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JEE Advanced 2016 Paper 1 · Chemistry · Solutions, Solid State and Surface Chemistry · medium

(s) regarding crystal lattices. (Atomic mass of Fe=55.85 g mol^-1, NA=6.022×10^23 mol^-1.)

One or more options correct

Select the correct statement(s) regarding crystal lattices. (Atomic mass of Fe=55.85 g mol−1\mathrm{Fe}=55.85\ \mathrm{g\,mol^{-1}}, NA=6.022×1023 mol−1N_A=6.022\times10^{23}\ \mathrm{mol^{-1}}.)
  1. A. The packing efficiency of a body-centred cubic arrangement of identical atoms is about 68%68\%.
  2. B. Iron is bcc with unit cell edge 287 pm287\ \mathrm{pm}; its density is about 7.85 g cm−37.85\ \mathrm{g\,cm^{-3}}.
  3. C. In a face-centred cubic lattice of atoms of radius rr, the largest sphere that fits in an octahedral void has radius 0.414 r0.414\,r.
  4. D. In a hexagonal close-packed structure, the number of tetrahedral voids equals the number of atoms.
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Answer: A, B, C

(A) Correct. In bcc, atoms touch along the body diagonal, 3a=4r\sqrt3a=4r, with 22 atoms per cell; packing fraction =2⋅43πr3a3=3π8=0.68=\dfrac{2\cdot\frac43\pi r^3}{a^3}=\dfrac{\sqrt3\pi}{8}=0.68. (B) Correct. Two atoms per cell: ρ=2×55.856.022×1023×(2.87×10−8)3=7.85 g cm−3\rho=\dfrac{2\times55.85}{6.022\times10^{23}\times(2.87\times10^{-8})^3}=7.85\ \mathrm{g\,cm^{-3}} (the accepted value is close to this). (C) Correct. In fcc atoms touch along the face diagonal, a=22 ra=2\sqrt2\,r; an octahedral void sits at the edge centre, so its radius is a2−r=(2−1)r=0.414 r\dfrac a2-r=(\sqrt2-1)r=0.414\,r. (D) Incorrect. In hcp and ccp there is one octahedral void per atom but two tetrahedral voids per atom, so tetrahedral voids are twice the number of atoms.
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