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NEET 2018
Exam
NEET
Year
2018
Subject
Chemistry
Chapter
Solid State

NEET 2018 · Chemistry · Solid State

Iron exhibits BCC structure at room temperature. Above 900 ^ ° C ,...

Iron exhibits BCC structure at room temperature. Above 900°C{900}^{°}C, it transforms to FCC structure. The ratio of the density of iron at room temperature to that at 900°C{900}^{°}C is (assuming molar mass and atomic radii of iron remains constant with temperature)

Options

  1. A3342\dfrac{3\sqrt{3}}{4\sqrt{2}}
  2. B4332\dfrac{4\sqrt{3}}{3\sqrt{2}}
  3. C32\dfrac{\sqrt{3}}{\sqrt{2}}
  4. D12\dfrac{1}{2}

Correct answer

A. 3342\dfrac{3\sqrt{3}}{4\sqrt{2}}

Step-by-step solution

BCC=4r=3a⇒a=4r3BCC = 4r = \sqrt{3}a ⇒ a = \dfrac{4r}{\sqrt{3}}

FCC=4r=2a⇒a=4r2FCC = 4r = \sqrt{2}a ⇒ a = \dfrac{4r}{\sqrt{2}}

dBCCdFCC=ZBCC×MNAa3ZFCC×MNAa3=2×MNA(4r3)34×MNA×(4r2)3=3432\dfrac{{d}_{BCC}}{{d}_{FCC}} = \dfrac{\dfrac{{Z}_{BCC} \times M}{{N}_{A}{a}^{3}}}{\dfrac{{Z}_{FCC} \times M}{{N}_{A}{a}^{3}}} = \dfrac{\dfrac{2 \times M}{{N}_{A}{\left(\dfrac{4r}{\sqrt{3}}\right)}^{3}}}{\dfrac{4 \times M}{{N}_{A} \times {\left(\dfrac{4r}{\sqrt{2}}\right)}^{3}}} = \dfrac{3}{4}\sqrt{\dfrac{3}{2}}.
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