A metal crystalizes into two cubic phases, face centred cubic (FCC) and body centred cubc (BCC), whose unit cell lengths are 3.5 and `3.0A^(@)`, respectively. Calculate the ratio of densities of FCC and BCC.

Options

A. 1.259
B. 12.59
C. 0.259
D. 0.0259

Answer

A

Explanation

Density, `d=(zxx"Formula mass of substance")/(N_(0)xxa^(3))`
Since for FCC, `z=4 and` for `BCC,z=2`
`d_(F C C)=(4xx"Formula mass of metal")/(N_(0)xx(3.5)^(3)) and d_(B C C)=(2xx"Formula mass of metal")/(N_(0)xx(3)^(3))`
Dividing `d_(F C C) and d_(B C C),(d_(F C C ))/(d_(BC C))=(4)/(2)xx((3)^(3))/((3.5)^(3))=2xx0.6297=1.259`