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  • Can someone help me with this, 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 remai

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

  • Option 1)

    \frac{3\sqrt{3}}{4\sqrt{2}}

  • Option 2)

    \frac{4\sqrt{3}}{3\sqrt{2}}

  • Option 3)

    \frac{\sqrt{3}}{\sqrt{2}}

  • Option 4)

    \frac{1}{2}

 

Answers (1)

As we learnt that

Density of cubic unit cell -

d = \frac{zM}{a^3N_o}

 

- wherein

Where,

d = density of crystal

z = no. of effective constituent particles in one unit cell

M = molecular weight

a = edge length of unit cell

No = 6.022*1023

 

 For BCC , a = \frac{4r}{\sqrt{3}}

For FCC , a = \frac{4r}{\sqrt{2}}

\frac{d_{BCC}}{d_{FCC}} = \frac{\frac{Z_{BCC}XM}{N_{A}Xa^{3}}}{\frac{Z_{FCC}XM}{N_{A}Xa^{3}}} = \frac{2X(\frac{4r}{\sqrt{2}})^{3}}{(\frac{4r}{\sqrt{2}})^{3} X 4} = \frac{3}{4}\sqrt{\frac{3}{2}}

 


Option 1)

\frac{3\sqrt{3}}{4\sqrt{2}}

This is correct.

Option 2)

\frac{4\sqrt{3}}{3\sqrt{2}}

This is incorrect.

Option 3)

\frac{\sqrt{3}}{\sqrt{2}}

This is incorrect.

Option 4)

\frac{1}{2}

This is incorrect.

Posted by

Vakul

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