Answer:
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
![\rho=n\times\dfrac{m}{V_{c}\times N_{A}}](https://tex.z-dn.net/?f=%5Crho%3Dn%5Ctimes%5Cdfrac%7Bm%7D%7BV_%7Bc%7D%5Ctimes%20N_%7BA%7D%7D)
....(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
![\rho=\dfrac{1}{\dfrac{12.5}{4.27}+\dfrac{87.5}{6.35}}\times100](https://tex.z-dn.net/?f=%5Crho%3D%5Cdfrac%7B1%7D%7B%5Cdfrac%7B12.5%7D%7B4.27%7D%2B%5Cdfrac%7B87.5%7D%7B6.35%7D%7D%5Ctimes100)
![\rho=5.98](https://tex.z-dn.net/?f=%5Crho%3D5.98)
We calculate the mass of the alloy
![m=\dfrac{1}{\dfrac{12.5}{61.4}+\dfrac{87.5}{125.7}}\times100](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B1%7D%7B%5Cdfrac%7B12.5%7D%7B61.4%7D%2B%5Cdfrac%7B87.5%7D%7B125.7%7D%7D%5Ctimes100)
![m=111.15](https://tex.z-dn.net/?f=m%3D111.15)
Put the value into the equation (I)
![n=\dfrac{5.9855\times(0.395\times10^{-9}\times10^{2})^3\times6.023\times10^{23}}{111.15}](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7B5.9855%5Ctimes%280.395%5Ctimes10%5E%7B-9%7D%5Ctimes10%5E%7B2%7D%29%5E3%5Ctimes6.023%5Ctimes10%5E%7B23%7D%7D%7B111.15%7D)
Hence, The number of atoms in the unit cell is 2, the crystal structure for the alloy is body centered cubic.