Lithium has a bcc structure .Its density is `530 kg m^(-3)` and its atomic mass is `6.94 g mol^(-1)` .Calculate the edge length of a unit cell of lithium metal `(N_(A) = 6.02 xx 10^(23) mol^(-1))`

Options

A. 527 pm
B. 264 pm
C. 154 pm
D. 352 pm

Answer

a

Explanation

When a is in pm and other quantities oin CGS units, we have
` p = ( Z xx M)/( a^(3) xx N_(0) xx 10^(-30)) g//cm^(3)`
for bcc, Z =2 , M = 6.94 ` g " mol"^(-1)`
` p = 530 kg m^(-3) = ( 530 xx 1000)/( 1xx (100)^(3) cm^(3)) = 0.53 " gcm"^(-3)`
`a^(3) = ( 2 xx 6.94)/( 0.53 xx6.02 xx 10^(23) xx 10^(-30))`
` = 4.35xx 10^(7) =43.5 xx 10^(6)`
` a= ( 43.5)^(1//3) xx 10^(2) = 3.52 xx 10^(2) "pm" = 352 "pm" `