Question 11.34:
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 the early 1970s 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.)

Hint: \(\mathrm{E}^{2}=\mathrm{p}^{2} \mathrm{c}^{2}+\mathrm{m}_{0}^{2} \mathrm{c}^{4 }\)

Step 1: Find the momentum of a proton.
The momentum of a proton or a neutron is given as:

p=hλ=6.6×10341015=6.6×1019 kg m/s

Step 2: Find the electron energy emitted.
The relativistic relation for energy (E) is given as:

E2=p2c2+m02c4=(6.6×1019×3×108)2+(0.8176×1013)2=392.04×1022+0.6685×1036392.04×1022E=1.98×1010 J=1.98×10101.6×1019=1.24×109eV=1.24BeV

Thus, the electron energy emitted from the accelerator at Stanford, USA might be of the order of 1.24 BeV.