# Diffusion as a Probability.

Diffusion as a probability for a random walk - please see the attached question.

No big derivation is required and this may be able to be answered in just a few lines.

The main point is to show the probability of hopping using only the values given at the bottom of the attached pdf.

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#### Solution Preview

Please see the attached file for the complete solution.

Our model of diffusion in one dimension consists of a grid with N slots (N is assumed to be large), each containing a finite number of particles, each slot labeled with an index k running from 1 to N. The spacing of the slots is (please see the attached file) which is assumed to be small. After each small time interval a particle has a small probability p of jumping from slot k to slot The grid contains (please see the attached file) particles in slot k at time interval l. From this ...

#### Solution Summary

In this solution we derive the one-dimensional diffusion equation using basic properties of a random walk. Response includes Microsoft Word attachment.