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.)

Wavelength of a proton or a neutron, λ ≈ 10^-15 m

Rest mass energy of an electron:

moc² = 0.511 MeV = 0.511 x 10⁶x 1.6 x 10⁻¹⁹ = 0.8176 x 10⁻¹³ J

Planck’s constant, h = 6.6 x 10⁻³⁴Js

Speed of light, c = 3x 10^s m/s

The momentum of a proton or a neutron is given as:

p=h/λ = (6.6 x 10⁻³⁴)/ 10^-15

= 6.6 x 10⁻¹⁹   kg m/s

The relativistic relation for energy (E) is given as:

E = p²c² + m²oc⁴

= (6.6 x 10⁻¹⁹ x 3 x 10⁸ )²+ (0.8176 x 10⁻¹³)² = 392.04 x 10⁻²² + 0.6685 x 10⁻²⁶

≈392.04 x 10⁻²²

Therefore ,E = 1.98 x 10⁻¹⁰

= ( 1.98 x 10⁻¹⁰ )/(1.6 x 10⁻¹⁹) = 1.24 x 10⁹ eV

= 1.24 BeV

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