Gallium has an orthorhombic structure, with a0 = 0.45258 nm, b0 = 0.45186 nm, and c0 = 0.76570 nm. The atomic radius is 0.1218 nm. The density is 5.904 g/cm3, and the atomic weight is 69.72 g/mol. Determine (a) the number of atoms in each unit cell; and (b) the packing factor in the unit cell.

a) atoms/cell =  8 atoms

b) FE = 0.3876

Explanation:

You have the following data:

ao=0.45258 nm

bo=0.45186 nm

co=0.76570 nm

density=p=5.904 g/cm^3

atomic weight=69.72 g/mol

Avogadro number = 6.02x10^23 atom/mol

a) The number of atoms per cell is calculated by clearing it from the density formula:

atoms/cell = (px(cell volume)x(Avogadro number))/atomic weight

cell volume = aoxboxco = (0.45258x10^-7cm)x(0.45186x10^-7cm)x(0.76570x10^-7cm) = 1.5659x10^-22 cm^3

replacing values:

atoms/cell = ((5.904 g/cm^3)x(1.5659x10^-22 cm^3)(6.02x10^23 atoms/cell))/69.72 g/mol = 7.9 atoms = 8 atoms

b)the packing factor is calculated by:

FE = ((atoms/cell)x(atom volume))/cell volume

atom volume = 4pixr^3/3 = 4pix(0.1219x10^-7 cm)^3/3 = 7.5875x10^-24 cm^3

FE = (8x7.5875x10^-24)/(1.5659^-22 cm^3) = 0.3876

the seeing the electronic configuration we can say that the element is fluorine.

fluorine is the most electronegative element in the periodic table.

but by only seeing the configuration we cannot say about its reactivity because we don't know if its configuration after excitation or by addition of electrons.

but if not then, it is the lightest halogen and exists as a highly toxic pale yellow diatomic gas at standard conditions. as the most electronegative element, it is extremely reactive: almost all other elements, including some noble gases, form compounds with fluorine.