Ahypothetical metal has an orthorhombic unit cell for which the a, b, and c lattice parameters are 0.413 nm, 0.665 nm, and 0.876 nm, respectively. (a) if there are 8 atoms per unit cell and the atomic packing factor is 0.536, determine the atomic radius (in nm). (b) if the density is 3.99 g/cm3, calculate the metal's atomic weight (in g/mol).

atomic radius  R = 0.157 nm

metal atomic weight = 72.27 g/mol

Explanation:

given data

parameters a =  0.413 nm

parameters b = 0.665 nm

parameters c =  0.876 nm

atomic packing factor = 0.536

density = 3.99 g/cm³

to find out

atomic radius and  atomic weight

solution

we apply  here atomic packing factor (x) that is

atomic packing factor (x) =  ..................1

put here value we get

atomic packing factor =

R =

R =  

atomic radius  R = 0.157 nm

and

now we get here metal atomic weight that is

metal atomic weight =   ....................2

metal atomic weight =  

metal atomic weight = 72.27 g/mol