Question

The density of potassium, which has the BCC structure, is 0.855 g/cm3. The atomic weight of potassium is 39.09 g/mol. Calculate (a) the lattice parameter; and (b) the atomic radius of potassium

Answer 1

lattice parameter = 5.3355x10^-8 cm

atomic radius = 2.3103x10^-8 cm

Step-by-step explanation:

known data:

p=0.855 g/cm^3

atomic mass = 39.09 g/mol

atoms/cell = 2 atoms

Avogadro number = 6.02x10^23 atom/mol

a) the lattice parameter:

Since potassium has a cubic structure, its volume is equal to:

v = [(atoms/cell)x(atomic mass)/(p)x(Avogadro number)]

substituting values:

v =[(2)x(39.09)/(0.855x6.02x10^23)]=1.5189x10^-22 cm^3

but as the cell volume is

a^3 =v

`a=\sqrt[3]{v}=\sqrt[3]{1.5189x10^(-22) } = 5.3355x10^-8` cm

for a BCC structure, the atomic radius is equal to

`r=(ax√(3) )/(4)=(5.3355x10^(-8)x√(3) )/(4)=2.3103x10^(-8)cm`