Solving the Uncertainty Principle Homework

In summary, the problem involves calculating the energy using the equations P=h/lambda and E=p^2/2m. However, the given answer is different from the calculated answer. It is important to consider relativistic effects at high energies and use the equation E^2 = m_0^2 c^4 + p^2 c^2 instead. This provides the correct answer of 12 GeV.
  • #1
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Homework Statement


http://img340.imageshack.us/img340/3249/question.jpg

Homework Equations


P=h/lambda
E=p^2/2m


The Attempt at a Solution



Well, I calculated P using a wavelength of .1 femtometer. Then I plugged it into the energy equation. However, I got 1.5e14 eV, while the answer sheet says it's supposed to be 12 GeV. Have I done something wrong wrong? On the answer sheet my professor calculated P, and I got the same answer he got, but after that he just says therefore E=12GeV, not showing how he came to that conclusion.

Thanks for any help!
 
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  • #2
You cannot neglect relativistic effects at such high energies, thus the equation
[tex]E = \frac{p^{2}}{2m}[/tex] does not hold.
Instead you should use the relativistic equation
[tex]E^{2} = m_{0}^{2} c^{4} + p^{2} c^{2}[/tex]
 
  • #3
Ahh that makes sense and gives e the right answer. Thanks!
 

FAQ: Solving the Uncertainty Principle Homework

What is the Uncertainty Principle?

The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental concept in quantum mechanics that states that certain pairs of physical properties, such as position and momentum, cannot be simultaneously measured with arbitrary precision.

Why is it important to study the Uncertainty Principle?

The Uncertainty Principle is important because it challenges our classical understanding of the physical world and provides a deeper understanding of the behavior of subatomic particles. It also has practical applications in fields such as quantum computing and cryptography.

How does the Uncertainty Principle affect our daily lives?

The Uncertainty Principle primarily affects our daily lives through its impact on technology. For example, the principles of quantum mechanics and the uncertainty principle are the basis for the function of many electronic devices, such as computer chips and lasers.

Can the Uncertainty Principle be proven?

The Uncertainty Principle has been extensively tested and is considered a fundamental law of quantum mechanics. While it cannot be proven in the same way as a mathematical theorem, it has been confirmed through numerous experiments and is widely accepted by the scientific community.

How can the Uncertainty Principle be applied in scientific research?

The Uncertainty Principle is often applied in scientific research to study and understand the behavior of particles at the quantum level. It also has practical applications in fields such as quantum computing, where it is used to manipulate and control individual particles for various purposes.

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