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Iron exhibits bcc structure at room temp...

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

A

`1/2`

B

`sqrt3/sqrt2`

C

`(3sqrt3)/(4sqrt2)`

D

`(4sqrt3)/(3sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
C
For bcc lattice, number of atoms present in unit cell = 2 and edge length of unit cell, a = `(4r)/sqrt3`. For fcc lattice, number of atoms present in unit cell = 4 and edge length of unit cell, a = `2sqrt2r`.
`(d_(25^(@)C))/(d_(900^(@)C))=((ZM)/N_(A^(a^(3))))_(bc c)/(((ZM)/(N_(A^(a^(3)))))_(fc c))=2/4((2sqrt2r)/((4r)/sqrt3))^(3)=((3sqrt3)/(4sqrt2))`
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