BIOPHYSICS

RANDOM WALKS AND DIFFUSION

$1.$ A random walk results in the random walker being in a position $54$ units away from the origin after taking $87$ steps.

a$)$ Is this result possible $=$

b$)$ What is the probability of this result happening

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345=1\mathrm{.}23$E$-4$ WITHOUT multiplying by $100\%$

If not possible, write NA

$=$

$2.$ A random walk results in the random walker being in a position $72$ units away from the origin after taking $88$ steps.

a$)$ Is this result possible $=$

b$)$ What is the probability of this result happening

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345=1\mathrm{.}23$E$-4$ WITHOUT multiplying by $100\%$

If not possible, write NA

$=$

$3.$ A random walk results in the random walker being in a position $80$ units away from the origin after taking $85$ steps.

a$)$ Is this result possible $=$

b$)$ What is the probability of this result happening

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345=1\mathrm{.}23$E$-4$ WITHOUT multiplying by $100\%$

If not possible, write NA

$=$

$4.$ Calculate the probability of a dust particle floating on air to be at a position $96$ units given $68$ seconds to move.

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345=1\mathrm{.}23$E$-4$ WITHOUT multiplying by $100\%.$

Note that for stochastic processes, even values of a which are not divisible by $2$ can still have a probability of happening.

Also, there is no if a process is not possible, you just indicate it's probability of happening as zero.

Answer:

$5.$ Calculate the probability of a dust particle floating on air to be at a position $92$ units given $123$ seconds to move.

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345=1\mathrm{.}23$E$-4$ WITHOUT multiplying by $100\%.$

Note that for stochastic processes, even values of a which are not divisible by $2$ can still have a probability of happening.

Also, there is no if a process is not possible, you just indicate it's probability of happening as zero.

Answer:

$6.$ Calculate the probability of a dust particle floating on air to be at a position $39$ units given $218$ seconds to move.

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345=1\mathrm{.}23$E$-4$ WITHOUT multiplying by $100\%.$

Note that for stochastic processes, even values of a which are not divisible by $2$ can still have a probability of happening.

Also, there is no if a process is not possible, you just indicate it's probability of happening as zero.

Answer:

$7.$ pon unloading a bag of cement on a riverbank, some cement dust falls into the fresh water.

Given the following conditions:

Diameter of cement dust $=3$ microns $(1$ micron $=10^-6$ m$)$

Temperature $=22$ degrees Celsius

Viscosity of river water $=0\mathrm{.}9544$ mPa$*$s

Moles of cement dust particles $=8$ moles

a$)$ Calculate the Stokes$-$Einstein Diffusion Coefficient for the system

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345=1\mathrm{.}23$E$-4$

$=\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ square millimeters$/$second

b$)$ Calculate p$(3\mathrm{.}7$ mm$,36400$ s$)$

Use scientific notation with $2$ decimal places in the format $0\mathrm{.}00012345=1\mathrm{.}23$E$-4$ WITHOUT multiplying by $100\%$