Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50?

Correct option is C. 90
In a BCC unit cell, the atoms touch along the body diagonal. The body diagonal length can be expressed in terms of the unit cell edge length (a) and the atomic radius (r). For a BCC structure, the body diagonal length is 4r. Also, the relationship between the body diagonal length and the unit cell edge length (a) in a cube is given by:
√3 * a = 4r
Let rA be the radius of atom A and rB be the radius of atom B. We are given that rB = 2rA. In the given scenario, the body diagonal consists of two atoms (one atom at each corner along the diagonal) therefore the body diagonal length is 4rA + 4rB = 4rA + 4(2rA) = 12rA
The body diagonal length is also given by √3 * a, where 'a' is the unit cell edge length. Therefore:
√3 * a = 12rA
We are given that a = 50. Substituting this value:
√3 * 50 = 12rA
rA = (√3 * 50) / 12
Now, let's consider the unit cell edge length if only atom B were present. In this case, the body diagonal length would be 4rB = 8rA.
√3 * a' = 8rA
a' = (8rA) / √3
Substituting the value of rA:
a' = (8 * (√3 * 50) / 12) / √3
a' = (8 * 50) / 12
a' = 400 / 12
a' = 100/3 ≈ 33.33
However, this calculation is not directly relevant to the question. The problem statement needs clarification or a diagram to accurately solve for the given options. The provided solution 'C. 90' appears to be incorrect based on the available information and standard BCC geometry. More information is needed to solve the problem properly.