Question

manganese has a body-centered structure cubic unit cell and has a density of 7.88 g/cm^3. from this information determine the length of the edge of the cubic cell

Answer 1

The body-centered cubic unit cell is shown below:

Number of Mn atoms in unit cell = 8 x 1/8 + 1 x 1 (8 corner + 1 center)

= 2 atoms

Mass of Mn atoms in unit cell = number/Avogadro's number x molar mass of Mn

= 2/6.022 x 10²³ x 54.938

= 1.8246 x 10^-22 g

Volume of unit cell = mass/density

= 1.8246 x 10^-22 /7.88

= 2.3155 x 10^-23 cm³

Unit cell edge length = (volume)^1/3

= (2.3155 x 10^-23)^1/3

= 2.85 x 10^-8 cm = 2.85 x 10^-10 m = 2.85 Angstroms = 285 pm