Answer:
the lattice constant is 0.270 inches
Explanation:
Given the data in the question;
For FCC lattice;
a = b = c, ∝ = β = α = 90°
from the image below;
AC = 0.19 + 0.19/2 + 0.19/2 + 2(0.001) inch
AC = 0.19 + 0.095 + 0.095 + 0.002
AC = 0.382 inches
Now using Pythagoras theorem
AC² = AB² + BC²
since a = b = c
AC² = a² + a²
(0.382)² = 2a²
2a² = 0.145924
a² = 0.145924 / 2
a² = 0.072962
a = √0.072962
a = 0.27011 ≈ 0.270 inches
Therefore, the lattice constant is 0.270 inches
