Ahypothetical alloy has an atomic weight of 43.1 g/mol, a density of 6.40 g/cm3, and an atomic radius of 0.122 nm. determine whether its crystal structure is fcc, bcc, or simple cubic

Option 2: BCC

The expression for density of cell is as follows:

...... (1)

Here, n is number of atom per unit cell, A is atomic mass, is volume of crystal and is Avagadro's number.

Also, the expression for volume of crystal is as follows:

The atomic weight, density and Radius of atom is given 43.1 g/mol, and 0.122 nm respectively.

Converting radius into cm:

Thus,

Putting the value to calculate volume first:

Now, putting all the values in equation (1)

On rearranging,

The number of atom per unit cell is 2 for body centered cubic lattice thus, correct option is BCC.