Calculator
Example Data Table
| Method | Input | Model | Momentum (kg·m/s) | Momentum (eV/c) | Wavelength (pm) |
|---|---|---|---|---|---|
| Velocity | 2.50e7 m/s | Relativistic | 0 | 4.276167e+4 | 28.994238 |
| Wavelength | 50 pm | Wave relation | 0 | 2.479684e+4 | 50.000000 |
| Kinetic Energy | 200 eV | Classical | 0 | 1.429684e+4 | 86.721412 |
| Voltage | 25 kV | Relativistic | 0 | 1.617867e+5 | 7.663434 |
Formula Used
1. Classical velocity form
p = mₑv
2. Relativistic velocity form
p = γmₑv, where γ = 1 / √(1 - v²/c²)
3. De Broglie relation
p = h / λ
4. Kinetic energy form
p = √(2mₑK) for classical calculations
5. Relativistic energy or accelerating voltage form
p = (1/c)√[(K + mₑc²)² - (mₑc²)²], with K = eV for accelerating voltage
How to Use This Calculator
- Choose the input method: velocity, wavelength, kinetic energy, or accelerating voltage.
- Pick classical or relativistic physics when the selected method supports both.
- Enter the value and choose the correct unit from the dropdown menu.
- Set decimal places, chart points, and chart span if you want finer output.
- Click Calculate Momentum to display the result above the form.
- Review momentum, wavelength, energy equivalent, speed ratio, and Lorentz factor.
- Use the CSV and PDF buttons to export the result summary.
- Check the example table and formulas to verify your setup or compare methods.
FAQs
1. What does electron momentum represent?
Electron momentum measures the motion carried by an electron. It depends on mass, speed, wavelength, or energy, depending on the method you choose.
2. When should I use the relativistic model?
Use the relativistic model when the electron speed is a noticeable fraction of light speed, or when accelerating voltages and kinetic energies become large.
3. Why is wavelength related to momentum?
Quantum mechanics links particles and waves. The De Broglie relation states that momentum equals Planck’s constant divided by wavelength.
4. Is classical momentum always wrong for electrons?
No. Classical momentum works well at low speeds and low energies. It becomes less accurate as the electron approaches relativistic conditions.
5. Why does the calculator show momentum in eV/c?
Physicists often use eV/c because it matches energy-based calculations neatly and makes particle-scale momentum values easier to compare.
6. Does accelerating voltage directly set kinetic energy?
For an electron accelerated through a potential difference V, the gained kinetic energy is approximately eV, assuming negligible additional losses.
7. Can I use this for negative charge direction?
This tool reports momentum magnitude only. Direction depends on the coordinate system and field orientation used in your physics setup.
8. What do the export buttons include?
The CSV export saves the summary table. The PDF export saves the summary table and the plotted momentum trend chart.