Debye Length Calculator

What Is the Debye Length?

The Debye length $\lambda_D$ characterizes how far electrostatic effects persist in an electrolyte solution. Beyond this distance, ion screening reduces the electric field of a charged surface or particle.

Debye Length Formula

For a 1:1 electrolyte (e.g. NaCl):

$$\lambda_D = \sqrt{\frac{\varepsilon_0 \varepsilon_r k_B T}{2 n N_A e^2}}$$

$T$ is temperature in kelvin, $n$ is molar ionic concentration in mol/m³, $\varepsilon_r$ is the relative permittivity (dielectric constant), and $e$ is the elementary charge.

Real-World Applications

Debye length appears in colloid science, electrochemistry, semiconductor interfaces, double-layer capacitance, and plasma physics when modeling ionic screening.

Frequently Asked Questions

What is a 1:1 electrolyte?

A salt that dissociates into singly charged ions of equal magnitude, such as Na⁺ and Cl⁻. The formula assumes equal concentrations of cations and anions.

How does concentration affect Debye length?

Higher ionic concentration means stronger screening and a shorter Debye length. It scales as $1/\sqrt{n}$.

What dielectric constant should I use for water?

Water at room temperature has $\varepsilon_r \approx 80$. Use the value appropriate for your solvent and temperature.

What units should concentration be in?

Enter concentration in mol/m³. To convert from mol/L, multiply by 1000 (e.g. 0.1 mol/L = 100 mol/m³).

Does temperature matter?

Yes. Debye length increases with $\sqrt{T}$ because thermal motion opposes electrostatic ordering at higher temperatures.

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What Is the Debye Length?

Debye Length Formula

Real-World Applications

Frequently Asked Questions

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