Interplanar Spacing and Atomic Radius of Niobium Atom

What is the interplanar spacing for the (211) set of planes in niobium?

a) Approximately 0.0851 nm

What is the atomic radius of the niobium (Nb) atom?

b) Approximately 0.0738 nm

Interplanar Spacing and Atomic Radius Calculation

(a) The interplanar spacing for the (211) set of planes in niobium is approximately 0.0851 nm. (b) The atomic radius of the niobium (Nb) atom is approximately 0.0738 nm.

Calculating the interplanar spacing for the (211) set of planes in niobium and the atomic radius of the Nb atom involves using Bragg's law and the formula for interplanar spacing in a BCC crystal structure.

Interplanar Spacing Calculation:

Bragg's law states: nλ = 2d sinθ

Using the given values and rearranging the formula, we find that the interplanar spacing is approximately 0.0851 nm.

Atomic Radius Calculation:

The interplanar spacing (d) and atomic radius (r) are related in a BCC crystal structure. By rearranging the formula, we calculate the atomic radius to be approximately 0.0738 nm.

Therefore, the interplanar spacing for the (211) set of planes in niobium is about 0.0851 nm, and the atomic radius of the niobium atom is approximately 0.0738 nm.