Particle through a slit Uncertainty of position

In summary, the conversation discusses the use of an air rifle to shoot 1.0-g particles at 100 m/s through a hole of diameter 2.0 mm. The question is how far an observer must be from the rifle to see the beam spread by 1.0 cm due to the uncertainty principle. The suggested equation to solve this problem is \Delta{x}\Delta{p} \geq \frac{\bar{h}}{2}, where \Delta{x} represents the uncertainty in position and \Delta{p} represents the uncertainty in momentum. The suggested approach of solving for \Delta{x} by expanding p to mv and plugging it in is deemed incorrect. The conversation suggests looking into Fraunhofer
  • #1
darkfall13
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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



[tex]\Delta{x}\Delta{p} \geq \frac{\bar{h}}{2}[/tex]

The Attempt at a Solution



If we solve for [tex]\Delta{x}[/tex] and expand [tex]p[/tex] to [tex]mv[/tex] and plug in we receive [tex]\Delta{x} = 5.275\cdot{10}^{-34}[/tex]. 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!
 
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  • #2
I realize this is an old thread, but I have the exact same question... so bump!
 

1. What is the uncertainty principle in particle physics?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental concept in quantum mechanics that states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

2. How is the uncertainty principle demonstrated through the particle through a slit experiment?

The particle through a slit experiment is a classic demonstration of the uncertainty principle. It involves shooting a particle, such as an electron, through a narrow slit. The resulting diffraction pattern shows that the particle's position and momentum cannot both be known with certainty at the same time.

3. What is the significance of the uncertainty principle in the field of quantum mechanics?

The uncertainty principle is significant because it challenges our traditional understanding of the physical world. It suggests that at a fundamental level, the behavior of matter and energy is not predictable and is subject to a degree of randomness.

4. Is the uncertainty principle limited to particles or does it apply to larger objects as well?

The uncertainty principle applies to all objects, regardless of their size. However, its effects are most noticeable at the quantum level, where the wave-like nature of particles becomes apparent.

5. How does the uncertainty principle affect our ability to measure and observe particles?

The uncertainty principle places a fundamental limit on our ability to measure and observe particles. It means that we can never know both the exact position and momentum of a particle at the same time. This has significant implications for experiments and technologies that rely on precise measurements of particles.

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