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. 2.335
B. 1.259
C. 1.555
D. 2.232

Answer

B

Explanation

Density `(rho) =(Z_("eff") xx M_(W))/(a^3 xx N_A)`
For fcc , `Z_("eff") = 4 `
`rho`fcc `=( 4xx M_w)/((3.5 xx 10^(-8))^3xx N_A)`
for bcc, `Z_("fcc") = 2 `
`rho`fcc = `(2xx M_w)/((3.5xx10^(-8))^3 xx N_A)`
`(rho "f1")/(rho f"cc") = (4 xx (3)^3)/(3.5)^3 xx 2) = 1.26`