A student assembles ball bearings that are 0.19 inches in diameter into an FCC lattice using glue which makes for a 0.001 inch thick bond between bearings. What is the lattice constant in inches of this FCC crystal? Three significant digits and fixed point notation.

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

po-215 i got it right on the quiz