Question

Show that the mean square displacement of a Brownian particle suspended in a liquid is directly proportional to the absolute temperature of the liquid.​

Answer 1

Answer:

Concept:

The molecular-kinetic theory of heat predicts that due to the molecular motions of heat, bodies suspended in a liquid that are small enough to see through them will move in a way that makes it possible to see them clearly under a microscope.

Explanation:

It's possible that the movements being addressed here are the same as the so-called "Brownian molecular motion," but the information I have on that is so imprecise that I can't make any conclusions about it (I).

                                          $P=\frac{e^{-x^{2} / 4 D t}}{2 \sqrt{\pi D t}}$

The amount of motion that one could anticipate to see would grow with smaller particle size, less viscous fluid, and greater temperature. The particle would eventually start to move away from its initial location, and using the principles of kinetic theory, it is possible to calculate the probability (P) of a particle moving a specific distance (x) in any direction over a specific time period (t) in a medium with a known coefficient of diffusion (D), where D is equal to one-half the average of the square of the displacement in the x-direction. P can be plotted against x using this probability "density" formula.

#SPJ3

Answer 2

Concept Introduction:

A body floating in a liquid that is tiny enough to be seen through is predicted to move in a way that makes it feasible to view it clearly underneath a microscope by the molecular-kinetic concept of heat.

Explanation:

We have been given a question about the Brownian motion.

We have to write the mean square displacement of a Brownian particle suspended in a liquid is directly proportional to the absolute temperature of the liquid.

With narrow particle size distribution, less viscosity fluid, and higher temperature, one may expect to witness more movement. The particle would ultimately begin to migrate away from its starting point, and by applying the concepts of kinetic theory, it is feasible to determine the likelihood (P) of a particle traveling a particular distance (x) in any direction over a specific amount of time (t) in a medium with a specified coefficient of diffusion (D), where D is equal to one-half the average of the square of the displaced in the x-direction. With the use of this probability "density" formula, P may be plotted versus x.

Final Answer:

The final answer is it's possible that the movements being addressed here are the same as the so-called "Brownian molecular motion," but the information I have on that is so imprecise that I can't make any conclusions about it (I).

#SPJ2