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An element cyrstallises in a structure h...

An element cyrstallises in a structure having a fcc unit cell of and edge 200 pm. Calculate its density if 200 g of this element contains `24xx 10^(23)` atoms.

A

`"41.66 g cm"^(-3)`

B

`"313.9 g cm"^(-3)`

C

`"8.117 g cm"^(-3)`

D

`"400 g cm"^(-3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Molar mass of the element =`200/(24xx10^23)xx6.023xx10^23="50.19 g mol"^(-1)`
For fcc, Z=4 , `V=a^3 =(200 xx 10^(-10))^3`
`d=(ZxxM)/(N_AxxV)=(4xx50.19)/(6.023xx10^23xx(200xx10^(-10))^3)`
`=41.66 g cm^(-3) `
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