Your answer is partially correct.

$($a$)$ Derive the linear density expressions for the FCC $[100]$ direction in terms of the atomic radius $R.$

$\sqrt[\phantom{2}]{\frac{3}{4R}}$

$\frac{1}{R\sqrt[\phantom{2}]{2}}$

$\frac{1}{2R\sqrt[\phantom{2}]{2}}$

$($b$)$ Compute linear density value for the same direction for copper. Round your answer to $3$ significant digits.

$n{m}^{-1}.$