In a face-centered cubic (FCC) structure, the length of the diagonal of the face is equal to four times the atomic radius. The interplanar spacing for the (110) and (111) planes can be calculated using the formula d = a / sqrt(2 * h^2 + k^2 + l^2), where a is the lattice constant and (hkl) represents the Miller indices of the plane.
Step-by-step explanation:
Lead crystallizes in a face-centered cubic (FCC) structure, which means that it has atoms at all the corners and centers of each face of the cube. In the FCC structure, the length of the diagonal of the face is equal to four times the atomic radius (d = 4r).
To calculate the interplanar spacing for the (110) plane, we can use the formula:
d110 = a / sqrt(2 * h2 + k2 + l2)
where a is the lattice constant and (hkl) represents the Miller indices of the plane. For the (110) plane, h = 1, k = 1, and l = 0.
Similarly, for the (111) plane, the Miller indices are h = 1, k = 1, and l = 1.
Using the given lattice constant of 4.95 Å, we can substitute the values into the formula to calculate the interplanar spacing for both planes.