Monochromatic X-rays having energy 2.8 × 10⁻¹⁵ J diffracted (first order) from (200) plane of a cubic crystal… · ABC26PH0803
Subject: Physical Chemistry · Chapter: Solid State Chemistry · Topic: Solid State – General · Exam: JAM 2001-2022 · Marks: 2 · Difficulty: Medium
Monochromatic X-rays having energy $2.8 \times 10^{-15} \mathrm{J}$ diffracted (first order) from (200) plane of a cubic crystal at an angle $8.5^{\circ}$. The length of unit cell in $\AA$ of the crystal (rounded off to one decimal place) is (Given: Planck's constant, $\mathrm{h}=6.626 \times 10^{-34} \mathrm{J} \mathrm{s} ; \mathrm{c}=3.0 \times 10^{8} \mathrm{m} \mathrm{s}^{-1}$ )
(a)9.8
(b)4.8
(c)2.4
(d)3.4
Answer
Answer: B ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
λ = hc/E = 6.626×10⁻³⁴ × 3×10⁸/2.8×10⁻¹⁵ = 7.1×10⁻¹¹ m = 0.71 Å. Bragg: d₂₀₀ = λ/(2 sin 8.5°) = 0.71/0.2956 = 2.40 Å; a = 2d₂₀₀ = 4.8 Å.