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 t

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.

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Thiên Di 3 years 2021-07-29T01:12:54+00:00 1 Answers 51 views 0

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  1. thanhha
    0
    2021-07-29T01:14:38+00:00
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    Answer:

    0.5447

    Explanation:

    The atomic packing fraction factor is given by

    APF = Volume of sphere/ Volume of unit cell

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

    Solving we get

    APF = 0.54427

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