The Most Energetic Rays

Subatomic particles like protons, neutrons, or electrons can only come from collisions of rays that vibrate very rapidly, because each particle requires a large amount of energy to make it. By the mid-20th century there were accelerators powerful enough to produce pairs of particles from pure energy. The minimum energy for pair production is that required to produce an electron and a positron. The energy a ray can provide is directly proportional to its vibration rate, and inversely proportional to its wavelength. Let’s work with the wavelength, because it is the easier to visualize.

## Only X- or Gamma-Rays Make Particles

The wavelengths of the rays that make subatomic particles must be very small. Obviously, subatomic particles are smaller than atoms. The rays that make them must likewise have wavelengths smaller than the size of atoms. We can get an exact maximum for the wavelengths we need to make subatomic particles by considering wave energy and particle mass.

Consulting the table in Appendix A, we find the wavelength of a ray that can make an electron, 2.4 micro-micrometers. To make a proton or neutron we need rays with a wavelength of 1.3 thousandths of a micro-micrometer.

To see how much shorter these wavelengths are than those of visible light, let’s first choose a color for comparison, one whose wavelength is a convenient number near the middle of the visible light spectrum. Blue light has a wavelength of 470 thousandths of a micrometer and green light about 528 thousandths of a micrometer. Therefore 485 thousandths of a micrometer corresponds to a greenish blue. The wavelength of an energetic X-ray or gamma ray that will make an electron is 200 000 times shorter than the wavelength of greenish-blue light. The X-ray or gamma ray is vibrating 200 000 times faster and is 200 000 times more energetic than greenish-blue rays.

Now multiply the proton or neutron wavelength by 2000 times 200 000, or 400 000 000. That gives a wavelength of 528 thousandths of a micrometer, the wavelength of green light. The energetic X-rays or gamma rays one needs to make a proton or a neutron are 400 000 000 times more energetic than rays of green light. It is clear that only very energetic X-rays or gamma rays can make particles by colliding.

In the above examples we have calculated the energy of the photon needed to make one particle. Of course we need another photon of equal energy in a colliding ray to make another particle, identical with the first but opposite in sign if the first particle carries an electric charge. This second particle is called the antiparticle of the first. The antiparticle of an electron is a positron. A proton’s antiparticle is an antiproton. A neutron is the antiparticle of another neutron.

We might think that we could use lower energies to make pairs of neutrinos, since these very lightweight particles have very little mass. An ultraviolet photon provides enough energy to materialize the mass of a neutrino. However, neutrinos do not come from pure energy reactions. They come from decaying nuclei. One type of decay ejects an electron and a neutrino and converts a neutron to a proton. Another type of decay ejects a positron and a neutrino and converts a proton to a neutron. There is always matter present before and after the reaction takes place, in the form of a proton or a neutron. Therefore two photons, colliding in space far from any material, cannot produce neutrinos.

Gamma-ray wavelengths are very small. To interact, it is not enough for the paths of two gamma rays to cross. The photons must arrive at the interaction region at about the same time. This means that gamma-ray photons can travel long times and great distances in random directions before materializing.

Consulting the table in Appendix A, we find the wavelength of a ray that can make an electron, 2.4 micro-micrometers. To make a proton or neutron we need rays with a wavelength of 1.3 thousandths of a micro-micrometer.

To see how much shorter these wavelengths are than those of visible light, let’s first choose a color for comparison, one whose wavelength is a convenient number near the middle of the visible light spectrum. Blue light has a wavelength of 470 thousandths of a micrometer and green light about 528 thousandths of a micrometer. Therefore 485 thousandths of a micrometer corresponds to a greenish blue. The wavelength of an energetic X-ray or gamma ray that will make an electron is 200 000 times shorter than the wavelength of greenish-blue light. The X-ray or gamma ray is vibrating 200 000 times faster and is 200 000 times more energetic than greenish-blue rays.

Now multiply the proton or neutron wavelength by 2000 times 200 000, or 400 000 000. That gives a wavelength of 528 thousandths of a micrometer, the wavelength of green light. The energetic X-rays or gamma rays one needs to make a proton or a neutron are 400 000 000 times more energetic than rays of green light. It is clear that only very energetic X-rays or gamma rays can make particles by colliding.

In the above examples we have calculated the energy of the photon needed to make one particle. Of course we need another photon of equal energy in a colliding ray to make another particle, identical with the first but opposite in sign if the first particle carries an electric charge. This second particle is called the antiparticle of the first. The antiparticle of an electron is a positron. A proton’s antiparticle is an antiproton. A neutron is the antiparticle of another neutron.

We might think that we could use lower energies to make pairs of neutrinos, since these very lightweight particles have very little mass. An ultraviolet photon provides enough energy to materialize the mass of a neutrino. However, neutrinos do not come from pure energy reactions. They come from decaying nuclei. One type of decay ejects an electron and a neutrino and converts a neutron to a proton. Another type of decay ejects a positron and a neutrino and converts a proton to a neutron. There is always matter present before and after the reaction takes place, in the form of a proton or a neutron. Therefore two photons, colliding in space far from any material, cannot produce neutrinos.

Gamma-ray wavelengths are very small. To interact, it is not enough for the paths of two gamma rays to cross. The photons must arrive at the interaction region at about the same time. This means that gamma-ray photons can travel long times and great distances in random directions before materializing.