Question

Copper crystallizes as an FCC unit cell. If the atomic radius of copper is 1.28 $\overset{\text{o}}{\mathop{\text{A}}}\,$, then what is the edge length (in $\overset{\text{o}}{\mathop{\text{A}}}\,$ ) of the unit cell?
A. 2.16
B. 3.63
C. 3.97
D. 4.15

Answer 1

Hint: FCC means face centered cubic packing. FCC has six faces and eight corners. There is a relationship between radius and edge length of the unit cell in FCC and it is as follows.
\[r=\dfrac{\sqrt{2}a}{4}\]
Here, r = atomic radius and a = edge length of the unit cell.

Complete step by step answer:
- In question it is given that copper crystallizes as an FCC unit cell and given the atomic radius of the copper.
- We have to calculate the edge length of the unit cell in FCC formed by crystallization of copper.
- The formula used to calculate the edge length of the unit cell in FCC having relationship with the atomic radius is as follows.
\[r=\dfrac{\sqrt{2}a}{4}\]
Here, r = atomic radius = 1.28 $\overset{\text{o}}{\mathop{\text{A}}}\,$ and
a = edge length of the unit cell.
- Substitute all the known values in the above formula to get the edge length of the unit cell in FCC.
\[\begin{align}
& r=\dfrac{\sqrt{2}a}{4} \\
& a=\dfrac{4r}{\sqrt{2}} \\
& a=\dfrac{4\times 1.28}{\sqrt{2}} \\
& a=3.63\overset{\text{o}}{\mathop{\text{A}}}\, \\
\end{align}\]
- Therefore the edge length of the unit cell in FCC formed by crystallization of copper is 3.63 $\overset{\text{o}}{\mathop{\text{A}}}\,$ .

- So, the correct option is B.

Note: We can express the edge length in Angstroms and Pico meters (pm) also. The relationship between angstroms and Pico meter is as follows.
1 angstrom = 100 pm
Means one angstrom is equal to 100 Pico meters.