Question

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.

Answer 1

0.3323

Step-by-step 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 = (\rho * V_c *N_A)/(A) \\ \\ n = ((10.6) * (5.7)^2 (3.41)*(10^(-24)) *(6.022*10^(23)))/(176.8)`

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:

`(Vs)/(Vc) = (4 * (4)/(3)\pi *R^3 )/(a^2 *c) \\ \\ \\ (Vs)/(Vc) = (4 * (4)/(3)\pi *(1.30*10^(-8))^3 )/((5.70*10^(-8))^2 *(3.41*10^(-8)))`

= 0.3323