Hey there, budding physicist! 🌌✨ Ready to dive into the fascinating world of the Compton effect? Let's do it!

• Setting the Stage: It's the 1920s. Einstein's ideas about photoelectricity are buzzing in the minds of physicists.
• The Main Actor: Arthur H Compton. This cool American scientist decided to take a deeper look at high-energy, short-wavelength X-radiation.
• His Discovery: When these X-rays bounced off elements with small proton numbers, their wavelengths increased!

• He used a carbon target.
• To produce the X-radiation, he zapped electrons onto a molybdenum target using a potential difference of 17kV.
• These X-rays were then focused onto the carbon block.
• A special detector picked up the scattered X-ray photons.
• He noticed
  • Two peaks in the spectrum at every scattering angle (except straight-on).
  • One from atom scattering (small peak) and another from free-electron scattering (big peak).
  • The wavelength shift increased with the scattering angle.

• Energy of an X-ray photon is given by E =\(\frac {hc}{ λ}\).
• Compton proved that the difference in wavelengths before and after scattering is - Δλ = \(\frac {h}{me × c}\) (1− cosθ), where θ is the scattering angle and me is the mass of the electron.

• Why do X-rays scatter? They bump into free electrons in carbon. A teeny bit of their energy ionizes the carbon atoms. The rest? Interacts with a free electron, making the electron scoot and the X-ray scatter.
• The scattering is like a two-dimensional collision (imagine two balls colliding in mid-air!).
• Photon-Electron Interaction is a tango dance! The electron "recoils" and the X-ray photon is left with lesser energy, dancing away with a longer wavelength!

Bonus Round: Compton's results tossed wave models of light out the window. Why? Classical explanations didn't predict a wavelength shift with small radiation intensity, but Compton's experiments did!