The Nobel Prize for physics was awarded to Robert Hofstadter for experimental wo

Question

The Nobel Prize for physics was awarded to Robert Hofstadter for experimental work involving scattering of 20-GeV electrons from atomic nuclei.

(a) what is the de Broglie wavelength of a beam of 20-GeV electrons?

(b) how does this wavelength compare to typical size of an atomic nucleus, which is about 10-15 m? (It is impossible to examine objects with kind of beam whose wave length is much larger than object in question: the beam will diffract around the object rather than reflect from it and will thus not produce a sharp image.)

(c) Does it much matter whether the "20 GeV" here refers to the total or just the relativistic kinetic energy of the electrons?

Explanation / Answer

A beam of electrons is E = 20 GeV                                          = 20*10^9 eV                                           = 20*10^9 * 1.6*10^-19J                                            = 32*10^-10 J K.E = 1/2 m v^2 32*10^-10 J = 1/2 * 9.11*10^-31 kg * v^2 speed of the electrons is v = 8.38*10^10 m/s             debrogile wavelength is = h / mv                                    = 6.625*10^-34 J s / 9.11*10^-31 kg * 8.38*10^10 m/s                                   = 8.67*10^-15 m b) wavelength compare to typical size of an atomic nucleus, is                8.67*10^-15 m / 10^-15 m            = 8.67 c) Total mass energy is 20 GeV and the relativistic mass energy is 0.511 MeV so it is not much matter to the total energy

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