Question

Sodium (Na) exhibits body-centered-cubic (BCC) crystal structure with atomic radius 0.186 nm. The lattice parameter of Na unit cell is ................... nm.

Hint:

For BCC crystals, the lattice parameter is related to the atomic radius by \( a = \frac{4r}{\sqrt{3}} \).

Answer 1

Correct Answer: 0.42

Step 1: Use the relation for BCC crystal structure.
In a body-centered cubic (BCC) structure, the relation between the atomic radius \( r \) and the lattice parameter \( a \) is given by: \[ a = \frac{4r}{\sqrt{3}} \] where \( r = 0.186 \, \text{nm} \) is the atomic radius.
Step 2: Calculate the lattice parameter.
Substituting the value of \( r \): \[ a = \frac{4 \times 0.186}{\sqrt{3}} = 0.528 \, \text{nm} \]
Step 3: Conclusion.
Thus, the lattice parameter of Na unit cell is 0.528 nm.