Heisenberg Uncertainty Principle

In summary, the conversation discusses the use of the angular spread of the central diffraction pattern to estimate the uncertainty in the y-component of momentum of an electron. This is then used, along with the Heisenberg uncertainty principle, to estimate the minimum uncertainty in the y-coordinate of an electron after passing through a slit. The calculation involves using equations 1, 2, and 3 to determine the wavelength of the electron, the angular spread of the diffraction pattern, and the uncertainty in the momentum and position of the electron. The relationship between the distance from the screen and the certainty of the momentum is also discussed.
  • #1
EEWannabe
32
0

Homework Statement


A beam of 50eV electrons travel towards a slit of width 6 micro metres. The diffraction pattern is observed on a screen 2m away.

Use the angular spread of the central diffraction pattern (+/- lambda / slit width) to estimate the uncertainty in the y-component of momentum of an electron.

Use this result and the Heisenberg uncertainty principle to estimate the minimum uncertainty in the y-coordinate of an electron just after it has passed trough the slit. Comment on this result.

Homework Equations


n[tex]\lambda[/tex] = d sin[tex]\theta[/tex] [1]
[tex]\lambda[/tex] = [tex]\frac{h}{p}[/tex] [2]
E = [tex]\frac{p^{2}}{2m}[/tex] [3]

The Attempt at a Solution



Okay, well I first began by using equation 3 combined with equation 2 to work out the wavelength of the electron. This came out as 1.74 * 10^-10 m.

Re-arranging equation 1 i get [tex]sin\theta[/tex] = +/- lambda/d = +/- 2.9*10^-5

Now i get to the crux of my problem

QM.jpg


It asks to work out the uncertainty in the y component of the momentum, is the uncertainty in the y position given by what's labelled there in the picture, or is it from the central point to the top of the fringe?

Assuming that it is what I've drawn, that leads me to the uncertainty in momentum being = 4.55*10^-31. Well okay.

However again I'm troubled by the next part, it says using the result of the past bit...I can't see how they relate at all! :(. Also i can't see how the further away the screen gets, the more certain the momentum will become! I'm confused.

Thanks for reading this far !

I appreciate any help you can offer!
 
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  • #2
any help would be great- this is in for tomorrow :(
 

FAQ: Heisenberg Uncertainty Principle

What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics that states it is impossible to simultaneously know the exact position and momentum of a particle. In other words, the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

Who discovered the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927.

How does the Heisenberg Uncertainty Principle impact our understanding of the world?

The Heisenberg Uncertainty Principle challenges the classical notion of determinism, which suggests that if we know the initial conditions of a system, we can predict its future behavior. This principle shows that at the quantum level, there is inherent uncertainty and randomness in the behavior of particles, which has major implications for our understanding of the physical world.

Is the Heisenberg Uncertainty Principle still relevant today?

Yes, the Heisenberg Uncertainty Principle remains a fundamental principle in quantum mechanics and is widely accepted by the scientific community. It has also been confirmed by numerous experiments and has been incorporated into many modern theories in physics.

How does the Heisenberg Uncertainty Principle relate to everyday life?

While the Heisenberg Uncertainty Principle is most commonly applied in the realm of quantum mechanics, it can also be seen in everyday life. For example, when we measure the position of an object, we alter its momentum, and vice versa. This principle also has implications in fields such as technology, where it is used in devices like MRI machines, and in philosophy, where it has sparked debates about the nature of reality.

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