How Does the Uncertainty Principle Apply to a Particle in a Femtometer Sphere?

In summary, the conversation discusses the momentum of a particle confined within a spherical radius of one femtometer. There are four possible options for the momentum: 20 keV/c, 200 keV/c, 200 MeV/c, and 2 GeV/c. The speaker suggests using the Heisenberg uncertainty principle to solve the problem, but notes that the answer may not be precise due to the problem being about volume. They also clarify that the uncertainty in the x-coordinate is 2 times the radius, not the radius itself.
  • #1
doubt
3
0
A particle is confined within a spherical radius of one femtometer(10^-15 m)?

Its momentum can be expected to be about-
1. 20 keV/c
2. 200 keV/c
3. 200 MeV/c
4. 2 GeV/c

How should I go about using HUP on a problem like this one? I tried substituting x=10^-15 meters in px=h/4 pi but the answer is wrong. Apparently because the problem is about volume.
 
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  • #2
We can only estimate the magnitude order of it; the answer is no way precise. Just pick the answer which is nearest to your answer.
By the way, the uncertainty in x-coordinate is 2R, not R.
 

Related to How Does the Uncertainty Principle Apply to a Particle in a Femtometer Sphere?

1. What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle.

2. Who discovered the uncertainty principle?

The uncertainty principle was first proposed by physicist Werner Heisenberg in 1927.

3. How does the uncertainty principle affect our understanding of the physical world?

The uncertainty principle challenges our classical understanding of the physical world by showing that the position and momentum of particles cannot be known with absolute certainty. It also highlights the probabilistic nature of quantum mechanics and the limitation of our ability to observe and measure particles.

4. Can the uncertainty principle be violated?

No, the uncertainty principle is a fundamental principle of quantum mechanics and has been supported by numerous experiments. It is a fundamental property of the physical world and cannot be violated.

5. What are the practical implications of the uncertainty principle?

The uncertainty principle has many practical implications, including its role in the development of technologies such as lasers and transistors. It also has implications in fields such as cryptography and quantum computing. Additionally, the uncertainty principle has led to a deeper understanding of the behavior of subatomic particles and the nature of the universe.

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