Q1. Answer the following sub-questions.
- (a)) A metallic element has a density of 7.15 g cm³, a lattice constant of 2.880 Å and an atomic weight of 51.9961. Calculate the number of atoms per unit cell of this element and predict its lattice crystal structure. (200 words)
- (b)) Show that the volume of the primitive cell in the reciprocal lattice space is inversely proportional to the volume of the primitive cell in the direct lattice. (200 words)
- (c)) At what angle will a diffracted beam emerge from the (110) planes of a cubic crystal of unit cell length 0.6 nm? Assume diffraction occurs in the first order and that the X-ray wavelength is 0.154 nm ? (200 words)
Key Points:
- Density formula ρ = (n * M) / (a³ * N_A) relates macroscopic density to atomic parameters.
- Number of atoms per unit cell (n) determines crystal structure; n=2 indicates BCC lattice.
- Primitive cell volume in direct lattice: V = |a₁ ⋅ (a₂ × a₃)|.
- Primitive cell volume in reciprocal lattice: V* = |b₁ ⋅ (b₂ × b₃)| = (2π)³/V.
Answer: This answer addresses key concepts in Condensed Matter Physics, specifically calculating atomic properties from macroscopic data, understanding the relationship between direct and reciprocal lattices, and applying Bragg's Law for X-ray diffraction. These topics are fundamental to understanding crystal structures and their characterization, as typically covered in an IGNOU MPH-012 course. The calculations presented demonstrate the practical application of theoretical formulas, linking macroscopi...