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.

For a: The edge length of the crystal is 533.5 pm

For b: The atomic radius of potassium is 231.01 pm

Explanation:

To calculate the lattice parameter or edge length of the crystal, we use the equation:

where,

= density =

Z = number of atom in unit cell = 2  (BCC)

M = atomic mass of metal = 39.09 g/mol

= Avogadro's number =

a = edge length of unit cell = ?

Putting values in above equation, we get:

Conversion factor:  

Hence, the edge length of the crystal is 533.5 pm

To calculate the edge length, we use the relation between the radius and edge length for BCC lattice:

where,

R = radius of the lattice = ?

a = edge length = 533.5 pm

Putting values in above equation, we get:

Hence, the atomic radius of potassium is 231.01 pm

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