A component A spreads from a point source as a result of Brownian motion in one dimension. At time t = 0, all molecules are located at x = 0.

During a 0.5 s time step, each molecule has the same probability of jumping a distance of 1.0 cm in either the positive or the negative x direction or to stay put. After 0.5 s, the process is repeated with each molecule having the same probability of traveling for another 0.5 s at the same speed in either positive or negative direction. Consider 1,000 molecules starting at x = 0 and plot their distribution as a function of distance from the source after 25, 50, 100, and 200 s, which correspond to 50, 100, 200, and 400 time steps, respectively. What is the diffusion coefficient? Can the simulated distribution be described by a Gaussian function?