Consider a hypothetical metal that has a density of 10.6 g/cm3, an atomic weight of 176.8 g/mol, and an atomic radius of 0.130 nm. Compute the atomic packing factor if the unit cell has tetragonal symmetry, values for the a and c lattice parameters are 0.570 and 0.341, respectively.

0.3323

Explanation:

GIven that:

Density of the metal = 10.6 g/cm^3

atomic weight = 176.8 g/mol

atmic radius = 0.130 nm

values of a and c = 0.570 nm and 0.341 nm respectively

For us to determine the atomic packing factor, we need to first determine the volume of all spheres (Vs) and the volume of unit cell (Vc).

However, the number of atoms  in the unit cell (n) can be computed as:

n = 4.0

Thus, the number of atoms in the unit cell is 4

∴

The atomic paking factor (APF) is calculated by using the formula:

= 0.3323

explanation:

metals have excess of electrons whereas non-metals have deficiency of electrons. thus, in order to gain stability metals easily donate their electrons to the non-metals.

for example, electronic configuration of sodium is and electronic configuration of phosphorous is .

when a phosphorous atom and sodium atom combine together then sodium will donate is extra one electron to the phosphorous atom. as a result there will be formation of ionic bond between sodium and phosphorous.

the reaction will be as follows.

there, are three sodium sodium atoms and each of them will donate its one extra electron to phosphorous atom. thus, the sub-shell of phosphorous gets completely filled.  

thus, we can conclude that electrons are transferred from atoms of sodium to atoms of phosphorous. this transfer makes the sodium atoms donate one electron and the phosphorous atoms to gain one electron. as a result, the sodium and phosphorus atoms strongly attract each other.