$$

$$

Calculate the LD along the direction $\frac{?}{\text{b}\text{a}\text{r}}(1)10$ in a FCC unit cell. Answer the following questions to reach the answer:

$1-$ How long is the $[110]$ direction shown in Figure in terms of the lattice narameter $($a$)?$

$2-$ How long is the $\frac{?}{\text{b}\text{a}\text{r}}(1)10$ direction shown in Figure in terms of the atomic radius $(R)?$

$3-$ How many atomic radii lie along the $[110]$ direction shown in Figure.

$4-$ The linear density is defined as $LD=\frac{\text{l}\text{e}\text{n}\text{g}\text{t}\text{h}of\text{a}\text{t}\text{o}\text{m}\text{s}in\text{t}\text{e}\text{r}\text{m}\text{s}ofR}{\text{L}\text{e}\text{n}\text{g}\text{t}\text{h}of\text{l}\text{i}\text{n}\text{e}in\text{t}\text{e}\text{r}\text{m}\text{s}ofR}$

What is the LD for the $[110]$ direction in a FCC unit cell $($in Figure$)?$