Answer
$\lambda = 90~nm$
Work Step by Step
We can find the final speed of the neutron:
$v = \sqrt{2ad}$
$v = \sqrt{(2)(9.8~m/s^2)(1.0~m)}$
$v = 4.427~m/s$
We can find the de Broglie wavelength:
$\lambda = \frac{h}{m~v}$
$\lambda = \frac{6.626\times 10^{-34}~J~s}{(1.67\times 10^{-27}~kg)(4.427~m/s)}$
$\lambda = 9.0\times 10^{-8}~m$
$\lambda = 90~nm$
