Option 2: BCC
The expression for density of cell is as follows:
[tex]d=\frac{nA}{V_{c}N_{A}}[/tex]...... (1)
Here, n is number of atom per unit cell, A is atomic mass, [tex]V_{c}[/tex] is volume of crystal and [tex]N_{A}[/tex] is Avagadro's number.
Also, the expression for volume of crystal is as follows:
[tex]V_{c}=\frac{64R^{3}}{3\sqrt{3}}[/tex]
The atomic weight, density and Radius of atom is given 43.1 g/mol, [tex]6.40 g/cm^{3}[/tex] and 0.122 nm respectively.
Converting radius into cm:
[tex]1 nm=10^{-7}cm[/tex]
Thus,
[tex]0.122 nm=0.122\times 10^{-7}cm[/tex]
Putting the value to calculate volume first:
[tex]V_{c}=\frac{64(0.122\times 10^{-7}cm)^{3}}{3\sqrt{3}}=2.23\times10^{-23} cm^{3}[/tex]
Now, putting all the values in equation (1)
[tex]6.40 g/cm^{3}=\frac{n\times 43.1 g/mol}{2.23\times 10^{-23}cm^{3}\times 6.023\times 10^{23}atom/mol}[/tex]
On rearranging,
[tex]n=\frac{6.40 g/cm^{3}\times 13.47 atom cm^{3}/mol}{43.1 g/mol}\approx 2atoms[/tex]
The number of atom per unit cell is 2 for body centered cubic lattice thus, correct option is BCC.
