Lithium has a bcc structure. Its density is 530 kg m 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

For bcc, `Z=2, rho=530 kg m^(-3), " at, mass of " Li=6.94 g mol^(-1), N_A = 6.02 xx 10^(23) mol^(-1)`
`rho=530 kg m^(-3) = (530xx1000 g)/(1xx(100)^3 cm^3) = 0.33 g cm^(-3)`
`rho = (ZxxAt. massa)/(N_A xxa^3), a^3 = (Zxx At. mass)/(N_d xxrho) = (2xx6.94)/(6.02xx10^(23)xx0.53)`
`a^3 = 4.35 xx 10^(-23) cm^3 = 43.5 xx 10^(-24) cm^3`
`a = 3.52 xx 10^(-8) cm`
`a=352 xx10^(-10) cm = 352` pm