A hypothetical element (atomic weight =300) crystallizes in a simple cubic lattice. For this crystal, the… · ABC26PH0818
Subject: Physical Chemistry · Chapter: Solid State Chemistry · Topic: Solid State – General · Exam: JAM 2001-2022 · Marks: 2 · Difficulty: Medium
A hypothetical element $($ atomic weight $=300)$ crystallizes in a simple cubic lattice. For this crystal, the first order X-ray diffraction with wavelength of $5 \AA$ appears at an angle of $30^{\circ}$. The density of the crystal is ____ g $\mathrm{cm}^{-3}$. [Avogadro number, $\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23}$ ]
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Answer: ≈ 3.99 g cm⁻³ — First-order reflection of a simple cubic lattice is (100): a = d = λ/(2 sin 30°) = 5 Å. ρ = M/(N_A a³) = 300/(6.02×10²³ × 1.25×10⁻²²) = 3.99 g cm⁻³.