Question on Heisenberg uncertainty principle

In summary, in a diffraction setup where particles with a de Broglie wavelength of 633 nm pass through a single slit of width 0.2 mm, the Heisenberg uncertainty principle can be used to estimate the minimum range of angles over which the particle distribution spreads out. This range is typically considered to extend from -π/2 to +π/2, with a central value of 0 radians. However, for a rough estimate, half the slit width can also be used as the initial position uncertainty. The resulting range can then be compared to the value obtained from the single slit diffraction equation, which gives 1/2 of the peak value.
  • #1
Nivlac2425
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Homework Statement


Particles pass through a single slit of width 0.2 mm in a diffraction setup. The de Broglie wavelength of each particle is 633 nm. After the particles pass through the slit, they spread out over a range of angles. Use the Heisenberg uncertainty principle to determine the minimum range of angles.


Homework Equations


Heisenberg uncertainty principle
sin [tex]\theta[/tex]= [tex]\lambda[/tex]/W


The Attempt at a Solution


I'm not sure exactly what a minimum range of angles mean. Is it all the possible angles through which the electrons can follow?
I believe I'm stuck on how to use the uncertainty principle to find an angle. I know that the equation for diffraction through a single slit might be useful.
 
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  • #2
Well, the wording of these sort of statements can be tricky. The particle distribution will actually extend through the full -π/2 to +π/2 range. However, the distribution becomes negligibly small beyond some angle.

Strictly speaking, "uncertainty" in physics usually means an rms deviation from a central value (in this case, 0 radians). Since, in this case, we are going after a ballpark figure, it's probably okay to use half the slit width as the initial position uncertainty.

The idea is to use the Heisenberg relation as an estimate, rather than the single slit diffraction equation. Of course, you are welcome to compare the two results afterward--in which case one might use the angle where the diffraction equation gives 1/2 of the peak value.
 
  • #3
I see, so the distribution includes the negative angles.
Thank you for a clear explanation!
 

Related to Question on Heisenberg uncertainty principle

1. What is the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle states that it is impossible to know both the exact position and momentum of a particle at the same time. This means that the more accurately we measure the position of a particle, the less accurately we can know its momentum, and vice versa.

2. Who discovered the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle was first proposed by German physicist Werner Heisenberg in 1927 as part of his uncertainty principle, which also includes the uncertainty of energy and time.

3. What is the significance of the Heisenberg uncertainty principle in quantum mechanics?

The Heisenberg uncertainty principle is a fundamental principle in quantum mechanics, which is the branch of physics that studies the behavior of subatomic particles. It tells us that there are inherent limitations to our ability to measure and predict the behavior of particles at a very small scale.

4. How does the Heisenberg uncertainty principle affect our daily lives?

The Heisenberg uncertainty principle may seem like it only applies to the microscopic world, but it actually has implications in our daily lives. For example, it is the reason why we cannot accurately predict the exact location and speed of a moving car at the same time.

5. Are there any exceptions to the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle is a fundamental principle in quantum mechanics and has been proven to hold true in countless experiments. However, there are theories that suggest it may not apply in certain extreme conditions, such as in black holes or during the early moments of the Big Bang.

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