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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
Solid State

NTA Abhyas 2020 · Chemistry · Solid State

Element X crystallizes in 12 co-ordination fcc lattice. On applying...

Element X crystallizes in 12 co-ordination fcc lattice. On applying high temperature it changes to 8 co-ordination bcc lattice. Find the ratio of the density of the crystal lattice before and and after applying high temperature

Options

  1. A1:1
  2. B3:2
  3. C2:3\sqrt{2}: \sqrt{3}
  4. D2(2)2{\left(\sqrt{2}\right)}^{3}: {\left(\sqrt{3}\right)}^{3}

Correct answer

D. 2(2)2{\left(\sqrt{2}\right)}^{3}: {\left(\sqrt{3}\right)}^{3}

Step-by-step solution

Co. number is 12 means it is fcc lattice

Co. number is 8 means it is bcc lattice

fcc bcc

ρ1=4×at.massNa×a13ρ2=2×at.massNa×a23{ρ}_{1} = \dfrac{4 \times at . mass}{{N}_{a} \times {a}_{1}^{3}}{ρ}_{2} = \dfrac{2 \times at . mass}{{N}_{a} \times {a}_{2}^{3}}

ρ1ρ2=42×a23a13=2×(4r3)3(22r)3\dfrac{{ρ}_{1}}{{ρ}_{2}} = \dfrac{4}{2} \times \dfrac{{a}_{2}^{3}}{{a}_{1}^{3}} = \dfrac{2 \times {\left(\dfrac{4\text{r}}{\sqrt{3}}\right)}^{3}}{{( 2\sqrt{2\text{r}} )}^{3}}

=2×4×4×42×2×2×2×2(33)= \dfrac{2 \times 4 \times 4 \times 4}{2 \times 2 \times 2 \times 2 \times \sqrt{2} ( 3\sqrt{3} )}

=4233=2(2)3(3)3= \dfrac{4\sqrt{2}}{3\sqrt{3}} = \dfrac{2 ( \sqrt{2}{)}^{3}}{( \sqrt{3}{)}^{3}}
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