Import Question JSON

$\text{Hint: To solve this numerical one must have the basic knowledge of the solid states.}$ $\text{When the metal crystallizes out with a cubic structure we need to determine the lattice first.}$ $\text{Once we come to know about the structure we can easily derive the relation between the radius and edge length of the atom.}$ $\text{Formula Used: The relation between the radius and edge length for FCC}$ $4r = \sqrt{2}a$ $\text{Where, } r \text{ is the radius of the atom,}$ $a \text{ is the edge length of the cubic structure.}$ $\text{Complete step by step answer:}$ $\text{First we will try to determine the lattice of a cubic structure.}$ $\text{For that we will read the question properly and we have given in the question that there are four metal atoms in one unit cell.}$ $\text{Therefore, } Z=4 \text{ where } Z \text{ represents the number of atoms in a unit cell.}$ $Z=4 \text{ is for the face centered cubic lattice (fcc).}$ $\text{Now we have determined the lattice of a cubic structure that is face centered cubic lattice.}$ $\text{So we will use the relation between radius and edge length for fcc.}$ $\text{We have, } a = 361 \text{ pm, we will substitute it in the relation of radius and edge length.}$ $4r = \sqrt{2}a - (1)$ $\text{Now substitute } a = 361 \text{ pm, in the above equation. we get,}$ $\Rightarrow 4r = \sqrt{2} \times 361 \text{ pm}$ $\Rightarrow r = \frac{\sqrt{2} \times 361}{4}$ $\Rightarrow r = 127.6 \text{ pm}$ $\text{From the above calculation, we get the radius of one atom as } r = 127.6 \text{ pm}$