GATE 2023 MT – Question 60
A polycrystalline BCC metal is examined with monochromatic X-rays of wavelength 0.25 nm. Its first diffraction peak has Bragg angle $\theta=30^\circ$. The atomic radius is ______ nm (two decimal places).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.13 to 0.17
Explanation
Bragg’s law gives $d=\lambda/(2\sin30^\circ)=0.25$ nm. The first BCC reflection is (110), so $a=\sqrt2d$. Body-diagonal contact gives $r=\sqrt3a/4=\sqrt6(0.25)/4=0.1531$ nm. Rounded answer: **0.15 nm**.