Problem: Titanium metal has a body-centered cubic unit cell. The density of titanium is 4.50 g/cm3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium. ( Hint: In a body-centered arrangement of spheres, the spheres touch across the body diagonal.)

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FREE Expert Solution

Step 1: Calculate volume of the unit cell from the density


volume=47.867 g Ti1 mol Ti×1 mol Ti6.022×1023 Ti atoms×2 Ti atoms1 unit cell ×1 cm34.50 g Ti

volume = 3.5328 x10-23 cm3/1 unit cell


Step 2: Calculate the edge length of the unit cell using the volume

volume of unit cell=volume of a cubevolume of unit cell=a3


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Problem Details

Titanium metal has a body-centered cubic unit cell. The density of titanium is 4.50 g/cm3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium. ( Hint: In a body-centered arrangement of spheres, the spheres touch across the body diagonal.)