Question

Lithium β is a solid phase of lithium still unknown to science. The only difference between it and ordinary lithium is that Lithium β forms a crystal with an fcc unit cell and a lattice constant =a0.430 nm. Calculate the density of Lithium β

Answer 1

Answer:

The density of Lithium β is 0.5798 g/cm³

Explanation:

For a face centered cubic (FCC) structure, there are total number of 4 atoms in the unit cell.

we need to calculate the mass of these atoms because density is mass per unit volume.

Atomic mass of Lithium is 6.94 g/mol

Then we calculate the mass of four atoms;

$= 4 .atoms*\frac{1.mole}{6.022 X10^{23} .atoms} *\frac{6.94g}{mole} = 4.6097 X10^{-23} g$

⇒next, we estimate the volume of the unit cell in cubic centimeter

given the edge length or lattice constant a = 0.43nm

a = 0.43nm = 0.43 X 10⁻⁹ m = 0.43 X 10⁻⁹ X 10² cm = 4.3 X 10⁻⁸cm

Volume of the unit cell = a³ = (4.3 X 10⁻⁸cm)³ = 7.9507 X 10⁻²³ cm³

⇒Finally, we calculate the density of Lithium β

Density = mass/volume

Density = (4.6097 X 10⁻²³ g)/(7.9507 X 10⁻²³ cm³)

Density = 0.5798 g/cm³