De Broglie Wavelength Calculator
Results
What is the De Broglie Wavelength?
The De Broglie Wavelength is a fundamental concept in quantum mechanics that describes the wave-like nature of matter. Proposed by Louis de Broglie in 1924, this hypothesis suggests that particles of matter (such as electrons) have dual properties: they act as particles and as waves.
This calculator helps you determine the wavelength associated with a massive particle moving at a specific velocity. This concept is crucial for understanding electron microscopy and quantum physics.
The De Broglie Equation
The wavelength ($\lambda$) is calculated using the following formula:
$\lambda = \frac{h}{p} = \frac{h}{m \cdot v}$
Where:
- $\lambda$ (lambda): The wavelength of the particle (in meters).
- $h$: Planck's Constant ($\approx 6.626 \times 10^{-34} \text{ J}\cdot\text{s}$).
- $p$: The momentum of the particle.
- $m$: The mass of the particle (in kilograms).
- $v$: The velocity of the particle (in meters per second).
How to Use This Calculator
1. Select a Particle: Choose a common particle like an Electron or Proton from the dropdown menu to auto-fill the mass, or select "Custom Mass" to enter your own value.
2. Enter Velocity: Input the speed at which the particle is traveling in meters per second (m/s).
3. Calculate: Click the button to see the resulting wavelength in meters, nanometers (nm), and Angstroms ($\mathring{A}$).
Example Calculation
Imagine an electron (mass $\approx 9.11 \times 10^{-31}$ kg) moving at $1 \times 10^6$ m/s.
Using the formula: $\lambda = (6.626 \times 10^{-34}) / (9.11 \times 10^{-31} \times 10^6)$.
The result would be approximately $7.27 \times 10^{-10}$ meters, or roughly 7.27 Angstroms.