A metal crystallizes into two cubic phases, face- centred cubic (fcc) and body -centred cubic (bcc)whose unit cell lengths are 3.5 and 3.0 Å respectively. Calculate the ratio of the densities of fcc and bcc.

A metal crystallizes into two cubic phases, face- centred cubic (fcc)

1.	A metal crystallizes into two cubic phases, face- centred cubic (fcc) and body -centred cubic (bcc)whose unit cell lengths are 3.5 and 3.0 Å respectively. Calculate the ratio of the densities of fcc and bcc.
Answer» <html><body><p></p>Solution :Denstiy ` (p) = ( Z <a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a> M)/(a^(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>) xx N_(<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>)) ` <br/> ForZ = 4,a = 3.5 Å= 3.5 Å= 3.5 ` xx 10^(-8)`cm . <br/>` p_("fcc")= (4xxM) /((3.5 xx 10^(-8))xx N_(0)) ` <br/> for bcc, Z =<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a> , a = 3.0 Å = 3.0 ` xx 10^(-8)`cm <br/>`p_("bcc")= ( 2xx M)/((3.0 xx10^(-8))^(3) xx N_(0)) therefore p_("fcc")/p_("bcc") = ( <a href="https://interviewquestions.tuteehub.com/tag/4xx-1883349" style="font-weight:bold;" target="_blank" title="Click to know more about 4XX">4XX</a> (3.0 xx 10^(-8))^(3))/(2xx (3.5 xx10^(-8))^(3) ) =1.259`</body></html>