GATE 2026 MT – Question 49
A metal with body-centered cubic structure is analyzed by X-ray diffraction using monochromatic X-rays of wavelength 0.154 nm. The diffraction angle $2\theta$ for the $\{200\}$ plane is $60^\circ$ for first-order reflection. The atomic radius is ________ nm. (Rounded off to three decimal places.)
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Correct answer: 0.132 to 0.134
Explanation
Bragg’s law gives $d_{200}=\lambda/(2\sin\theta)=0.154/(2\sin30^\circ)=0.154\ \mathrm{nm}$. Since $d_{200}=a/2$, $a=0.308\ \mathrm{nm}$.
In BCC, atoms touch along the body diagonal, so $4r=\sqrt3a$. Thus $r=\sqrt3(0.308)/4=0.133368\ \mathrm{nm}$, rounding to **0.133 nm**.