Question

Silver has FCC structure and its atomic radius is 1.414 amstrong. Find the volume of the unit cell?

Answer 1

Answer on Question #61295-Physics-Solid State Physics

Silver has FCC structure and its atomic radius is 1.414 amstrong. Find the volume of the unit cell?

Solution

Remember that a face-centered unit cell has an atom in the middle of each face of the cube. The square represents one face of a face-centered cube:

Here is the same view, with 'd' representing the side of the cube and '4r' representing the 4 atomic radii across the face diagonal.

Using the Pythagorean Theorem, we find:

$$d ^ {2} + d ^ {2} = (4 r) ^ {2}$$ $$r ^ {2} = \frac {d ^ {2}}{8}$$ $$d = \frac {r}{2 \sqrt {2}}$$

The volume of the unit cell is

$$d ^ {3} = \left(\frac {r}{2 \sqrt {2}}\right) ^ {3} = \frac {(1 . 4 1 4 \cdot 1 0 ^ {- 1 0} m) ^ {3}}{1 6 \sqrt {2}} = 1. 2 5 \cdot 1 0 ^ {- 3 1} m ^ {3}$$

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