The $\sin 2 \theta$ values obtained from X-ray powder diffraction pattern of a solid are $2 \mathrm{x}, 4 \mathrm{x}$, $6 \mathrm{x}, 8 \mathrm{x}$ where x is equal to 0.06 . The wavelength of X-ray used to obtain this pattern is $1.54 \AA$. The unit cell and the unit cell length, respectively are
(a)$\mathrm{BCC}, 3.146 \AA$
(b)$\mathrm{FCC}, 3.146 \AA$
(c)$\mathrm{SCC}, 6.281 \AA$
(d)$\mathrm{BCC}, 1.544 \AA$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
sin²θ in the ratio 2:4:6:8 (h²+k²+l² = 2, 4, 6, 8) is the bcc sequence (110), (200), (211), (220). From (110): a = λ√2/(2 sin θ) = 1.54 × 1.414/(2 × 0.3464) = 3.146 Å.