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

`rho = (Z xx M)/(a^3 xx N_A)`
For bcc, `Z = 2, M = 6.94 g mol^(-1)`
`rho = 530 kg m^(-3) = (530 g xx 10^(3))/(cm^3 xx 10^(6)) = 0.530 g cm^(-3)`.
`0.53 = (2 xx 6.94)/(a^3 xx 6.02 xx 10^(23))`
`a^3 = (2 xx 6.94)/(a^3 xx 6.02 xx 10^(23)) = 43.5 xx 10^(-24) cm^(3)`
`a = 3.52 xx 10^(-8) cm = 352 "pm"`.