A Beam of Neutrons $\left(m=939.6 \mathrm{MeV} / \mathrm{c}^{2}\right.$ ) of Momentum $12 \mathrm{keV} / \mathrm{c}$

A beam of neutrons $\left(m=939.6 \mathrm{MeV} / \mathrm{c}^{2}\right.$ ) of momentum $12 \mathrm{keV} / \mathrm{c}$ is passed through a single slit of width 0.1 $\mathrm{nm}$ . As a result of this, the neutron beam acquires an uncertainty in the component of the momentum that is transverse to the beam direction. The distance between the slit and a screen onto which the neutrons are projected is $1.5 \mathrm{~m}$ . Using the uncertainty principle, estimate the expected width of the neutron distribution on the screen.

A) $0.1 \mathrm{~mm}$
B) $5 \mathrm{~m}$
C) $50 \mathrm{~cm}$
D) $1 \mathrm{~cm}$