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Iron exhibits bcc structure at roomj tem...

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

A

`sqrt(3)/sqrt(2)`

B

`(4sqrt(3))/(3sqrt(2))`

C

`(3sqrt(3))/(4sqrt(2))`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
C
For bcc lattice, `Z=2, a=(4r)/sqrt(3)`
For fcc lattice, `Z=4, a=2sqrt(2r)`
`(rho("room temp."))/(rho(90^(@)C))=(((ZM)/(N_(0)a^(3)))"bcc")/(((ZM)/(N_(0)a^(3)))"fcc")`
For the same metal iron, both M and r are constant
`(rho("room temp."))/(rho(190^(@)C))=2/4((2sqrt(2r))/(4r//sqrt(3)))^(3)=((3sqrt(3))/(4sqrt(2)))`
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