Lithium has a bcc structure .its density is `530Kgm^(-1)` and its atomic mass is `6.94 g mol^(-1)`. Calculate the edge length of a unit cell of Lithium metal. `(N_(A)=6.02xx10^(23)mol^(-1))`

Options

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

Answer

D

Explanation

`a^(3)=(ZxxM)/(rhoxxN_(0)xxO^(-3))`
`z=2, M=6.94 g " mol"^(-1)`
`rho=530 kgm^(3)=(530xx1000)/(1xx(100)^(3)cm^(3))=0.53 g " cm"^(-3)`
`a^(3)=(2xx(6.94 g " mol"^(-1)))/((0.53g" cm"^(-3))xx(6.02xx10^(23)" mol"^(-1)))`
`4.35xx10^(-23)" cm"^(3)=43.5xx10^(-24)" cm"^(3)`
`a=(43.5xx10^(-24)" cm"^(3))^(1//3)=3.52xx10^(-8)cm`
`=352xx10^(-10)cm=352 "pm"`