1) Units of D are m2/s.
Because we can rewrite the formula as follows:
is dimentionless. r and t have dimentions of length and time respectively. Therefore units are m2/s.
2) We can take the data by capturing a picture of the microscope slide under microscope at some known time intervals. We can measure the displacement of each particle using the number of pixels moved by the particles. We can use some smaller scale to calibrate the pixels.
where and are number of pixels moved by ith particle in x and y directions respectively and and are calibrateed distances per pixel.
3) It is just the average over all particles.
We get diffusion constant from equation in first part.
4) The spheres will move away from their respective starting positions but their average displacement will be zero. but .
1) Units of D are m2/s.
Because we can rewrite the formula as follows:
is dimentionless. r and t have dimentions of length and time respectively. Therefore units are m2/s.
2) We can take the data by capturing a picture of the microscope slide under microscope at some known time intervals. We can measure the displacement of each particle using the number of pixels moved by the particles. We can use some smaller scale to calibrate the pixels.
where and are number of pixels moved by ith particle in x and y directions respectively and and are calibrateed distances per pixel.
3) It is just the average over all particles.
We get diffusion constant from equation in first part.
4) The spheres will move away from their respective starting positions but their average displacement will be zero. but .
So, how do we describe diffusive motion? If a particular object moves a distance Ar from...
part b and c In class we derived a Fokker-Planck equation for the velocity distribution P(et) starting from the assumption of small random changes in velocity at each time step f.(t) where f(t) is chosen from a distribution WU: ). Einstein's original approach to Brownian motion had a different starting point, focusing on position differences at each time step x(t + Δt)-x(t) + E(t) where £(t) is a random displacement chosen from some distribution W(E). Underlying this ap- proach is...
some context Problem 3: Use simple kinetic theory of gases discussed in section 1.3.2 as well as Fourer's law of condustion to prove: 2 R373 D11 = 3113/202pm Dal We were unable to transcribe this imageof a nes. the xed the led negligible The following assumptions about the structure of the cases are made in order to investigate the statistical rules of the random motion of the molecules: The size of the gas molecules is negligible compared with the distance...