Copper crystallizes in fcc with a unit cell length of $$361$$ pm. What is the radius of copper atom?

In an FCC lattice, atoms touch each other along the face diagonal. The relationship between the edge length $a$ and the atomic radius $r$ is given by:

$$4r = \sqrt{2}a$$

Rearranging the formula to solve for the radius $$r$$:

$$r = \frac{\sqrt{2}a}{4} = \frac{a}{2\sqrt{2}}$$

Edge length ($$a$$) = $$361\text{ pm}$$
$$\sqrt{2} \approx 1.414$$

$$r = \frac{1.414 \times 361}{4}$$

$$r = \frac{510.454}{4}$$

$$r \approx 127.6\text{ pm}$$