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Problem: The densities of the elements K, Ca, Sc, and Ti are 0.86, 1.5, 3.2, and 4.5 g/cm3, respectively. One of these elements crystallizes in a body-centered cubic structure; the other three crystallize in a face-centered cubic structure.Which one crystallizes in the body-centered cubic structure? Justify your answer.

FREE Expert Solution

We have to determine which one of the given four metals should have a body-centered cubic unit cell.


A unit cell is the smallest repeating unit in a crystal lattice. Whole crystal lattice can be built by repeating the unit cell in three dimensions.

The body-centered and face-centered cubic unit cells are shown below:

 

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Problem Details

The densities of the elements K, Ca, Sc, and Ti are 0.86, 1.5, 3.2, and 4.5 g/cm3, respectively. One of these elements crystallizes in a body-centered cubic structure; the other three crystallize in a face-centered cubic structure.

Which one crystallizes in the body-centered cubic structure? Justify your answer.

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 Miller's class at UNG.