Explanation:
Formula to calculate the atomic packing factor is as follows.
APF = [tex]\frac{\text{volume of sphere}}{\text{volume of unit cell}}[/tex]
= [tex]\frac{N \times V_{N}}{V_{C}}[/tex]
It is given that atomic radius is 0.123 nm and density of metal is 7.45 [tex]g/cm^{3}[/tex].
Hence, number of atoms will be calculated as follows.
No. of atoms = [tex]\frac{density}{\text{atomic radius \times Avogadro's number}}[/tex] = 4
APF = [tex]\frac{4 \times \frac{4}{3} \pi (0.123 nm)^{3}}{(0.434)^{2}(0.357)}[/tex]
= 1.3905
Thus, we can conclude that atomic packing factor if the unit cell has a tetragonal symmetry is 1.3905.
