1. √(3)/√(2) 2. 3√(3)/4√(2) 3. 4√(3)/3√(2) 4. 1/2

Answer: 2. 3√(3)/4√(2) Density =Z M/a³ N_A . Since M and atomic radius r are the same, compare Z/a³ . bcc: Z=2 , a=4r/sqrt3 . fcc: Z=4 , a=2sqrt2 r . dfracρ_bccρ_fcc=2/4·(2sqrt2 rsqrt3/4r)³=1/2(sqrt6/2)³=3sqrt6/8=3sqrt3/4sqrt2 .

Topic: Kossel-Lewis approach, ionic and covalent bonds· Chemical Bonding and Molecular Structure

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

1. \(\frac{\sqrt{3}}{\sqrt{2}}\)

2. \(\frac{3\sqrt{3}}{4\sqrt{2}}\)

3. \(\frac{4\sqrt{3}}{3\sqrt{2}}\)

4. \(\frac{1}{2}\)

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Answer: 2. \(\frac{3\sqrt{3}}{4\sqrt{2}}\)

Density \(=\dfrac{Z\,M}{a^3 N_A}\). Since M and atomic radius \(r\) are the same, compare \(Z/a^3\).

bcc: \(Z=2\), \(a=\dfrac{4r}{\sqrt3}\).
fcc: \(Z=4\), \(a=2\sqrt2\,r\).

\(\dfrac{\rho_{bcc}}{\rho_{fcc}}=\dfrac{2}{4}\cdot\left(\dfrac{2\sqrt2\,r\sqrt3}{4r}\right)^3=\dfrac12\left(\dfrac{\sqrt6}{2}\right)^3=\dfrac{3\sqrt6}{8}=\dfrac{3\sqrt3}{4\sqrt2}\).

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

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