# Uncertainly Principle Fast Neutrons

1. Oct 29, 2012

### 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

1. The problem statement, all variables and given/known data
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

2. Relevant equations

(Δx) x ((m)(Δv)) ≥ h/(4∏)

3. 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

2. Oct 29, 2012

### Staff: Mentor

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.