Question

You are given a small bar of an unknown metal X. You find the density of the metal to be 10.5g/cm3. An x-ray diffraction experiment measures the edge of the face-centered cubic unit cell as 4.09 A. (1A=10^-10m) Identify X.

Answer 1

a = edge of unit cell = 4.09 A^o = 4.09 x 10^-8 cm.
volume of unit cell = (4.09 x 10^-8 cm)³.

mass = volume x density = volume from last step x 10.5 g/cc = xx g mass/unit cell.

There are 4 atoms per unit cell in a fcc; therefore, xx g/4 = mass of one atom and that times 6.022 x 10^23 atoms/mol = atomic mass of the element. Check my arithmetic; I obtained about 108.1 or so. Look that up on the periodic table to identify the element X.

Answer 2

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