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

D

Explanation

When a is in pm and other quantities in CGS units, we have `rho=(ZxxM)/(a^3xxN_0xx10^(-30))g//cm^3`
For bcc, Z=2 , M=`6.94 "g mol"^(-1)` , `rho=530 kg m^(-3)=(530xx1000)/(1xx(100)^3cm^3)=0.53 g cm^(-3)`
`therefore a^3=(2xx6.94)/(0.53xx6.02xx10^23xx10^(-30))`
`=4.35xx10^7=43.5xx10^6`
`therefore a=(43.5)^(1//3)xx10^2 =3.52xx10^2` pm =352 pm