The atomic radius of magnesium is 160 pm.Estimate its density,given that the metal has a close-packed structure.

Question

Quizplus · Accepted Answer

Magnesium has a close-packed structure, which means that its atomic packing factor is 0.74.

The volume of one atom can be calculated as:
V = (4/3)πr^3
V = (4/3)π(160 pm)^3
V = 2.18 x 10^-23 cm^3

The volume of one unit cell can be calculated as:
Vc = a^3
where a is the edge length of the unit cell

The number of atoms in one unit cell can be calculated as:
N = 4

The density can be calculated as:
ρ = mass/volume = (NmM)/(VcNa)
where mM is the molar mass of magnesium, N is the number of atoms in one unit cell, and Na is Avogadro's number (6.022 x 10^23)

Substituting the values, we get:
ρ = (4 x 24.31 g/mol)/(2.18 x 10^-23 cm^3 x 6.022 x 10^23)
ρ = 1.74 g/cm^3

Therefore, the best choice is A.

The Atomic Radius of Magnesium Is 160 Pm