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DiKsa [7]
3 years ago
15

Copper crystallizes in a face-centered cubic lattice (the Cu atoms are at the lattice points and at the face centers). If the de

nsity of the metal is 8.96 g/cm3, what is the unit cell edge length in pm? × 10 pm
Chemistry
1 answer:
Delvig [45]3 years ago
8 0

Answer:

The unit cell edge lenght in pm is equal to 361 pm

Explanation:

Data provided:

ρ=Copper density=8.96 g/cm3

Atomic mass of copper=63.54 g/mol

Atoms/cell=4 atoms (in theory)

Avogadro's number=6.02x10^{23} atoms/mol

Since copper has a cubic structure, its cell volume is equal to a^{3}, which can be obtained through the relationship:

cell volume=\frac{(atoms/cell)(atomic mass)}{(density)(Avogadros number)}

Substituting the values:

cell volume=\frac{(4 atoms)(63.54 g/mol)}{(8.96 g/cm3)(6.02x10^{23}) }=4.71x10^{-23}cm^{3}

clearing, we have:

a=\sqrt[3]{4.71x10^{-23}cm^{3}  }=3.61x10^{-8}cm

We convert from centimeter to picometer, 1cm=1x10^{10}pm

a=3.61x10^{-8}cmx\frac{1x10^{10}pm }{1cm} =361 pm

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