De Broglie Wavelength Calculator Formula

Understand the math behind the de broglie wavelength calculator. Each variable explained with a worked example.

Formulas Used

De Broglie Wavelength

wavelength = 6.626e-34 / (mass * velocity)

Wavelength (nm)

wavelength_nm = 6.626e-34 / (mass * velocity) * 1e9

Wavelength (pm)

wavelength_pm = 6.626e-34 / (mass * velocity) * 1e12

Variables

VariableDescriptionDefault
massParticle Mass(kg)9.109e-31
velocityParticle Velocity(m/s)1000000

How It Works

De Broglie Wavelength

Louis de Broglie proposed that all matter has wave-like properties, with a wavelength inversely proportional to momentum.

Formula

lambda = h / p = h / (m v)

  • *h* = 6.626 x 10^-34 J s (Planck constant)
  • *m* = particle mass
  • *v* = particle velocity
  • This wavelength is measurable for electrons and neutrons, and is the basis of electron microscopy.

    Worked Example

    Electron (m = 9.109e-31 kg) at v = 1e6 m/s.

    mass = 9.109e-31velocity = 1000000
    1. 01lambda = h / (m v)
    2. 02p = 9.109e-31 * 1e6 = 9.109e-25 kg m/s
    3. 03lambda = 6.626e-34 / 9.109e-25
    4. 04lambda = 7.274e-10 m = 0.727 nm

    Frequently Asked Questions

    Can macroscopic objects have a de Broglie wavelength?

    Technically yes, but it is negligibly small. A 1 kg ball at 1 m/s has a wavelength of about 6.6 x 10^-34 m, far too tiny to ever detect.

    How is the de Broglie wavelength measured?

    By diffraction experiments. Electrons scattered off crystal lattices produce interference patterns consistent with their predicted wavelength.

    Why is this important for electron microscopes?

    Electron wavelengths at high energies are much shorter than visible light, allowing electron microscopes to resolve atomic-scale features.

    Ready to run the numbers?

    Open De Broglie Wavelength Calculator