1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Radial distribution function in Debye-Huckel theory

  1. Mar 1, 2015 #1

    CAF123

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    For a plasma containing two ionic species with opposite charges but the same density ##n_{\infty}##, calculate the radial distribution functions ##g_{++}(r), g_{-+}(r), ##where ##n_{\infty}g_{ij}(r)## is the conditional probability density for finding a particle of type ##i## in a small volume at distance ##r## from one of type ##j##. You may assume Debye-Hueckel theory is valid and should use the result that $$\lambda_D^2 = \frac{\epsilon kT}{2q^2 n_{\infty}}$$ where ##\epsilon## is a dielectric constant and ##q## is the charge of the species.

    2. Relevant equations

    radial distribution function ##g(r) = e^{-\beta \phi(r) q}##

    3. The attempt at a solution

    Can write the number density of particles from some reference particle at the origin, ##n(r) = n_{\infty} [ e^{q\beta \phi} + e^{-q\beta\phi}] = 2n_{\infty} \cosh (q \beta \phi) ##. The solution to the Debye Huckel equation is that $$\phi = \frac{q}{4 \pi \epsilon} \frac{e^{-r/\lambda_d}}{r},$$ where ##\lambda_D## is given . I think it makes sense that the ##g_{-+}(r)## would be more sharply peaked or not as suppressed as ##g_{++}(r)## , but I am not quite sure how to extract the explicit forms.

    Thanks!
     
  2. jcsd
  3. Mar 6, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Radial distribution function in Debye-Huckel theory
  1. Radial distribution (Replies: 1)

  2. Radial Wave Function (Replies: 12)

Loading...