Heisenberg's uncertainty principle, find uncertainty in position

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SUMMARY

The discussion focuses on calculating the uncertainty in the position of a proton using Heisenberg's uncertainty principle. The relevant formula is Δx ≥ h/(4mΔvπ), where h is Planck's constant, m is the mass of the proton, and Δv is the uncertainty in velocity. The user is attempting to solve for Δx with a given speed of (5.00±0.01) x 10^4 m/s but is unclear on how to incorporate the ±0.01 into the calculation. The expected result for the uncertainty in position is approximately 3 x 10^-10 meters.

PREREQUISITES
  • Understanding of Heisenberg's uncertainty principle
  • Familiarity with Planck's constant (h = 6.626 x 10^-34 J·s)
  • Knowledge of the mass of a proton (m = 1.6726 x 10^-24 kg)
  • Basic calculus for handling uncertainties in measurements
NEXT STEPS
  • Learn how to calculate uncertainties in physics experiments
  • Study the concept of relative vs. absolute uncertainty
  • Explore applications of Heisenberg's uncertainty principle in quantum mechanics
  • Investigate the implications of uncertainty in particle physics
USEFUL FOR

Students studying quantum mechanics, physics educators, and anyone interested in the mathematical applications of Heisenberg's uncertainty principle.

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Homework Statement


Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of a proton moving at a speed of (5.00±0.01) x 10^4 m/s.


Homework Equations


Δx\geq \frac{h}{4mΔv\pi}


The Attempt at a Solution


x\geq (6.626*10^-34)/(4pi(1.6726*10^-24)(5±0.01 * 10^4)

I get how to solve it, I just don't really understand what to do with the ±0.01. I'm assuming it's in meters, so I have to do 0.01/5 and then multiply that by 5*10^4, but I'm supposed to be getting 3*10^-10

Thanks in advance (:
 
Physics news on Phys.org
The formula says \Delta x=\frac{h}{4\pi m\Delta v}
What is \Delta v? Is it a relative or an absolute uncertainty?
 

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