Similar to electron diffraction, neutron diffraction is also used for the determination of the structure of molecules. If the wavelength used is $800 \, pm$, calculate the characteristic velocity associated with the neutron.

According to de Broglie's equation, $\lambda = \frac{h}{mv}$.
Rearranging for velocity, we get $v = \frac{h}{m\lambda}$.
Given:
$h = 6.626 \times 10^{-34} \, J \cdot s$
$m = 1.67493 \times 10^{-27} \, kg$ (mass of a neutron)
$\lambda = 800 \, pm = 800 \times 10^{-12} \, m$
Substituting the values:
$v = \frac{6.626 \times 10^{-34}}{(1.67493 \times 10^{-27}) \times (800 \times 10^{-12})}$
$v = \frac{6.626 \times 10^{-34}}{1.339944 \times 10^{-36}}$
$v \approx 494.5 \, m \cdot s^{-1}$.
Thus, the characteristic velocity associated with the neutron is approximately $494.5 \, m \cdot s^{-1}$.