Formula Used
1. Pair rest energy: E = 2mec2 = 1.022 MeV
2. Total available energy: Etotal = 2mec2 + Ke- + Ke+
3. Average photon energy: Eavg = Etotal / N
4. Equal two-photon case: Egamma = Etotal / 2
5. Frequency: f = E / h
6. Wavelength: λ = hc / E
7. Photon momentum: p = E / c
8. Lorentz factor: γ = 1 + K / (mec2)
9. Speed ratio: β = √(1 - 1 / γ2)
The equal two-photon output is exact for a symmetric case. For moving particles, real photon energies can differ with angle and frame.
How to Use This Calculator
- Select a calculation mode.
- Enter electron and positron kinetic energies.
- Choose the input energy unit.
- Choose the output energy unit.
- Set the photon count for average photon energy.
- Press Calculate Result.
- Review the result block above the form.
- Use the CSV or PDF buttons for export.
Example Data Table
| Case |
Mode |
e- KE |
e+ KE |
Photons |
Total Energy |
Average Photon Energy |
Average Wavelength |
| 1 |
at_rest |
0 MeV |
0 MeV |
2 |
1.021998 MeV |
0.510999 MeV |
2.426310e-12 m |
| 2 |
moving_pair |
0.75 MeV |
0.25 MeV |
2 |
2.021998 MeV |
1.010999 MeV |
1.226353e-12 m |
| 3 |
moving_pair |
1.2 MeV |
0.8 MeV |
3 |
3.021998 MeV |
1.007333 MeV |
1.230817e-12 m |
Electron Positron Annihilation in Physics
Electron positron annihilation is a core process in modern physics. An electron carries negative charge. A positron is its antimatter partner. When both meet, they can vanish as particles. Their mass and kinetic energy turn into radiation. That radiation usually appears as gamma photons. This is a direct demonstration of mass energy equivalence.
Why the energy matters
The rest energy of one electron is about 0.511 MeV. A particle pair therefore starts with 1.022 MeV before motion is included. If either particle is moving, kinetic energy adds more released energy. That makes the final photons more energetic. A calculator helps you combine rest energy and motion without mistakes.
What the outputs show
This calculator estimates total annihilation energy, average photon energy, and equal two photon energy. It also converts photon energy into wavelength, frequency, and momentum. These outputs are useful in radiation problems, detector estimates, and conceptual learning. The tool also reports gamma and beta values for each input particle. That helps relate kinetic energy to relativistic motion.
Why wavelength and frequency are useful
Gamma photons can be described in several ways. Energy is often the first quantity. Frequency shows how rapidly the wave oscillates. Wavelength shows how short the radiation scale is. Momentum matters in conservation problems. Using all four views gives a clearer physical picture. It also makes unit checks easier during homework and lab work.
Common applications
Electron positron annihilation appears in particle physics, nuclear instrumentation, and PET imaging discussions. It is also used in classroom problems on conservation laws. Engineers use related calculations when thinking about detector response and gamma interactions. Students use them to understand why 511 keV photons are so important. With added kinetic energy, the outputs show how real collisions can move beyond the simple at rest case.
FAQs
1. Why is 1.022 MeV important here?
It is the combined rest energy of one electron and one positron. Each contributes about 0.511 MeV. Together they define the minimum annihilation energy before any kinetic energy is added.
2. Why are 511 keV photons common?
When the pair annihilates at rest into two photons, the total 1.022 MeV splits evenly. Each photon then carries about 0.511 MeV, or 511 keV.
3. Can annihilation create more than two photons?
Yes. Multi photon outcomes can occur in some conditions. This calculator uses photon count to estimate average photon energy, not a full angular or quantum state solution.
4. Does motion change photon energy?
Yes. Added kinetic energy raises the total available energy. In real moving cases, photon energies can also depend on direction and frame, not only total energy.
5. What does beta mean in the result?
Beta is the particle speed divided by the speed of light. It shows how relativistic the electron or positron is for the entered kinetic energy.
6. What does gamma mean in the result?
Gamma is the Lorentz factor. It links kinetic energy, time dilation, and relativistic motion. A larger gamma means stronger relativistic effects.
7. Is the equal two-photon value always exact?
No. It is exact for a symmetric two photon case. For moving particles in the lab frame, real photon energies can be unequal.
8. When should I use CSV or PDF export?
Use CSV for spreadsheet work, logs, and analysis. Use PDF when you need a quick printable summary of the current result.