De Broglie Wavelength Calculator
de broglie wavelength calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
De Broglie Wavelength Calculator
Calculator
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Formula: λ = h/p = h/(mv)
Worked example — 0.727 nm
Formula
λ = h/p = h/(mv)
Every particle has a wave nature. h = 6.626×10⁻³⁴ J·s.
Worked Examples
Example 1: Electron
Problem:mₑ=9.109×10⁻³¹ kg, v=10⁶ m/s
Solution:λ=6.626e-34/(9.109e-31×10⁶)=7.27×10⁻¹⁰ m
Result:0.727 nm
Frequently Asked Questions
What is the de Broglie wavelength?
The de Broglie wavelength is the quantum mechanical wave associated with any moving particle. It is given by λ = h/p = h/(mv), where h = 6.626×10⁻³⁴ J·s is Planck's constant, m is mass in kg, and v is velocity in m/s. This wave-particle duality was proposed by Louis de Broglie in 1924.
How do you calculate de Broglie wavelength?
Use λ = h/(mv). For an electron (m = 9.109×10⁻³¹ kg) moving at 10⁶ m/s: p = 9.109×10⁻³¹ × 10⁶ = 9.109×10⁻²⁵ kg·m/s, and λ = 6.626×10⁻³⁴ / 9.109×10⁻²⁵ ≈ 7.27×10⁻¹⁰ m = 0.727 nm, comparable to atomic spacings.
What units does the de Broglie calculator use?
Mass is entered in kilograms (kg) and velocity in meters per second (m/s). The output wavelength is in meters (m) and also converted to nanometers (nm). Momentum p = mv is shown in kg·m/s, and kinetic energy KE = ½mv² is shown in joules (J) and electron-volts (eV), where 1 eV = 1.602×10⁻¹⁹ J.
Can we observe de Broglie wavelength of everyday objects?
No — a 0.1 kg tennis ball at 50 m/s has λ = 6.626×10⁻³⁴ / (0.1 × 50) ≈ 1.3×10⁻³⁴ m, about 10¹⁹ times smaller than a proton. Wave effects become physically measurable only for particles lighter than about 10⁻²⁵ kg, such as electrons, protons, and neutrons.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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