De Broglie Wavelength Calculator
Wave Properties
What Is De Broglie Wavelength?
The De Broglie wavelength describes the wave nature of moving particles. It was introduced by Louis de Broglie, who showed that particles like electrons do not behave only like solid objects. They also behave like waves.
The basic equation is:
λ = h / p
Where:
- λ is the wavelength
- h is Planck’s constant
- p is momentum
Momentum depends on mass and velocity. So faster or heavier objects have shorter wavelengths.
Why a De Broglie Wavelength Calculator Is Useful
Doing these calculations by hand can be slow and error-prone, especially when energy units or relativistic effects are involved. This calculator solves those problems by:
- Handling unit conversions automatically
- Supporting different input methods
- Detecting when relativistic physics is required
- Showing momentum and physical regime clearly
It saves time and helps avoid mistakes.
What This Calculator Can Do
This calculator is more than a basic formula tool. It includes features that make it accurate and practical.
Supported Particle Types
You can choose from preset particles or enter a custom mass:
- Electron
- Proton
- Neutron
- Alpha particle
- Baseball (for scale comparison)
- Custom object
Each preset automatically fills in the correct mass.
Multiple Input Options
You can calculate wavelength using one of three inputs:
- Velocity (m/s)
Best when speed is known directly. - Kinetic Energy (eV)
Common in atomic and particle physics. - Accelerating Voltage (V)
Useful for electron guns and lab experiments.
The calculator adjusts the math based on your choice.
How the Calculator Works (Behind the Scenes)
This tool uses Planck’s constant and carefully selected physics rules to ensure accuracy.
Momentum Calculation
- At low speeds, it uses classical momentum:
p = m × v - At high speeds, it switches automatically to relativistic momentum, preventing incorrect results.
Relativistic Detection
If:
- Velocity exceeds 1% of the speed of light, or
- Energy becomes a significant fraction of rest energy
The calculator applies relativistic corrections and labels the result clearly.
Neutral Particle Protection
Neutral particles like neutrons cannot be accelerated by voltage. The calculator detects this and stops invalid calculations before they happen.
Understanding the Results
After calculation, you see three key outputs:
1. De Broglie Wavelength (λ)
Displayed in the most readable unit:
- Picometers (pm)
- Nanometers (nm)
- Scientific notation for very small values
2. Momentum (p)
Shown in kg·m/s, always in scientific notation for clarity.
3. Physics Regime
You will see one of the following:
- Classical (Non-Relativistic)
- Relativistic (High Energy or High Velocity)
This helps you understand which physical rules apply.
Example Use Cases
- Physics students checking homework problems
- Teachers demonstrating wave–particle duality
- Lab users calculating electron wavelengths from voltage
- Curious learners comparing electrons to everyday objects
Try calculating the wavelength of a baseball. You will see why quantum effects are invisible at human scales.
Why This Calculator Stands Out
This tool is designed for both accuracy and usability:
- Clean layout with clear labels
- Smart unit handling
- Automatic physics checks
- No unnecessary settings
- Works for beginners and advanced users
It teaches while it calculates.