What is the de Broglie wavelength?
The wavelength associated with a moving particle: λ = h/p. It reveals the wave nature of matter, confirmed by electron diffraction.
de Broglie Wavelength Calculator
λ = h/(mv)
Calculate the de Broglie wavelength of a particle. λ = h/(mv) = h/p — matter waves.
Calculate
Enter values above to calculate
How it calculates
1
h = 6.626×10⁻³⁴ J·s
2
λ = h / (m × v) = h / p
3
Result in metres
Formula
λ = h/(mv)
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| λ | de Broglie wavelength | m |
| h | Planck constant = 6.626×10⁻³⁴ | J·s |
| m | Mass | kg |
| v | Velocity | m/s |
| p | Momentum = mv | kg·m/s |
How to Use This Calculator
This de broglie wavelength calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula λ = h/(mv) is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
An electron (9.109×10⁻³¹ kg) at 10⁶ m/s. Find its de Broglie wavelength.
Step 1: λ = h/(mv)
Step 2: λ = 6.626×10⁻³⁴ / (9.109×10⁻³¹ × 10⁶)
Answer: λ ≈ 7.27×10⁻¹⁰ m ≈ 0.73 nm
Common Mistakes
- Macroscopic objects have absurdly tiny wavelengths (undetectable)
- Use relativistic momentum p = γmv at high speeds
- λ = h/p — the wavelength is inversely proportional to momentum
Related
Frequently Asked Questions
Why don't we see matter waves in daily life?
For macroscopic objects, mv is enormous, so λ is unimaginably small (~10⁻³⁴ m for a thrown ball) — far too tiny to observe.