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Nonrelativistic Matter Wave Wavelength

Find de Broglie wavelength from momentum, or relate it to positive rest mass and low speed with the nonrelativistic momentum approximation.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For mass 1 × 10⁻³⁰ kg and speed 1 × 10⁶ m/s, the nonrelativistic momentum is 1 × 10⁻²⁴ kg·m/s and the matter-wave wavelength is 0.662607015 nm.

λ = h/p, h = 6.62607015 × 10⁻³⁴ J·s exactly. The mass–speed branch uses p = m v for speeds much smaller than c.

Worked example

Enter these known values and leave the other values blank.

Rest mass
10 × 10⁻³¹ kg
Nonrelativistic speed magnitude
1000000 m/s
Momentum magnitude
1 × 10⁻²⁴ kg·m/s
Matter-wave wavelength
0.662607 nm

Assumptions and limitations

  • The wavelength relation λ = h/p uses momentum magnitude. This page’s additional mass–speed relation uses the nonrelativistic approximation p = m v.
  • Use the mass–speed branch only when speed is much smaller than c. Near c, relativistic momentum is required and this approximation is inaccurate; speeds at or above c are rejected.
  • The mass and momentum selectors are powers of ten in kg and kg·m/s, respectively. Changing an exponent changes the displayed scale while preserving the underlying quantity.
  • Mass, speed, momentum and wavelength must all be positive. Zero momentum does not give a finite wavelength in this formula.
  • The exact SI h does not imply exact measured mass, speed or momentum. This is an ideal translational matter-wave calculation, not a model of interactions or decoherence.
  • All four captured quantities and all 142 unit choices remain usable. Known momentum alone can give wavelength without supplying mass or speed.

Common questions

Is matter-wave wavelength the wavelength of emitted light?

No. It characterizes the translational quantum state through momentum. It is not necessarily an emitted photon wavelength.

Can I use this mass–speed formula near light speed?

No. It uses p = m v, which is a low-speed approximation. Relativistic momentum is needed near c.

What happens if momentum doubles?

Wavelength halves, because h is constant and λ = h/p.

Can I work backwards from wavelength?

Yes. Wavelength gives momentum. If rest mass is also known, the low-speed model can then infer speed; the subluminal condition still applies.

References

The matter-wave wavelength uses the exact SI Planck constant, with both wavelength–momentum directions preserved. Mass–speed momentum is the nonrelativistic relation. Rest mass, momentum magnitude, speed and wavelength must be positive. Speed must be below the vacuum speed of light. The mass–speed branch is a nonrelativistic approximation for speeds much smaller than c.

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