Calculating De Broglie Wavelength from Kinetic Energy

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SUMMARY

The de Broglie wavelength of a particle with mass m and kinetic energy KE is accurately expressed by the formula λ = hc / √(KE(KE + 2mc²). This equation derives from the relationship between energy and momentum in relativistic physics, specifically utilizing the kinetic energy equation E_k = √((pc)² + (mc²)²) - mc². The discussion emphasizes the necessity of understanding relativistic effects when calculating the de Broglie wavelength for particles with significant kinetic energy.

PREREQUISITES
  • Understanding of de Broglie wavelength concepts
  • Familiarity with kinetic energy equations in relativistic physics
  • Knowledge of momentum-energy relationships
  • Basic grasp of particle physics and mass-energy equivalence
NEXT STEPS
  • Study the derivation of the de Broglie wavelength formula
  • Learn about relativistic momentum and energy equations
  • Explore applications of de Broglie wavelength in quantum mechanics
  • Investigate the implications of relativistic effects on particle behavior
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Students and professionals in physics, particularly those focusing on quantum mechanics, particle physics, and relativistic dynamics.

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Homework Statement


Show that the de Broglie wavelength of a particle of mass m and kinetic energy KE is given by

\lambda = \frac{hc}{\sqrt{KE(KE + 2mc^2)}}



Homework Equations





The Attempt at a Solution


I know:

KE = {\gamma}mc^2 - mc^2 = pc - mc^2

But from here I am lost. I have a hunch that I need to use the equation that equates Energy and Momentum, but I'm lost.
 
Last edited:
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The problem is that your equation only applies to the relativistic limit, in general
<br /> E_k = \sqrt{(pc)^2 + (mc^2)^2} - mc^2<br />
Try using that.
 

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