Question

Lthium metal crystallises in a body centred cubic crystal. If the length of the side of the unit cell of lithium is $351\text{pm}$, the atomic radius of the lithium will be:
($\sqrt{3}=1.7$)

• A. $300.5\text{pm}$
• B. $240.8\text{pm}$
• C. $149.17\text{pm}$
• D. $75.5\text{pm}$

Answer 1

The correct option is C $149.17\text{pm}$

Here we are considering a BCC crystal.
In BCC, effective nuber of atoms is $Z=8\times \frac{1}{8}+1=2$
$\text{Again, unit cell length}\left(a\right)=351\text{pm}$
For, BCC crystal,
$a=\frac{4r}{\sqrt{3}},\text{where r is the radius of Li}$
$\therefore r=\frac{\sqrt{3}a}{4}=\frac{1.7\times 351}{4}=149.17pm$