Particle through a slit Uncertainty of position

[darkfall13]

Homework Statement

An air rifle is used to shoot 1.0-g particles at 100 m/s through a hole of diameter 2.0 mm. How far from the rifle must an observer be to see the beam spread by 1.0 cm because of the uncertainty principle? Compare this answer with the diameter of the Universe (2x10^26 m)

Homework Equations

\Delta{x}\Delta{p} \geq \frac{\bar{h}}{2}

The Attempt at a Solution

If we solve for \Delta{x} and expand p to mv and plug in we receive \Delta{x} = 5.275\cdot{10}^{-34}. So I believe I'm on the wrong track, how do we use the hole diameter (if even needed) and what else should I look at to begin this problem? Fraunhofer Diffraction? de Broglie waves?

Thank you!

 

[Bmop]

I realize this is an old thread, but I have the exact same question... so bump!