GATE 2025 MT – Question 49
X-ray diffraction using monochromatic radiation of wavelength 0.154 nm is performed on powder samples of metal A (FCC structure) and metal B (BCC structure). The first peak in each occurs at a Bragg angle $\theta=20^\circ$. The ratio (lattice parameter of metal A)/(lattice parameter of metal B) is ______ (rounded to two decimal places).
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Correct answer: 1.20 to 1.25
Explanation
Bragg’s law is $2d\sin\theta=\lambda$. Equal wavelength and angle therefore give equal first-peak plane spacings.
The first allowed FCC reflection is (111), so $a_A=\sqrt3d$. The first BCC reflection is (110), so $a_B=\sqrt2d$.
Thus $a_A/a_B=\sqrt{3/2}=1.2247\ldots$, giving **1.22**.