Light as a particle/ compton effect, conservation of energy and momentum

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SUMMARY

The discussion focuses on the application of conservation of energy and momentum in photon-electron interactions, specifically through various homework problems involving photon energy, momentum, and electron velocity. Key calculations include determining the final energy of a photon after colliding with an electron, the period of a monochromatic light beam, and the velocity of a helium nucleus post-collision with an x-ray photon. The equations utilized include E=hf, p=mv, and conservation principles, leading to definitive results such as a final photon energy of 32.4 eV and a helium nucleus velocity of 2 x 10^4 m/s.

PREREQUISITES
  • Understanding of photon energy calculations using E=hf
  • Knowledge of momentum conservation principles in collisions
  • Familiarity with the relationship between wavelength, frequency, and velocity of light
  • Basic grasp of kinetic energy equations, specifically E=1/2mv^2
NEXT STEPS
  • Study the Compton effect and its implications on photon-electron interactions
  • Learn about relativistic momentum and energy conservation in high-energy physics
  • Explore the derivation and applications of the de Broglie wavelength formula
  • Investigate advanced photon-electron collision scenarios using simulation tools
USEFUL FOR

Students in physics, particularly those studying quantum mechanics and particle physics, as well as educators seeking to enhance their understanding of photon interactions and conservation laws.

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Homework Statement



1. A photon with an initial energy of 33eV collides with an electron. If the speed of the electron after the collision is 4.56*10^5m/s the final energy of the photon is? [32.4eV]

2. Photons that compose a monochromatic beam of light each have a momentum of 1.50*10^-28 kgm/s. The period of this light [1.47*10^-14s]

3. an xray photon of wavelength .010nm strikes a helium nucleus (alpha particle) and bounces straight back. If the helium nucleus was originally at rest, calculate its velocity after interacting with the x-ray [2*104m/s]

4. A photon moving in an easterly direction with an energy of 6.21 *10^-15 J collides with an electron and scatters at an angle of 30 W of S. What is the velocity of the electron after the collision? [3.74 *10^7m/s [28 N of E]]

5. Calculate the frequency of an electron that has a speed of 9.2*10^5m/s [1.16*10^15hz]

Homework Equations



e=hf
E=1/2mv^2
conservation of momentum/energy
p=mv or h/lambda

The Attempt at a Solution



1.Energy of photon before = energy of electron after + energy of photon after.
energy of photon after = energy of photon before - energy of electron after

Ea = 33eV - (1/2 (9.11*10^-31) (4.56*10^5)^2)

i get 33eV seeing as how the energy of the electron is 9.47*10^-20 very small i can see why, what did i do wrong? this is my attempt maybe i did the whole thing wrong?2. I have no idea how to relate momentum of a photon (p=h/lambda) to time, no velocity some help here?

3. Is this conservation of energy? I tried hf=1/2mv^2 , but it didnt make sense and didnt work when you solve for v.

4. Am i not missing something in this question for conservation of energy i believe i don't have enough information, or at least i can't get it.

5. lambda = h/mv
lambda =(6.63*10^-34)/(9.11*10^-31)(9.2*10^5) =7.910 *10^-10 m

f = c/lambda = 3.79*10^17

i don't where else to get frequncy.. can't use Ek=hf
 
Last edited:
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