How Much Kinetic Energy Do Electrons Need to Resolve a 10fm Nucleus?

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SUMMARY

The discussion centers on calculating the kinetic energy required for electrons to resolve a nucleus of size 10 femtometers (fm). Participants utilized the de Broglie wavelength equation, leading to an initial calculation of 1.50 x 10^10 eV, but the correct answer is established as 1240 MeV. The discrepancy arises from the need to apply relativistic formulas due to the kinetic energy exceeding the rest energy of the electron. This highlights the importance of using appropriate equations in high-energy physics calculations.

PREREQUISITES
  • Understanding of de Broglie wavelength and its application in particle physics.
  • Familiarity with energy-momentum conservation principles.
  • Knowledge of relativistic energy equations, particularly for particles with significant kinetic energy.
  • Basic concepts of nuclear size measurements in femtometers (fm).
NEXT STEPS
  • Study the relativistic energy-momentum relation for particles.
  • Learn about the implications of de Broglie wavelength in high-energy physics.
  • Explore advanced kinetic energy calculations for electrons in particle physics.
  • Investigate the significance of femtometer-scale measurements in nuclear physics.
USEFUL FOR

This discussion is beneficial for physics students, educators, and researchers focusing on particle physics, particularly those interested in nuclear resolution techniques and relativistic effects in electron interactions.

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Homework Statement


To "obeserve" small objects,one measures the diffraction of the particles whose de Broglie wavelength is approximately equal to the object's size.
Find the kinetic energy(in electron volts) required by the electrons to resolve
c) a nucleus of size 10fm.


Homework Equations


I use the de broglie equation
~ = wavelenth
~= h/(2MeEk)^1/2
the ans i found is 1.50x10^10 eV
and energy-momentum conservation
E2=p2c2+Me2c4
but I can't find the correct answer for it
the ans i found is 124MeV

the real ans given is 1240Mev
is there any way to find it??
 
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I get the same answer you do.
 
does tat mean something wrong with the ans given??
or i should use relativistic formula since the kinetic energy of electron is larger thn rest energy of electron?
 

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