Calculator inputs
Formula used
This calculator uses the de Broglie matter-wave relation. The common form is λ = h / p, and for non-relativistic motion with momentum p = mv, it becomes λ = h / (mv). Rearranging gives h = λmv, m = h / (λv), and v = h / (λm).
| Variable | Meaning | Typical SI unit |
|---|---|---|
| λ | Associated matter wavelength | m |
| h | Planck constant or custom constant input | J·s |
| m | Particle mass | kg |
| v | Particle speed | m/s |
How to use this calculator
- Select which variable you want to solve.
- Enter the known values using the units you prefer.
- Keep the default h value for standard de Broglie work, or replace it for custom scenarios.
- Choose the graph axis and a sensible range.
- Press Calculate now to show results above the form.
- Download the summary as CSV or PDF when needed.
Example data table
| Example | Mass (kg) | Velocity (m/s) | Computed λ (m) | Computed λ (nm) |
|---|---|---|---|---|
| Electron | 9.109e-31 | 2.20e6 | 3.307e-10 | 0.3307 |
| Proton | 1.673e-27 | 1.00e6 | 3.961e-13 | 0.0003961 |
| Neutron | 1.675e-27 | 5.00e3 | 7.912e-11 | 0.07912 |
Frequently asked questions
1. What does lambda h mv mean?
It refers to the de Broglie relation λ = h/(mv). Lambda is wavelength, h is Planck’s constant, m is mass, and v is velocity.
2. When should I use λ = h/(mv)?
Use it for non-relativistic moving particles when momentum is well approximated by mv. At very high speeds, a relativistic momentum model is more appropriate.
3. Why does wavelength shrink when velocity rises?
Because wavelength is inversely proportional to momentum. If mass stays fixed and speed increases, momentum grows and the associated matter wavelength becomes smaller.
4. Can I solve for mass instead of wavelength?
Yes. Choose the mass mode and enter λ, h, and v. The calculator rearranges the same equation to isolate mass.
5. Why include custom h input?
A custom h field is useful for experimentation, teaching, symbolic checks, and sensitivity analysis. For normal physical calculations, keep the default Planck constant.
6. Which units work best here?
Use any provided unit, but SI units reduce mistakes. The calculator converts everything internally before solving and then shows several output formats.
7. What does the graph show?
The graph shows how wavelength changes across a selected mass or velocity range while the other input stays fixed. It helps visualize inverse behavior quickly.
8. Are these results exact for every particle?
They are exact for the chosen equation and inputs. Real systems may need relativistic corrections, uncertainty treatment, or experimental constraints not modeled here.