Modern Physics
Electron de Broglie wavelength
Raise K — λ = h/p shrinks as momentum grows.
Explore de Broglie matter waves by comparing electron wavelength to slit spacing. Connect wave-particle duality to diffraction and quantum mechanics.
de Broglie wavelength
Raise K — λ = h/p shrinks as momentum grows.
de Broglie proposed matter waves with wavelength λ = h/p. Electrons gain shorter wavelength as momentum rises, bridging particle and wave descriptions. This relation underlies electron microscopes and crystal diffraction where slits must be comparable to λ.
- λ = h/p
- λ ∝ 1/√K
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
Louis de Broglie proposed that particles like electrons have a wavelength too, not just light. Does a faster (higher kinetic energy) electron have a longer or shorter de Broglie wavelength?
Predictions to weigh
- Longer wavelength for faster electrons.
- Wavelength doesn't depend on kinetic energy.
- Shorter — higher kinetic energy means higher momentum, and wavelength is inversely proportional to momentum.
Variable roles
What you set:
- Kinetic energy K (eV)
What you measure:
- De Broglie wavelength λ (pm)
How the investigation runs
- Open the electron-de-broglie preset and press Reset.
- Enable the de Broglie wavelength readout.
- Set the electron's kinetic energy for each trial and record its de Broglie wavelength.
Governing equation
De Broglie Wavelength — λ = h/p
Every particle with momentum p has an associated wavelength λ = h/p. For a non-relativistic particle with kinetic energy K, this becomes λ = h/√(2mK) — a direct extension of light's wave-particle duality to matter.
What the printable worksheet asks students to work out
- For one trial, compute λ = h/√(2m_eK) using h = 6.626×10⁻³⁴ J·s, m_e = 9.109×10⁻³¹ kg (converting K from eV to joules). Compare to the table.
- Explain, using λ = h/p and p = √(2m_eK), why higher kinetic energy (and therefore higher momentum) produces a SHORTER wavelength — the opposite relationship from a photon's E = hc/λ.
Where this shows up beyond the lab
- Electron microscopes exploit an electron's tiny de Broglie wavelength (much shorter than visible light) to resolve details far smaller than an optical microscope ever could. Explain why using higher-energy electrons (shorter wavelength) generally improves an electron microscope's resolution.
- A thrown baseball also has a de Broglie wavelength, but far too small to ever notice. Using λ = h/p with a baseball's typical momentum, explain why matter-wave effects are only observable for extremely light particles like electrons.
- AP Physics 2 — Unit 15: Modern Physics
- IB Physics — E.2 Quantum physics
- General High School Physics — Modern physics intro
- NGSS High School Physics — Wave-particle duality of light
- Welcome to Electron De Broglie
- Select the electron
- Press Play
- Wavelength from momentum
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.