Question

Rhodium has a density of 12.41 g/cm3 and crystallizes with the face-centered cubic unit cell. Calculate the radius of a rhodium atom.

Answer 1

The radius of rhodium is 19.01nm

Data given;

• density = 12.41g/cm^3
• volume = ?
• atomic mass = 102.90
• Avogadro's number = 6.023*10^23

Mass of Atom

The mass of the atom can be calculated as

$mass of atom = \frac{atomic mass}{avogadro's number} * 4\\mass of atom = \frac{102.90}{6.023*10^2^3}*4 mass of atom = 6.837*10^-^2^2$

Density of Atom

using the density of the atom

$\rho=mass/volume\\12.4 = \frac{4 * 102.90}{6.023*10^2^3*a^3}\\ a^3= 411.6/7.468*10^2^4\\a^3 = 5.503*10^-^2^3\\a = 3.803*10^-8$

Let's solve for the atomic radius using this;

$a = 2\sqrt{2} r\\r=\frac{a}{2\sqrt{2} } \\r = \frac{3.803*10^-^8}{2\sqrt{2} }\\r = 2.69*10^-8\\r = 19.01nm$

The radius of rhodium is 19.01nm

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