Question

A metal crystallizes in a face-centered cubic closest packed structure. The radius of the metal atom is 2.14x10^-8 cm. calculate the density of solid metal if the atomic mass of the metal is known to be 87.62 g/mol. Identify the metal.

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Answer 1

A metal crystallizes in a face-centered cubic closest packed structure. The radius of the metal atom is 2.14x10^-8 cm. calculate the density of solid metal if the atomic mass of the metal is known to be 87.62 g/mol. Identify the metal.

for FCC

4r = ?2 a

so a = 4r / ?2

so a = 4 X 2.14 X 10^-8 / 1.414 = 6.053 X10^-8

density = M X Z / Na X a^3

M = atomic mass

Z = number of atoms = 4

Na = 6.023 X 10^23

a3 = (6.053 X10^-8)^3

density = 4 X 87.62 g/mol / 1335.74 X 10^23 X 10^-24 = 2.62 g / cm^3

The metal is Strontium