 Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2022/paper-2/section-b/23/iv/solution

n_{i}

, valences

z_{i}

ϵ

and common temperature,

λ_{D} = (\frac{ϵ k _{B} T}{e ^{2} \sum _{i} n _{i} z _{i}^{2}})^{1/2} .

Increasing salt concentration supplies more mobile charge to screen a surface perturbation, so a shorter distance is needed for the potential to decay. At fixed ion composition, permittivity and temperature,

λ_{D} \propto c^{- 1/2}

A fivefold concentration increase therefore gives

λ_{D}^{'} = λ_{D} / 5 = 0.447 λ_{D} .

Equivalently, the inverse screening length grows by

5

. Changing ion valence changes the ionic-strength weighting as well, and highly concentrated electrolytes can depart from this dilute-solution screening model.

 New to topics? Read the docs here!