Uncertainly Principle Fast Neutrons

[CGallin]

Hey everyone, I've been trying to figure out what went wrong here for abit now and I think maybe a fresh pair of eyes might help. If anyone could point me in the direction of my error that would be great.

Thanks

Homework Statement

An effective treatment for some cancerous tumors is irradiation with "fast" neutrons. The neutrons from this treatment have an average velocity of 3.0 x 10⁷ m/s. If the velocities of individual neutrons are known to be within 2% of this value, what is the uncertainty of one of them?

velocity = 3.0 x 10⁷ m/s
mass of neutron = 1.674920 x10^-21 kg
planck's constant = 6.626x10^-34m2 kg / s

Homework Equations

(Δx) x ((m)(Δv)) ≥ h/(4∏)

The Attempt at a Solution

Δx = (h/(4∏) / ((m)(Δv))

= ((6.626x10^-34m2 kg / s)/ (4∏)) / ((1.674920 x10^-21 kg)(3.0 x 10⁷ m/s)

Δx = 7.91 x 10^-22 meters

 

[mfb]

Is this really a quantum mechanics question?
Just based on the formulation, I would expect that "known to be" is just our ignorance about individual neutrons, not the fundamental uncertainty in the neutron wave function. In that case, the uncertainty would simply be a velocity uncertainty - and after some distance (and time), the beam is spread out in space as well.