Respuesta :
Answer : Yes, theoretical density can be computed from a tiny fundamental unit using the formula [tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex].
Explanation :
Nearest neighbor distance, r = [tex]0.124nm=1.24\times 10^{-8}cm[/tex] [tex](1nm=10^{-7}cm)[/tex]
Atomic mass (M) = 55.85 g/mol
Avogadro's number [tex](N_{A})=6.022\times 10^{23} mol^{-1}[/tex]
For BCC = Z = 2
Given density = [tex]7.87g/cm^3[/tex]
First we have to calculate the cubing of edge length of unit cell for BCC crystal lattice.
For BCC lattice : [tex]a^3=(\frac{4r}{\sqrt{3}})^3=(\frac{4\times 1.24\times 10^{-8}cm}{\sqrt{3}})^3=2.35\times 10^{-23}cm^3[/tex]
Now we have to calculate the density of unit cell for BCC crystal lattice.
Formula used :
[tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex] .............(1)
where,
[tex]\rho[/tex] = density
Z = number of atom in unit cell (for BCC = 2)
M = atomic mass
[tex](N_{A})[/tex] = Avogadro's number
a = edge length of unit cell
Now put all the values in above formula (1), we get
[tex]\rho=\frac{2\times (55.85g/mol)}{(6.022\times 10^{23}mol^{-1}) \times (2.35\times 10^{-23}Cm^3)}=7.89g/Cm^{3}[/tex]
From this information we conclude that, the given density is approximately equal to the given density.
Yes, theoretical density can be computed from a tiny fundamental unit using the formula [tex]\rho=\frac{Z\times M}{N_{A}\times a^{3}}[/tex].
