Counting Particles Passing Through a Hole

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SUMMARY

The discussion focuses on calculating the number of particles passing through a small hole under random motion without external forces. Key equations include the energy of a photon, represented as E=hν, and the energy of multiple photons, E=nhν. Additionally, the energy of particles is expressed as E=(nħ²k²)/(2m), where k is defined as k=(2π)/λ, and λ is related to the diffraction angle by λ=2d sin(θ). The importance of providing detailed context in questions is emphasized for clarity.

PREREQUISITES
  • Understanding of photon energy equations (E=hν)
  • Knowledge of wave-particle duality and diffraction principles
  • Familiarity with quantum mechanics concepts, including wave vectors (k) and Planck's constant (ħ)
  • Basic grasp of trigonometry related to angles and sine functions
NEXT STEPS
  • Study the principles of diffraction and its effects on particle behavior
  • Learn about quantum mechanics and the implications of wave-particle duality
  • Research the derivation and applications of the energy equations for photons and particles
  • Explore advanced topics in statistical mechanics related to particle motion
USEFUL FOR

Students and professionals in physics, particularly those interested in quantum mechanics, particle physics, and wave phenomena. This discussion is beneficial for anyone looking to deepen their understanding of particle behavior in various conditions.

Endarmacional
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I want to find out how many paricles on random move passing through a little hole ?
There is no condition or force acting on eachof them. :biggrin: :biggrin:Thanks guys:biggrin: :biggrin:
 
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[tex]E=h\nu[/tex]

which is the energy for one photon, then can you see what the energy of many photons is??

[tex]E=nh\nu[/tex]

where n is the number of photons, hence rearrage to get n,

i presume the photons get diffracted as they go through the hole in which case

[tex]E=\frac{nhc}{\lambda}[/tex]

where lambda is
[tex]\lambda=2d\sin\theta[/tex]

because you haven't given information on what you are given ie what values you have, I will also give you this for a particle,

[tex]E=\frac{n\hbar^{2}k^{2}}{2m}[/tex]

where

[tex]k=\frac{2\pi}{\lambda}[/tex]

and as before [tex]\lambda=2d\sin\theta[/tex]



also when asking questions, it is best to put more into them, your own workings and understanding and also a bit more in about the question, it is not easy to understand what you are asking with only 2 lines of writing

best wishes

Newo
 
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