De Broglie Wavelength Calculator Formula

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

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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

    Ready to run the numbers?

    Open De Broglie Wavelength Calculator