Answer
127.7pm
Work Step by Step
Cubic closest packed structure has packing density of [2]
d = π/(3∙√2) ≈ 0.74
One mole atoms is occupy a volume of
(M/ρ)∙d
and a single atom in closed packed structure occupies
V = M∙d/(ρ∙Na) = π∙M/(3∙√2∙ρ∙Na)
(Na is the Avogadro constant)
Since the atoms ar considered as solid spheres of radius r:
(4/3)∙π∙r³ = π∙M/(3∙√2∙ρ∙Na)
=>
r = ∛[ M/(4∙√2∙ρ∙Na) ]
= ∛[ 63.55g/mol / (4∙√2 ∙ 8.95d/cm³ ∙ 6.022×10²³mol⁻¹) ]
= 1.277×10⁻⁸ cm
= 1.277×10⁻¹⁰ m
= 127.7pm
