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Chemistry

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An element crystallizes in a body-centered cubic lattice. The edge of the unit cell is 2.77 , and the density of the crystal is 8.65 . Find the atomic weight of the element.

  • Chemistry - ,

    55.34g/mol^3

  • Chemistry - ,

    a=2.77 Å= 2.77•10⁻⁸ cm.
    The BCC-cell volume is
    V=a³=(2.77•10⁻⁸)³ = 2.13•10⁻²³ cm³.
    Density ρ =8.65g/cm³ per unit cell.
    Avogadro´s number N₀=6.022•10²³ mol⁻¹.
    The number of atoms in the BCC unit cell are calculated
    as follows:
    1 × 1 = 1 center atom
    8 × (1/8) = 1 corner atom
    => n=2 total atoms

    Atomic weight = N₀•V• ρ/n =
    =6.022•10²³•2.13•10⁻²³•8.65/2 = 55.34 g/mol³

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