A metal crystallizes into two cubic phases, face-centred cubic and body-centred cubic, which have unit cell lengths `3.5` and `3.0 A`, respectively. Calculate the ration of densities of fcc and bcc.

Options

A. `1.259:1`
B. `1:1.259`
C. `3:2`
D. `1.142:1`

Answer

A

Explanation

Unit cell length for fcc=3.5 Å
Unit cell length for bcc = 3.0 Å
`therefore` Density in fcc=`(n_1xx at.wt.)/(V_1xxN_A)`
Density in bcc =`(n_2xxat.wt.)/(V_2xxN_A)`
or `"Density (fcc)"/"Density (bcc)"=n_1/n_2xxV_2/V_1 =4/2xxV_2/V_1 [ {:(therefore , "for fcc,",n_1=4),(therefore , "for bcc,",n_2=2):}]`
Volume of fcc = `V_1=a^3=(3.5xx10^(-8))^3cm^3`
and volume for bcc =`V_2=a^3=(3.0xx10^(-8))^3 cm^3`
`therefore "Density (fcc)"/"Density (bcc)"=(4xx(3.0xx10^(-8))^3)/(2xx(3.5xx10^(-8))^3)`
=1.259 or 1.259:1