$($a$)$ Derive linear density expressions for BCC $[110]$ and $[111]$ directions in terms of the atomic radius R and $($b$)$ compute lin$$ar density values for these same two directions for tungsten.

$($a$)$

$[110]$: I $,$ atom $\frac{?}{R}$

$[111]$: atom$/$R

$($b$)$

$[110]$:

$\frac{1}{m}$

$[111]$:

$\frac{1}{m}$