{2}} \approx 127 \, \text{pm}