Uncertainty principle and tv picture tube

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SUMMARY

The discussion centers on calculating the uncertainty in the position of electrons striking a screen in a TV picture tube, given an accelerating voltage (V) and an aperture diameter (Δy). The uncertainty in position (Δy) directly influences the uncertainty in momentum, as defined by Heisenberg's uncertainty principle. The user seeks guidance on applying these principles to derive the momentum uncertainty, specifically focusing on the x-component of momentum due to the distance (x) from the aperture to the screen.

PREREQUISITES
  • Understanding of Heisenberg's uncertainty principle
  • Familiarity with the concepts of electron behavior in electric fields
  • Knowledge of Planck's constant (h) and its application in quantum mechanics
  • Basic principles of momentum in physics
NEXT STEPS
  • Study the application of Heisenberg's uncertainty principle in particle physics
  • Learn about the relationship between voltage and electron acceleration in vacuum tubes
  • Explore calculations involving momentum and position uncertainties
  • Research the behavior of electron beams in cathode ray tubes (CRTs)
USEFUL FOR

Physics students, educators, and anyone interested in quantum mechanics and the behavior of electrons in electric fields, particularly in the context of television technology.

matpo39
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hey, I am really confused with this problem, i have tried to solve it for a while now but i can't seem to get it, i really don't even know where to start with it.

In a TV picture tube the accelerating voltage is V, and the electron beam passes through an aperture with a diameter of Delta_y and hits a screen which is a distance of x away.

What is the uncertainty in position of the point where the electrons strike the screen?
Use h for Planck's constant, m_e for the mass of an electron, and e for the magnitude of the charge on an electron.

any help would be great.
 
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The idea is that the uncertainty in the position of the particle after it passes the aperture is [itex]\Delta y[/itex], which, if it is small enough, leads to an uncertainty in the momentum of the particle.

Use Heisenberg to find the order of this uncertainty in momentum.
 
when i find the uncertainty in the momentum that will be the x component of the momentum since it is a distance x away from the tv?
 

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