How to Calculate the Debye Length

Debye length is a measure for the electrostatic screening in plasma, colloids or in a semiconductor material. It is very relevant to determine the stability and the use of surfactants for colloidal solutions and also for the depth profiling technique used to measure the doping profile in semiconductor materials. It is denoted by the Greek letter Lamda and its unit is meter. It is calculated by taking the reciprocal of Kappa (1/Kappa), where Kappa is the Debye-Huckel parameter.

Determine Variables

    Determine the known variables: Boltzmann constant, electronic charge of an ion, Avogadro's number and the permittivity of vacuum are known variables. The values of these variables are always constant: k= 1.38_10^-23m^2kgs^-2K^-1 e=1.6022_10^-19 Columb No= 6.023_10^23 Eo= 8.854_10^-12(F/m)

    Determine unknown variables: Though temperature (T) of the solution is usually given, it should always be converted into absolute scale. The absolute temperature is measured in terms of Kelvin.

    Determine the ionic charge of the solution: The ionic charge of the solution is the sum of the individual ions present in the solution. It can be represented by: Ionic charge= Sum.cz _e^2, where cz is individual ions and e is the electronic charge (1.6022_10^-19 Columb).

    Determine the dielectric constant of the materials: The dielectric constant is unique to every material or solution. For a particular material used, the value will usually be given. It is the ratio of electric field produced without dielectric to the field with dielectric. Dielectric acts as an insulator when it is placed in an electric field.

    Determine Kappa: Kappa or the Dybye-Huckel parameter is determined by using this equation:

    Kappa= 1/(sqrt(Eo_Ep_k_T)/(2000_No_Sum.cz_e^2)), where means the square root.

    After determining Kappa, Debye length can be calculated by taking the reciprocal (1/K) of the Kappa. Lamda = 1/Kappa The unit of Kappa is inverse meter and the unit of Debye length is meter.

    Things You'll Need

    • Boltzmann constant (k)
    • Electronic charge (e)
    • Avogadro's number (N)
    • Temperature (T)
    • Electric permittivity of vacuum (Eo)
    • Dielectric constant(Ep)

    Tips

    • Debye length has a very practical implication in colloids technology in the formation of electric double layer. It is considered to be the characteristic thickness of the double layer.

    Warnings

    • The temperature is always measured in absolute scale. SI units are generally used for the variables.

Related Articles

How to Calculate the Degree of Polymerization
How to Calculate Torsion Constant
How to Calculate Magnetization
How to Calculate Interstitial Velocity
How to Calculate Power Rating
How to Calculate Conductance
How to Calculate the Henrys in a Coil
How to Calculate Particle Concentration
What Are Representative Particles of Elements?
How to Calculate the Magnetic Force of a Solenoid
How to Calculate the pH of Ammonia Water Using KB
What Is the Gauss Rating for a Strong Magnet?
How to Design an RC Snubber
How to Calculate the Osmolarity
How to Convert Conductivity Units
What Is the Unit for Enthalpy?
What Is a Magnetometer?
What Is Molarity & How Is It Calculated?
An Electrical Engineer's Vocabulary Words
How to Convert MG to MEQ