de Broglie Wavelength Calculator
An electron accelerated through 100 V has a de Broglie wavelength of 0.122643 nm, about the spacing of atoms in a crystal, from λ = h/√(2meV).
For charged particles accelerated from rest; uses the charge e (2e for alpha).
0.122642596615815 nm
Full answer, then cut to fewer decimals (not rounded):
- 0.122642596615815 nm
- 0.12264259661581 nm
- 0.1226425966158 nm
- 0.122642596615 nm
- 0.12264259661 nm
- 0.1226425966 nm
- 0.122642596 nm
- 0.12264259 nm
- 0.1226425 nm
- 0.122642 nm
- 0.12264 nm
- 0.1226 nm
- 0.122 nm
- 0.12 nm
- 0.1 nm
- In metres
- 1.226425966 × 10⁻¹⁰ m
- In ångströms
- 1.226425966 Å
- In picometres
- 122.6425966 pm
- Momentum p
- 5.402747767 × 10⁻²⁴ kg·m/s
- Speed (non-relativistic)
- 5930969.585 m/s
Step-by-step solution
- p = √(2mK) = √(2 × (9.109383702 × 10⁻³¹) × (1.602176634 × 10⁻¹⁷) J) = 5.402747767 × 10⁻²⁴ kg·m/s
- λ = h ÷ p = (6.62607015 × 10⁻³⁴) ÷ (5.402747767 × 10⁻²⁴)
- λ = 1.226425966 × 10⁻¹⁰ m = 0.1226425966 nm
de Broglie Wavelength Formula
λ = h / p = h / (m v) = h / √(2 m K)
h Planck constant, p momentum, m mass, v speed, K kinetic energy (= qV after acceleration through V volts)
Worked Example
An electron accelerated from rest through 100 V:
- p = √(2mK) = √(2 × (9.109383702 × 10⁻³¹) × (1.602176634 × 10⁻¹⁷) J) = 5.402747767 × 10⁻²⁴ kg·m/s
- λ = h ÷ p = (6.62607015 × 10⁻³⁴) ÷ (5.402747767 × 10⁻²⁴)
- λ = 1.226425966 × 10⁻¹⁰ m = 0.1226425966 nm
In ångströms: 1.226425966 Å · In picometres: 122.6425966 pm · Momentum p: 5.402747767 × 10⁻²⁴ kg·m/s · Speed (non-relativistic): 5930969.585 m/s
Electron microscopes
Electrons accelerated through 100 kV have wavelengths near 0.004 nm (relativistically corrected), thousands of times shorter than visible light, which is why electron microscopes resolve atoms.
More Modern Physics Calculators
-
Photon Energy Calculator
E = h f = h c / λ
h = 6.62607015 × 10⁻³⁴ J·s, c = 299,792,458 m/s (both exact), f frequency, λ wavelength
Example: A photon of green light with a wavelength of 500 nm: Photon energy E = 2.47968 eV.
-
E = mc² Calculator
E = m c²
E energy (J), m mass (kg), c = 299,792,458 m/s exactly
Example: Converting 1 gram of mass entirely into energy: Energy E = 89875500000000 J.
-
Half-Life Calculator
N = N₀ (½)^(t / T½)
N amount left, N₀ initial amount, t elapsed time, T½ half-life; λ = ln 2 / T½
Example: 100 g of carbon-14 (half-life 5730 years) after 11,460 years: Amount remaining N = 25.
Frequently asked questions
Is there a shortcut for electrons?
For an electron accelerated through V volts, λ ≈ 1.226/√V nm (non-relativistic). At 100 V that is 0.1226 nm.
Why don’t we see the wavelength of a ball?
Its momentum is enormous by comparison: a 0.145 kg baseball at 40 m/s has λ ≈ 10⁻³⁴ m, far below anything measurable.
Sources
- CODATA Recommended Values of the Fundamental Physical Constants: 2018, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). de Broglie Wavelength Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/de-broglie-wavelength-calculator/
IEEE
Scientific Converters, "de Broglie Wavelength Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/de-broglie-wavelength-calculator/