Question

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.

Answer 1

the lattice constant is 0.270 inches

Step-by-step 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