Brownian Motion

Due May 2, 2024

Problem 1: A particle having diameter $D$ is located 5 cm above a surface in the atmosphere (e.g. the ocean). The particle contains -1 charge. Construct a Table that contrasts the following quantities using the units given in row 2:

1. Particle mean free path.

2. Distance traveled due to gravitational setting (t=1 hr).

3. Stopping distance assuming the particle is settling with terminal settling velocity ($v_{ts}$).

4. Average distance traveled due to Brownian motion ($t$=1 hr).

5. Distance of a sodium chloride particle traveled due to thermophoresis ($t$=1 hr , $\Delta T = 1\;K\;cm^{−1}$. This corresponds to a strong temperature gradient between a surface leave and the overlying air in the morning resulting from radiative cooling).

6. Distance traveled by a particle carrying -1 charge in the electric field of the Earth ($t=1$ hr). Recall that $v=FE$ and $B=qEB$. The value of the elementary charge is $1.6×10^{−19}$ C. [Note: The electric field strength in the atmosphere near the surface of the earth is about 100 V/m and points downward. One 1 volt/meter [V/m] equals 1 newton/coulomb [N/C]. The E-field is maintained by lightning, which deposit negative charge to the ground.]

You may want to write program routines to compute the quantities, but you may also compute them using pen and paper. If you use a computer, please supply the program code.

Problem 2: The air is still (no turbulence, no mean velocity). Draw a diagram/sketch of the forces, including directions, that is acting on the particle.