Unit Cell Video Lessons

Video Thumbnail

Concept

Problem: When spheres of radius r are packed in a body-centered cubic arrangement, they occupy 68 % of the available volume. Use the fraction of occupied volume to calculate the value of a, the length of the edge of the cube in terms of r.

FREE Expert Solution

Recall: The body-centered cubic cell contains one atom in the center of the cube and an atom in each of the corners. It looks like this:

If r = radius of the sphere, then the diagonal d = 4r, since it spans through 2 spheres. We can express the diagonal b in terms of the length of the cube a, using Pythagorean theorem.

80% (132 ratings)
View Complete Written Solution
Problem Details

When spheres of radius r are packed in a body-centered cubic arrangement, they occupy 68 % of the available volume. Use the fraction of occupied volume to calculate the value of a, the length of the edge of the cube in terms of r.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Unit Cell concept. You can view video lessons to learn Unit Cell. Or if you need more Unit Cell practice, you can also practice Unit Cell practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Norton's class at FSCJ.