Calculator Form
Example Data Table
| Example Case | Input Summary | Calculated Wavelength |
|---|---|---|
| Electron accelerated through 150 V | Electron voltage mode | 0.100137 nm |
| Proton moving at 1000 m/s | Mass = proton mass, velocity = 1000 m/s | 0.396149 nm |
| Neutron moving at 2200 m/s | Mass = neutron mass, velocity = 2200 m/s | 0.17982 nm |
| Baseball moving at 40 m/s | Mass = 0.145 kg, velocity = 40 m/s | 1.142426e-34 m |
Formula Used
Core de Broglie relation: λ = h / p
Here, λ is wavelength, h is Planck’s constant, and p is momentum.
For classical mass and velocity: p = mv, so λ = h / mv
For classical kinetic energy: p = √(2mK), so λ = h / √(2mK)
For electrons accelerated through voltage V: λ = h / √(2mₑeV)
Relativistic option: p = γmv, or p = √((K + mc²)² - (mc²)²) / c
Use the relativistic setting when the speed becomes a noticeable fraction of light speed.
How to Use This Calculator
- Select the calculation method that matches your known values.
- Enter the particle mass, velocity, momentum, energy, or electron voltage.
- Choose the correct unit for every field you fill in.
- Enable the relativistic option for high-speed or high-energy cases.
- Press Calculate Wavelength to show the result above the form.
- Review the wavelength in meters, nanometers, picometers, and angstroms.
- Use the CSV and PDF buttons to export the result.
- Study the graph to see how wavelength changes with your chosen input.
Frequently Asked Questions
1. What is de Broglie wavelength?
It is the wavelength associated with a moving particle. The relation λ = h/p shows that every particle with momentum has wave-like behavior.
2. Why does wavelength decrease when momentum increases?
The equation λ = h/p makes wavelength inversely proportional to momentum. A faster or more massive moving particle usually has greater momentum and therefore a shorter wavelength.
3. When should I use the relativistic option?
Use it when particle speed becomes a significant fraction of light speed, or when electron accelerating voltage is high enough that classical formulas lose accuracy.
4. Why are electron wavelengths often useful in microscopy?
Electrons can have extremely small wavelengths, often comparable to atomic spacing. That makes them useful for resolving very fine structures in electron diffraction and microscopy.
5. Can this calculator work for large everyday objects?
Yes. The formula still applies, but the wavelength becomes unimaginably small. That is why wave behavior is not observed for objects like balls or cars.
6. Which input method should I choose?
Choose the method that matches the data you already know. Use momentum for direct momentum values, mass and velocity for ordinary motion, kinetic energy for energy-based problems, and electron voltage for accelerated electrons.
7. Why does the calculator show several wavelength units?
Particle wavelengths can vary enormously. Showing meters, nanometers, picometers, and angstroms makes it easier to read values across laboratory, atomic, and subatomic scales.
8. Is the graph useful for learning?
Yes. The graph shows how wavelength changes as velocity, momentum, energy, or voltage changes. It helps you see the inverse relationship instead of only reading a single answer.