Using Brownian Motion to solve for 4 things HELP

[jasminstg]

Using Brownian Motion to solve for 4 things PLZ HELP!

Brownian motion. Molecular motion is invisible in itself. When a small particle is suspended in a fluid, bombardment by molecules makes the particle jitter about at random. Robert Brown discovered this motion in 1827 while studying plant fertilization. Albert Einstein analyzed it in 1905 and Jean Perrin used it for an early measurement of Avogadro's number. The visible particle's average kinetic energy can be taken as , the same as that of a molecule in an ideal gas. Consider a spherical particle of density 1000 kg/m3 in water at 20°C.
(a) For a particle of diameter 35.50 µm, evaluate the rms speed.
1 __m/s
(b) The particle's actual motion is a random walk, but imagine that it moves with constant velocity equal in magnitude to its rms speed. In what time interval would it move by a distance equal to its own diameter?
2 ____ ms
(c) Repeat parts (a) and (b) for a particle of mass 71.0 kg, modeling your own body.
3 _____ m/s
4 ______ yr
(d) Find the diameter of a particle whose rms speed is equal to its own diameter divided by 3 s.
5 _____ m
(Note: You can solve all parts of this problem most efficiently by first finding a symbolic relationship between the particle size and its rms speed.)

 

[Redbelly98]

As a start, look for the relevant equations in your textbook or class notes. (You are supposed to do this in posting any homework question at Physics Forums.)

For example, in (a) you're looking for an equation that relates rms speed with a particle's mass and temperature.

 

[kerimek]

I would be happy to help you with your questions about using Brownian motion to solve for four different things. Brownian motion is a fascinating phenomenon that has been studied and utilized for many years. In order to solve for the four things you mentioned, let's first review the basics of Brownian motion.

Brownian motion is the random movement of small particles suspended in a fluid, caused by the bombardment of molecules in the fluid. This motion was first observed by Robert Brown in 1827 and later analyzed by Albert Einstein in 1905. Jean Perrin also used Brownian motion to measure Avogadro's number.

Now, let's move on to solving for the four things you mentioned. The first thing we need to do is find a relationship between the particle size and its rms speed. The rms speed is the root mean square speed, which is the average speed of the particles in a fluid. It can be calculated using the formula v(rms) = √(3kT/m), where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the particle.

(a) For a particle of diameter 35.50 µm, we can calculate its rms speed using the above formula. First, we need to convert the diameter to meters, which gives us 3.55x10^-5 m. Plugging in the values for k (1.38x10^-23 J/K) and T (293 K), we get v(rms) = √(3(1.38x10^-23 J/K)(293 K)/(1000 kg/m^3)). Solving this equation gives us a rms speed of approximately 2.42x10^-5 m/s.

(b) Now, let's imagine that the particle is moving with a constant velocity equal to its rms speed. In order to move a distance equal to its own diameter (3.55x10^-5 m), it would take the particle 3.55x10^-5 m / 2.42x10^-5 m/s = 1.47x10^-3 s, or 1.47 ms.

(c) For a particle with a mass of 71.0 kg, modeling your own body, we can use the same formula to calculate its rms speed. Plugging in the values for k, T, and m, we get v(rms) = √