Gold(at weight 197gmol-1) crystallizes in a cubic closest packed structures ( the face centred cubic ) and its density is 19.3 gcm-3 .calculate its atomic radius.?
To calculate the atomic radius of gold, we need to apply the formula:
density = (molar mass / (2 * atomic radius)^3)
Given:
Density of gold (ρ) = 19.3 g/cm³
Molar mass of gold (M) = 197 g/mol
Rearranging the formula, we get:
(2 * atomic radius)^3 = molar mass / density
Let's substitute the values and solve for atomic radius:
(2 * atomic radius)^3 = 197 g/mol / (19.3 g/cm³)
Cubing both sides, we have:
8 * (atomic radius)^3 = 197 g/mol / (19.3 g/cm³)
Simplifying further:
8 * (atomic radius)^3 = 10.2 cm³/g
Now, divide both sides by 8:
(atomic radius)^3 = 1.275 cm³/g
Taking the cubic root of both sides:
atomic radius = ∛(1.275 cm³/g)
Using a calculator, we find:
atomic radius ≈ 1.06 cm
Therefore, the atomic radius of gold is approximately 1.06 cm.