Question

The density of molybdenum is 10.28 g/cm^3 and it crystallizes in the face centered cubic unit cell. Calculate the edge length of the unit cell. (The atomic mass of Mo is 95.96 g/mole)

Answer 1

The edge length of the unit cell at the given atomic mass and density of the molybdenum is 314.2 pm.

What is  cubic unit cell?

The cubic unit cell is the smallest repeating unit when all angles are 90 degrees and all lengths are equal.

Volume of molybdenum

The volume of the molybdenum is calculated from mass and density of the molybdenum as shown below;

V = (zm/ρN)

where;

• z is 2 for cubic unit cell
• m is mass of the molybdenum
• ρ is density of the molybdenum

V = (2 x 95.96) / (10.28 x 6.02 x 10²³)

V = 3.10 x 10⁻²³ cm³

Edge length of the unit cell

a³ = V

a = (V)^¹/₃

a = ( 3.10 x 10⁻²³)^¹/₃

a = 3.142 x 10⁻⁸ cm

a = 3.142 x 10⁻¹⁰ m

a = 314.2 x 10⁻¹² m

a = 314.2 pm

Thus, the edge length of the unit cell at the given atomic mass and density of the molybdenum is 314.2 pm.

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