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Problem: Consider a body-centered cubic unit cell as shown here.a. How many corner atoms (orange) are shown in this image?b. What fraction of each corner atom is inside the boundaries of the cube? c. How many body atoms shown in this image? d. What fraction of each body atom is inside the boundaries of the cube? e. If you sum all the fractions of atoms, how many atoms are actually inside a body-centered cubic unit cell?

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Problem Details

Consider a body-centered cubic unit cell as shown here.

a. How many corner atoms (orange) are shown in this image?

b. What fraction of each corner atom is inside the boundaries of the cube? 

c. How many body atoms shown in this image? 

d. What fraction of each body atom is inside the boundaries of the cube? 

e. If you sum all the fractions of atoms, how many atoms are actually inside a body-centered cubic unit cell?

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

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Based on our data, we think this problem is relevant for Professor Toupadakis' class at UCD.