Question

Consider a hypothetical metal that has a density of 7.45 g/cm3, an atomic weight of 87.09 g/mol, and an atomic radius of 0.123 nm. Compute the atomic packing factor if the unit cell has tetragonal symmetry, values for the a and c lattice parameters are 0.471 and 0.350, respectively

Answer 1

Step-by-step explanation:

Formula to calculate the atomic packing factor is as follows.

APF =
`\frac{\text{volume of sphere}}{\text{volume of unit cell}}`

=
`(N * V_(N))/(V_(C))`

It is given that atomic radius is 0.123 nm and density of metal is 7.45
`g/cm^(3)`.

Hence, number of atoms will be calculated as follows.

No. of atoms =
`\frac{density}{\text{atomic radius * Avogadro's number}}` = 4

APF =
`(4 * (4)/(3) \pi (0.123 nm)^(3))/((0.434)^(2)(0.357))`

= 1.3905

Thus, we can conclude that atomic packing factor if the unit cell has a tetragonal symmetry is 1.3905.