Back to Directory
NEET PHYSICSMedium

Sodium has body-centered packing. The distance between the two nearest atoms is 3.7 A˚3.7\text{ \AA}. The lattice parameter is:

A

6.8 A˚6.8\text{ \AA}

B

4.3 A˚4.3\text{ \AA}

C

3.0 A˚3.0\text{ \AA}

D

8.6 A˚8.6\text{ \AA}

Step-by-Step Solution

  1. Identify the Given Data: Crystal structure: Body-centered cubic (bcc) Nearest neighbor distance, d=3.7 A˚d = 3.7\text{ \AA}
  2. Formula for bcc Lattice: In a bcc lattice, the nearest neighbor distance dd is the distance between a corner atom and the atom at the body center. This distance is half of the body diagonal. The relationship between the nearest neighbor distance dd and the lattice parameter aa (edge length) is given by d=3a2d = \frac{\sqrt{3}a}{2}.
  3. Calculate Lattice Parameter (aa): Rearranging the formula to solve for aa: a=2d3a = \frac{2d}{\sqrt{3}} Substitute the given value: a=2×3.73=7.41.732≈4.27 A˚≈4.3 A˚a = \frac{2 \times 3.7}{\sqrt{3}} = \frac{7.4}{1.732} \approx 4.27\text{ \AA} \approx 4.3\text{ \AA}
  4. Conclusion: The lattice parameter is approximately 4.3 A˚4.3\text{ \AA}.
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started