Which of the following is the correct relationship between edge length (a) and radius of sphere (r) located in a fcc unit cell?
Answer & explanation
Correct answer: option 4
The correct answer is option 4. All of these.
Face centered cubic unit cell (FCC)
let the unit cell edge length be ‘a’ and face diagonal AC = b.
In ∆ ABC
AC2 = b2 = BC2 + AB2 = a2 + a2 = 2a2 or b = \(\sqrt{2}\)a
If r is the radius of the sphere, we find b = 4r = \(\sqrt{2}\)a or a = \(\frac{4r}{\sqrt{2}}\)
a = 2\(\sqrt{2}\)r
we can also write, r = \(\frac{a}{2\sqrt{2}}\)