Answer
0.559 nm.
Work Step by Step
The maxima occur at angles $\theta$ given by $2d sin \theta=m \lambda$, where d is the spacing between adjacent atomic planes, 0.440 nm. “First order” means that m = 1.
$$\lambda =\frac{2 d sin \theta }{1 }=\frac{ 2(0.440\times10^{-9}m) sin 39.4^{\circ}}{1 }=5.59\times10^{-10}m$$
