Some hypothetical alloy is composed of 12.5 wt% of metal a and 87.5 wt% of metal b. if the densities of metals a and b are 4.27 and 6.35 g/cm3, respectively, and their respective atomic weights are 61.4 and 125.7 g/mol, determine whether the crystal structure for this alloy is simple cubic, face-centered cubic, or body-centered cubic. assume a unit cell edge length of 0.395 nm.

The number of atoms in the unit cell is 2, the crystal structure for the alloy is body centered cubic.

Explanation:

Given that,

Weight of metal A = 12.5%

Weight of metal B = 87.5%

Length of unit cell = 0.395 nm

Density of A = 4.27 g/cm³

Density of B= 6.35 g/cm³

Weight of A = 61.4 g/mol

Weight of B = 125.7 g/mol

We need to calculate the density of the alloy

Using formula of density

....(I)

Where, n = number of atoms per unit cells

m = Mass of the alloy

V=Volume of the unit cell

N = Avogadro number

We calculate the density of alloy

We calculate the mass of the alloy

Put the value into the equation (I)

Hence, The number of atoms in the unit cell is 2, the crystal structure for the alloy is body centered cubic.

the answer is b ) square root of 5