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9 June, 15:02

Strontium has density of 2.64 g/cm3 and crystallizes with the face-centered cubic unit cell. part a calculate the radius of a strontium atom.

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  1. 9 June, 15:16
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    You are given the density of a strontium atom at 2.64 g/cm3 and crystallizes with the face-centered cubic unit cell. You are asked to find the radius of a strontium atom. Use the density equation where D = M/V. Of course, the M part, because it is focused on the atom part, is equivalent to ZM/A where Z is the number of atoms in a unit cell, M is the molecular weight of the atom and A is the Avogadro's constant. Because it is a face centered cubic cell, the volume would be a ³.

    In a face center cubic cell, there are 4 atoms. There are eight 1/8 at the corners and six 1/2 on the faces making it 4 atoms. Plugging in all the values to get the side of the cubic cell,

    D = [ZM/A]/a ³

    2.64 grams / cm³ = [ (4 atoms) (87.62 grams/mol) / (6.023 x 10²³ atoms/mole) ] / a³

    a³ = 2.205 x 10⁻²²

    a = 6.041 x 10⁻⁸ cm

    The relationship between the side of the cube and the radius of the cell is a/r = 2√2 where a is the side of the cube and r is the radius of the atom.

    a/r = 2√2

    6.041 x 10⁻⁸ cm/r = 2√2

    r = 2.136 x 10⁻⁸ cm
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