The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure of protons and neutrons appears at the minute length-scale of 10–15 m or less. This structure was first probed in early 1970’s using high energy electron beams produced by a linear accelerator at Stanford, USA. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron = 0.511 MeV.)

Given:


Order of length of quark structure, λ = 10-15m


Rest mass energy of electron = 0.511 MeV


i.e. m0c2 = 0.511 MeV


→ m0c2 = 0.511 × 1.6 × 10-19


→ m0c2 = 0.817 × 10-13 J


By using De-Broglie wavelength equation we can write,



Where,


p = momentum of particle


h = Planck’s constant = 6.6 × 10-34Js


λ = wavelength


The equation of energy at relativistic speed is,


E2 = p2c2 + m20c4


E2 = (6.6 × 10-19 × 3 × 108)2 + (0.817 × 10-13)2


→ E = (392.07 × 10-22)0.5


→ E = 1.9 × 10-10J


Hence the energy of electron emitted from linear accelerator is 1.9 × 10-10J.


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