De Broglie Wavelength Calculator Physics

Wavelength: --
De Broglie Wavelength (lambda) = --

What is the De Broglie Wavelength Calculator?

Quick Answer: A tool that computes the de Broglie wavelength (λ = h/p) of a moving particle from its mass and velocity or kinetic energy. It visualizes wave–particle duality with a sine wave and a moving particle, demonstrating the wave nature of matter.

Theory of de Broglie Wavelength

According to de Broglie's hypothesis, every moving particle has an associated wavelength given by λ = h / p, where h = 6.626×10-34 J·s is Planck's constant and p = mv is the momentum (non‑relativistic). For electrons, this wavelength explains diffraction patterns. If kinetic energy K is known (in eV), momentum can be found from p = √(2mK) for non‑relativistic speeds. The calculator accepts mass in kg or atomic mass units (u), and velocity in m/s or kinetic energy in eV. The animated canvas shows a traveling sine wave scaled to the computed wavelength, with a particle moving along it to illustrate wave‑particle duality.

Step-by-Step Examples

Example 1: Electron in a TEM

  1. Mass = 9.11e-31 kg (electron), velocity = 1e6 m/s. Click Calculate.
  2. Momentum p = 9.11e-31 × 1e6 = 9.11e-25 kg·m/s, λ = 6.626e-34 / 9.11e-25 = 7.27e-10 m (0.727 nm).
  3. The canvas shows a wave with wavelength ~0.73 nm; the particle moves across the screen.

Example 2: Baseball (Macroscopic)

  1. Mass = 0.145 kg, velocity = 40 m/s. λ is extremely small (~1e-34 m) – beyond detection.
  2. The wavelength display shows a negligible value, emphasizing that macroscopic objects have undetectable wave properties.

Example 3: Using kinetic energy

  1. Clear velocity, enter kinetic energy = 100 eV for an electron. Mass remains 9.11e-31 kg.
  2. The tool converts 100 eV to J (1.602e-17 J), computes p = √(2×9.11e-31×1.602e-17) = 5.4e-24, λ = 1.23e-10 m.

Frequently Asked Questions

Why do we not see wave nature in daily life?

Because Planck's constant is extremely small, macroscopic objects have wavelengths far too tiny to observe. Only particles with very small mass (like electrons) exhibit measurable wave behavior.

What is the formula for de Broglie wavelength?

λ = h / p = h / (mv). For particles with kinetic energy K, p = √(2mK) (non‑relativistic). The tool uses these equations.

Does this apply to photons?

Yes, but photons already have a wavelength given by λ = c/f. For massless particles, the de Broglie relation merges with the photon momentum p = h/λ.

What units are accepted?

Mass in kg or atomic mass units (u), velocity in m/s, kinetic energy in eV. The result is displayed in meters, with appropriate SI prefixes.

Is the animation to scale?

The wave is drawn with a representative wavelength; the exact scale is adjusted to fit the canvas, but the relative proportion is maintained for comparison.