Question

How many atoms are effectively present per unit cell in this hypothetical crystal lattice?

• A. $\frac{3}{2}$
• B. $\frac{7}{2}$
• C. 4
• D. 7

Answer 1

The correct option is B $\frac{7}{2}$

I. 4 corner atom $\times \left(\frac{1}{8}\right)$ atom per unit cell = (1/2) atom

II. 4 face-centered atoms $\times \left(\frac{1}{2}\right)$ atom per unit cell = 2 atom

III. $(12\times \frac{1}{3})$ edge-centered atoms $\times \left(\frac{1}{4}\right)$ atom per unit cell = 1 atom

So, Total number of atoms per unit cell = $\left(\frac{1}{2}\right)+2+1=\left(\frac{7}{2}\right)$ atoms