Problem: An oxide of titanium crystallizes with the following unit cell (titanium = gray; oxygen = red).What is the formula of the oxide?

🤓 Based on our data, we think this question is relevant for Professor Roychowdhury's class at RUTGERS.

FREE Expert Solution

There are 9 titanium atoms in the structure of which eight are at the corners of the unit cell and one in the center.

Contribution of one atom at the corner: 1/8

There are 8 atoms hence

8×18=1

Contribution of 1 atom at the center: 1

Total number titanium atoms: 2

There are 6 oxygen atoms in the structure, four of which are at the face centers and two are close to the center.

In face centers, the contribution is 1/2

Therefore the number of oxygen atoms is:

(2×1)+(4×12)=4

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Problem Details

An oxide of titanium crystallizes with the following unit cell (titanium = gray; oxygen = red)

The unit cell for an oxide of tin. The unit cell has one gray atom (tin) within the cell and eight gray atoms at the corners of the cell (one eighth in and seven eighths out). The unit cell also has two red atoms (oxygen) within the cell and four red atoms within the faces of the cell (half in and half out)..

What is the formula of the oxide?

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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 Roychowdhury's class at RUTGERS.