Uncertainty for a particle diffracted through a single slit

In summary, the question is asking for the minimum uncertainty in the vertical component of the momentum of a photon passing through a narrow slit, given the wavelength of the light and the distance from the slit to the screen. The equation used to solve this problem involves Planck's constant (h) and the uncertainty principle. The correct answer may differ depending on the value used for Planck's constant.
  • #1
GMarks
1
0

Homework Statement



A horizontal beam of laser light of wavelength 486 nm passes through a narrow slit that has width 0.0590 mm . The intensity of the light is measured on a vertical screen that is 2.90 m from the slit.
What is the minimum uncertainty in the vertical component of the momentum of each photon in the beam after the photon has passed through the slit?

Homework Equations


ΔyΔPy ≥ h

The Attempt at a Solution


I tried simply substituting the slit width for Δy and solving for momentum, but that gave me the wrong answer. I'm extremely confused, as this shouldn't be a hard question but I can't seem to get an answer the system will accept. Can anyone help?
 
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  • #2
GMarks said:
ΔyΔPy ≥ h
You mean ##\hbar##, right?
Please post your working and, if you know it, the official answer.
 

1. What is the definition of uncertainty for a particle diffracted through a single slit?

The uncertainty for a particle diffracted through a single slit refers to the inherent unpredictability in determining the exact position and momentum of the particle as it passes through the slit. This uncertainty is a fundamental principle in quantum mechanics and is described by the Heisenberg uncertainty principle.

2. How does the width of the slit affect the uncertainty of the diffracted particle?

The width of the slit directly affects the uncertainty of the diffracted particle. A narrower slit will result in a larger uncertainty, as the particle has a higher chance of striking the edges of the slit and changing its momentum. A wider slit will result in a smaller uncertainty, as the particle has a higher chance of passing through without changing its momentum.

3. What is the relationship between uncertainty and diffraction pattern for a particle through a single slit?

The uncertainty of a diffracted particle is directly related to the diffraction pattern. As the uncertainty increases, the diffraction pattern becomes wider and less defined. This is because a higher uncertainty means a larger range of possible paths for the particle to take, resulting in a wider spread of the diffraction pattern.

4. Can the uncertainty of a particle diffracted through a single slit be reduced?

No, the uncertainty of a particle diffracted through a single slit cannot be reduced. This is a fundamental principle in quantum mechanics and is not affected by any external factors. However, the uncertainty can be better understood and predicted through the use of mathematical models and calculations.

5. How does the uncertainty of a particle through a single slit differ from that of a double-slit experiment?

The uncertainty for a particle through a single slit differs from that of a double-slit experiment in that the single-slit experiment only has one path for the particle to take, resulting in a larger uncertainty. In contrast, the double-slit experiment has two possible paths for the particle, which can interfere with each other, resulting in a smaller uncertainty and a more defined diffraction pattern.

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