Mobile charges rearrange to cancel out electric fields beyond a short distance – the Debye length. It defines when an ionised gas behaves as a plasma, and in salty water it sets how far electrostatic forces between colloids and biomolecules reach.
How to use the Debye Length Calculator
- Medium
- Electron temperature
- Electron density
- Temperature
- Relative permittivity of the solvent
- Ionic strength (mol/L)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose plasma or electrolyte and enter the parameters. For an electrolyte, ionic strength is in mol/L (0.15 for physiological saline).
Inputs explained
| Field | What to enter |
|---|---|
| Medium | Choose one: Plasma, Electrolyte |
| Electron temperature | Units: eV, K |
| Electron density | Units: m⁻³, cm⁻³ |
| Temperature | Units: K, °C |
| Relative permittivity of the solvent | A number |
| Ionic strength (mol/L) | A number |
Example values
How the main result changes when Electron temperature changes and everything else stays at the example values above:
| Electron temperature (eV) | Debye length λ_D (nm) |
|---|---|
| 5 | 0.7855 |
| 7.5 | 0.7855 |
| 10 | 0.7855 |
| 12.5 | 0.7855 |
| 15 | 0.7855 |
| 20 | 0.7855 |
Formula
Plasma: λ_D = √(ε₀·k·T_e / (n_e·e²)) · Electrolyte: λ_D = √(ε₀·ε_r·k·T / (2·N_A·e²·I))
Worked example
Inputs — Medium: Electrolyte; Temperature: 298.15 K; Relative permittivity of the solvent: 78.5; Ionic strength (mol/L): 0.15.
Results — Debye length λ_D = 0.78546 nm.
Key terms
- Ionic strength
- ½·Σcᵢzᵢ², a measure of ion concentration.
Frequently asked questions
What is the Debye length of seawater?
Under 1 nm (ionic strength ≈ 0.7 mol/L).
Why does it define a plasma?
A plasma must be much larger than its Debye length so collective effects dominate.
How does salt affect it?
More ions shorten the screening length (λ ∝ 1/√I).
What is it in physiological saline?
About 0.8 nm.