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.)

To understand the energy of the electron beams used to probe the quark structure of protons and neutrons, we need to consider the relationship between energy and wavelength in particle physics. The wavelength of a particle is inversely related to its momentum, which is influenced by its energy. When probing structures at the scale of 10^-15 meters, we are dealing with very high energies.

Energy-Wavelength Relationship

The de Broglie wavelength formula gives us a way to relate the wavelength (λ) of a particle to its momentum (p):

λ = h / p

Here, h is Planck's constant (approximately 6.626 x 10^-34 Js). The momentum of a particle can also be expressed in terms of its energy (E) and mass (m) using the relativistic relation:

E² = (pc)² + (m₀c²)²

For an electron, the rest mass energy is 0.511 MeV, but when we accelerate it to high energies, we need to consider the total energy, which includes kinetic energy.

Calculating the Required Energy

To probe structures on the order of 10^-15 meters, we can rearrange the de Broglie wavelength equation to find the required momentum:

p = h / λ

Substituting λ = 10^-15 m into the equation gives:

p = 6.626 x 10^-34 Js / 10^-15 m = 6.626 x 10^-19 kg·m/s

Finding the Energy

Now, we can relate momentum to energy. For relativistic particles, we can use:

E = pc

Using c (the speed of light, approximately 3 x 10⁸ m/s), we find:

E = (6.626 x 10^-19 kg·m/s) x (3 x 10⁸ m/s) ≈ 1.988 x 10^-10 J

To convert this energy into MeV (1 eV = 1.6 x 10^-19 J), we divide by the conversion factor:

E ≈ (1.988 x 10^-10 J) / (1.6 x 10^-19 J/eV) ≈ 1240 MeV

Conclusion on Energy Levels

Thus, the energy of the electron beams used in the early 1970s to probe the quark structure of protons and neutrons was on the order of approximately 1 GeV (giga-electronvolt), which is equivalent to 1000 MeV. This high energy was necessary to achieve the short wavelengths required to investigate the minute structures within protons and neutrons effectively.

In summary, the probing of quark structures required electron beams with energies around 1 GeV, demonstrating the significant energy scales involved in particle physics and the intricate relationship between energy, momentum, and wavelength.