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The new Large Hadron Collider (LHC) at CERN in Geneva, Switzerland accelerates protons to 3.5 TeV, and will ev?
The new Large Hadron Collider (LHC) at CERN in Geneva, Switzerland accelerates protons to 3.5 TeV, and will eventually accelerate then to 7 TeV. What is the wavelength of a 3.5 TeV proton? (This wavelength is the smallest size detail that a proton of this energy can resolve.)
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1 Answer
- oldprofLv 79 years agoFavorite Answer
Total energy E^2 = e^2 + k^2; where k = 3.5 TeV = 3.5E12 eV = 1.6E-19*3.5E13 Joules kinetic energy and e = 9.6 MeV = 9.6E6 eV = 1.6E-19*9.6E6 Joules rest mass energy.
The de Broglie wavelength, then, is found from E = hf = hc/L; so that L = hc/E = hc/sqrt(e^2 + k^2) = (6.63E-34*299E6)/(4E-10*sqrt((3.5E12)^2 + (9.6E6)^2)) = 1.42E-28 meters. ANS.
Note, despite how tiny this is, it's still 10^7 times bigger than the Planck Length 10^-35 m. We've a long way to go.
