Question

Consider a hypothetical metal that has a density of 3.55 g/cm3, an atomic weight of 40.48 g/mol, and an atomic radius of 0.135 nm. Compute the atomic packing factor if the unit cell has tetragonal symmetry, values for the a and c lattice parameters are 0.545 and 0.255, respectively.

Answer 1

0.5447

Step-by-step explanation:

The atomic packing fraction factor is given by

APF = Volume of sphere/ Volume of unit cell

`APF = (N* V_N)/(V_C)`

The atomic radius = 0.135 nm

The Density of the metal = 3.55 g/cm^3

To calculate the number of atoms

= desnsity/(atomic radius×Avagadro's number)

Putting values and solving we get

the number of atoms = 4

Now,

`APF = (4* 4/3\pi(0.135*10^(-9))^3)/((0.545*10^(-9))^2(0.255*10^(-9)))`

Solving we get

APF = 0.54427