Answer
The velocity of the neutron needed is $v=3.165\times10^3m/s$.
Work Step by Step
*The de Broglie relationship: $$\lambda=\frac{h}{mv}$$
$\lambda$: wavelength of object
$h$: Planck's constant ($h=6.626\times10^{-34} J.s$)
$m$: mass of object
$v$: velocity of object
1) Find the known variables
- Wavelength of the neutron: $\lambda=1.25{\buildrel _{\circ} \over {\mathrm{A}}}=1.25\times10^{-10}m$
- Mass of the neutron: $m\approx1.675\times10^{-27}kg$
2) Calculate the velocity of the neutron
$v=\frac{h}{m\lambda}=\frac{6.626\times10^{-34}}{(1.675\times10^{-27})\times(1.25\times10^{-10})}\approx3.165\times10^{3}m/s$
