Heisenberg uncertainty principle calculations

In summary, there is some confusion about the uncertainties in the Heisenberg principle. The chemistry book presents two problems, one involving a marble and the other involving an electron, and gives different values for the uncertainties. Upon further research, it is found that there are different methods for calculating uncertainties, but ultimately it is not a precise measurement and a rough estimate is sufficient. A more accurate analysis would require advanced concepts such as wave functions and Fourier transformations.
  • #1
Jzhang27143
38
1
I am having some trouble understanding what to use for the uncertainties in the Heisenberg principle. My chemistry book has two problems on this principle. One asks to find the minimum uncertainty in the position of a marble of mass 1.0g given that its speed is known within +- 1.0 mm/s. The other asks to find the minimum uncertainty in the speed of an electron confined to within the diameter of 200. pm.

The book says that the uncertainty of the speed in the first problem is 2.0 mm/s and the uncertainty of position in the second problem is 200. pm. I thought that the uncertainties are 1.0 mm/s in the first problem and 100. pm since uncertainty is defined as estimate +- uncertainty. I went to other sources and found a good number that use my book's reasoning and others that use my reasoning. What do I actually use when calculating uncertainty?
 
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  • #2
It does not matter, as both methods just give a rough estimate. A proper analysis would have to take the exact shape of the distribution into account, which probably means you would need to set up some wave function and do a Fourier transformation on it. I guess you did not learn that yet, so the rough estimate is fine - and a factor of two does not matter there.
 

1. What is the Heisenberg uncertainty principle?

The Heisenberg 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. This means that the more precisely we know the position of a particle, the less we can know about its momentum, and vice versa.

2. How is the Heisenberg uncertainty principle calculated?

The Heisenberg uncertainty principle is calculated using the following equation: Δx × Δp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant.

3. What are some applications of the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle has numerous applications in quantum mechanics, including in the prediction and understanding of the behavior of subatomic particles, the development of quantum computing and cryptography, and the creation of advanced technologies such as MRI machines.

4. Can the Heisenberg uncertainty principle be violated?

No, the Heisenberg uncertainty principle is a fundamental principle of quantum mechanics and has been tested and confirmed through numerous experiments. It is considered a fundamental limitation of our ability to measure and understand the behavior of particles at the quantum level.

5. Are there any criticisms of the Heisenberg uncertainty principle?

While the Heisenberg uncertainty principle is widely accepted and has been supported by experimental evidence, there have been some criticisms and alternative theories proposed. Some scientists argue that the uncertainty principle is due to our limited understanding and measurement capabilities, rather than a fundamental property of particles.

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