De Broglie Matter Waves: An Electron's Wavelength
1 · Predict
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?
- Shorter — higher kinetic energy means higher momentum, and wavelength is inversely proportional to momentum.
- Longer wavelength for faster electrons.
- Wavelength doesn't depend on kinetic energy.
2 · Set Up
- 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.
3 · Collect Data
| Kinetic energy K (eV) | De Broglie wavelength λ (pm) |
|---|---|
| 50 | |
| 100 | |
| 200 |
Plot wavelength λ (y-axis) against 1/√K (x-axis) for your three trials. Is the line straight through the origin?
4 · Analyze
- 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.
5 · Extend
- 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.
The Physics Behind This Experiment
De Broglie Wavelength
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.