Answer : The crystal structure of Rhodium is, FCC (Z=4)
Explanation :
Nearest neighbor distance, r = 0.1345nm=1.345\times 10^{-8}cm (1nm=10^{-7}cm)
Atomic mass of rhodium (M) = 102.9 g/mole
Avogadro's number
First we have to calculate the cubing of edge length of unit cell for BCC and FCC crystal lattice.
For BCC lattice :
For FCC lattice :
Now we have to calculate the density of unit cell for BCC and FCC crystal lattice.
Formula used :
.............(1)
where,
= density
Z = number of atom in unit cell (for BCC = 2, for FCC = 4)
M = atomic mass
= Avogadro's number
a = edge length of unit cell
Now put all the values in above formula (1), we get
From this information we conclude that, the given density is approximately equal to the density of FCC unit lattice.
So, the crystal structure of Rhodium is, FCC (Z=4)