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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.

Sagot :

Manetho

Answer:

0.5447

Explanation:

The atomic packing fraction factor is given by

APF = Volume of sphere/ Volume of unit cell

[tex]APF = \frac{N\times V_N}{V_C}[/tex]

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,

[tex]APF = \frac{4\times 4/3\pi(0.135\times10^{-9})^3}{(0.545\times10^{-9})^2(0.255\times10^{-9})}[/tex]

Solving we get

APF = 0.54427

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