Electrons accelerated to an energy of 49 GeV have a de Broglie wavelength ? smal

Question

Electrons accelerated to an energy of 49 GeV have a de Broglie wavelength ? small enough for them to probe the structure within a target nucleus by scattering from the structure. Assume that the energy is so large that the extreme relativistic relation p = E/c between momentum magnitude p and energy E applies. (In this extreme situation, the kinetic energy of an electron is much greater than its rest energy.)

(a) What is ??
fm

(b) If the target nucleus has radius R = 4.9 fm, what is the ratio R/??

Explanation / Answer

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Electrons accelerated to an energy of 49 GeV have a de Broglie wavelength ? small enough for them to probe the structure within a target nucleus by scattering from the structure. Assume that the energy is so large that the extreme relativistic relation p = E/c between momentum magnitude p and energy E applies. (In this extreme situation, the kinetic energy of an electron is much greater than its rest energy.)

(a) What is ??
fm

(b) If the target nucleus has radius R = 4.8 fm, what is the ratio R/??

Answer

energy   E   = 49 GeV     = 49*10^9   eV (   1.6*10^-19 J /eV )   = 78.4 *10^-10 J

(a)

wave length   ?   = hc / E    = (6.63*10^-34 J ) ( 3*10^8 m/s) / 78.4 *10^-10 J

              ?   = 0.253*10^-16    = 0.0253 fm

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(b)

radius   = 4.8 fm

R / ?    =   4.8fm   /   0.0253 fm    = 189.72

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