Ants are release from the center point of a smooth table and after 1 minute a snapshot is taken and the ants are counted at concentric 5cm circles. There are 10 outer circles ( The most outer circle being 50cm from origin). The number of ants at each ring starting from origin: 3, 5, 15, 19, 37, 23, 11, 1, 0, 0, 2, respectively.
What are the average displacement, root-mean-squared displacement, and diffusion constant?
Average displacement is sum of the squared value of each counted # of ants at each ring,, divided by the number of rings? == [(x1)^2 + (x2)^2 + ... + (xn)^2]/11 ? I'm not sure about this, it seems to easy, and I'm not confident that I understand exactly what is being asked for.
Root-mean-squared displacement: √[(1/11)*(x1)^2+(x2)^2+ ... + (xn)^2].
This seems straight forward, but then again, I'm not sure that I started out on the right path.
Diffusion constant: This is where I'm very lost, I have t = (x^2)/2D but my teacher hinted that the solution was the Gaussian distribution and I have no idea how to derive or arrive at that conclusion. Thanks guys