Enter particle details
Use rest mass for relativistic calculations. A signed velocity is accepted, but wavelength uses speed magnitude.
Formula used
λ is de Broglie wavelength. h is Planck’s constant, 6.62607015 × 10−34 J·s. p is momentum.
Relativistic: p = γmv, where γ = 1 / √(1 − v²/c²)
The calculator uses |v| for wavelength magnitude. Relativistic calculations require velocity below light speed.
How to use this calculator
- Enter the particle’s mass and choose its unit.
- Enter velocity and select the matching velocity unit.
- Choose automatic, classical, or relativistic momentum.
- Select a preferred wavelength display unit and precision.
- Press Calculate wavelength to view results above the form.
- Download CSV or use Save as PDF for records.
Example data
| Particle | Mass | Velocity | Approximate wavelength |
|---|---|---|---|
| Electron | 9.109 × 10−31 kg | 1.00 × 106 m/s | 0.727 nm |
| Neutron | 1.675 × 10−27 kg | 2,200 m/s | 0.180 nm |
| Proton | 1.673 × 10−27 kg | 1.00 × 105 m/s | 3.96 pm |
Velocity and de Broglie wavelength
Understanding de Broglie Wavelength
Every moving particle has a wave nature. Louis de Broglie connected particle motion with wavelength. His idea applies to electrons, atoms, neutrons, and larger objects. The wavelength becomes smaller as momentum becomes larger. Fast, heavy particles therefore have extremely short wavelengths. Light particles moving slowly can show measurable wave behavior. This calculator turns velocity and mass into a de Broglie wavelength quickly.
Why Momentum Matters
Velocity alone does not determine the wavelength. Mass changes the result strongly. A fast electron and a fast baseball have very different wavelengths. Momentum combines mass and velocity into one quantity. Classical momentum is mass multiplied by velocity. This relationship works well at ordinary speeds. At very high speeds, relativity increases the calculated momentum. The calculator can apply that correction automatically or on request.
Choosing Suitable Units
Enter mass in kilograms, grams, milligrams, atomic mass units, or electron masses. Select a velocity unit that matches your data. Common choices include meters per second, kilometers per second, kilometers per hour, and fractions of light speed. The tool converts every value into standard SI units internally. This keeps the calculation consistent. Results appear in meters, nanometers, picometers, and angstroms. Small-scale units make quantum wavelengths easier to read.
Classical and Relativistic Results
The classical approach uses p equals mv. It is reliable when velocity is far below light speed. The relativistic approach uses p equals gamma times mv. Gamma rises as velocity approaches light speed. The difference may be tiny for laboratory speeds. It becomes essential for particles in accelerators. Auto mode selects the relativistic method when speed reaches ten percent of light speed. You may also choose either method directly for comparisons.
Reading the Calculation
The main result is wavelength, represented by lambda. The results panel also shows converted velocity, momentum, the selected model, gamma, and kinetic energy. These values help you check the input and understand the scale. A negative velocity has the same wavelength magnitude as positive velocity. Direction changes momentum sign, not wavelength size. A wavelength near atomic dimensions can produce diffraction in crystals. Very tiny wavelengths usually need specialized experimental equipment.
Useful Scientific Applications
De Broglie calculations support electron microscopy, diffraction experiments, neutron scattering, and quantum mechanics lessons. Electron microscopes use short wavelengths to resolve fine details. Crystal diffraction reveals spacing between atoms. Particle beams require relativistic corrections at high energy. Students can compare objects to see why quantum effects are hidden in daily life. The calculator also supports repeatable reporting. Export the result as a CSV file or save the page as a PDF record.
Accuracy and Good Practice
Use measured mass and velocity values whenever possible. Keep enough significant figures during input. Select a relativistic model for speeds near light speed. Do not enter a speed equal to light speed. Massive particles cannot reach that limit. Check each unit before calculating. Compare the displayed momentum against your expectations. The wavelength uses the magnitude of momentum. Repeat calculations with different units to confirm consistency. Clear inputs carefully before starting a new problem.
Frequently asked questions
1. What does this calculator find?
It finds the de Broglie wavelength of a moving massive particle. The calculation uses its mass and velocity to determine momentum, then divides Planck’s constant by that momentum.
2. Why does mass affect wavelength?
Wavelength depends on momentum, not velocity alone. A larger mass creates more momentum at the same speed. More momentum produces a shorter de Broglie wavelength.
3. Can I enter electron mass directly?
Yes. Select Electron masses from the mass-unit list and enter the number of electron masses. Enter 1 for a single electron at rest mass.
4. When should I select relativity?
Choose relativity when speed is a meaningful fraction of light speed. Automatic mode switches at 0.10 c. You can select relativity manually whenever your experiment requires it.
5. Why is zero velocity rejected?
A particle with zero momentum has an infinitely large de Broglie wavelength in this idealized formula. A finite numeric wavelength cannot be displayed for that case.
6. Does velocity direction change the wavelength?
No. Reversing direction changes momentum’s sign, but the wavelength magnitude remains the same. This calculator uses speed magnitude to report a positive wavelength.
7. Can massive particles reach light speed?
No. Special relativity prevents objects with rest mass from reaching light speed. The calculator requires every entered speed to remain below that limit.
8. Which wavelength unit should I use?
Use nanometers for many electron and neutron examples. Use picometers or angstroms for atomic-scale work. Automatic selection chooses a readable unit from the result size.
9. What does the Lorentz factor mean?
The Lorentz factor, gamma, measures relativistic change with speed. It equals one at low speeds and grows rapidly near light speed. It increases relativistic momentum.
10. Is this suitable for photons?
No. Photons have zero rest mass and require a different approach. Use wavelength, frequency, or photon energy relationships instead of entering a photon mass here.
11. Can I save the results?
Yes. After calculating, download a CSV file for data work. Select Save as PDF to open your browser print dialog and create a PDF record.