Problem about uncertainty principle

In summary, the conversation discusses the calculation of Δx and Δp for an electron pulse with a width of 1 nanosecond and a kinetic energy of 1 keV. There is a question about the uncertainty of momentum and how to calculate the position uncertainty when both Δx and Δp are unknown. The solution involves calculating the velocity based on the length of 1 ns.
  • #1
Andurien
5
0
We have an electron pulse of width 1 nanosecond and with kinetic energy of 1keV. We have to calculate Δx and Δp.

I have a question regarding this problem. If they give us the kinetic energy of the electron pulse then we know exactly the momentum right? And so the uncertainty of momentum would be 0 and therefore Δx=∞ for the uncertainty principle ΔxΔp≥h. However I feel this reasoning is incorrect otherwise the problem would be trivial.
 
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  • #2
The momentum, together with the energy, have some small uncertainty (<<1 keV). You can calculate the minimal uncertainty of this, based on the position uncertainty.
 
  • #3
And how do I calculate the position uncertainty? Both Δx and Δ p are unkown.
 
  • #4
Δx is known. It is hidden in the "length" of 1ns, and you can calculate the velocity.
 
  • #5
Thank you I finally solved I didn't understand the meaning of that 1ns.
 

1. What is the Uncertainty Principle?

The Uncertainty Principle is a fundamental concept in quantum mechanics, which states that it is impossible to simultaneously know the exact position and momentum of a particle. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

2. Who discovered the Uncertainty Principle?

The Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927. Heisenberg's principle was based on his observations of the behavior of subatomic particles, which challenged the traditional notion of determinism in classical physics.

3. How does the Uncertainty Principle affect our understanding of the physical world?

The Uncertainty Principle has significant implications for our understanding of the physical world. It fundamentally challenges the idea of a deterministic universe, where everything can be predicted with certainty. Instead, it suggests that there is inherent randomness and unpredictability at the subatomic level.

4. Can the Uncertainty Principle be applied to macroscopic objects?

While the Uncertainty Principle is typically associated with the behavior of subatomic particles, it can also apply to larger objects. However, the effects are so small that they are practically unnoticeable at the macroscopic level. This is because the uncertainty in position and momentum of larger objects is incredibly small compared to that of subatomic particles.

5. How has the Uncertainty Principle been tested and verified?

The Uncertainty Principle has been extensively tested and verified through numerous experimental studies in quantum mechanics. One example is the double-slit experiment, where the behavior of particles passing through two slits is observed. The results of this experiment align with the predictions of the Uncertainty Principle, providing strong evidence for its validity.

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