Understanding Molecular Motion: Diffusion of Phospholipids in Bacteria

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Phospholipid molecules in a monolayer exchange positions every 10^-7 seconds, with diffusion across a bacterium taking about 1 second over a distance of 2 micrometers. The diameter of a phospholipid head is 0.5 nm, raising questions about the consistency of these diffusion rates. In a hypothetical scenario where a lipid molecule is the size of a ping pong ball (4 cm), it would move at a speed of 144 km/h, taking approximately 1.5 seconds to cross a 6-meter room. The discussion emphasizes the need for algebraic calculations to analyze both biological and scaled scenarios. Understanding these molecular motions is crucial for grasping diffusion processes in bacteria.
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Within a monolayer phospholipid molecules exchange places with their neighbors every 10^-7 seconds. It takes about 1 second for a phospholipid to diffuse from one end of the bacterium to the other, a distance of about 2 micrometers.

A) Are these numbers in agreement? Assume that the diameter of a phospholipid head is 0.5 nm. Explain why or why not.

B) To gain an appreciation for the speed of molecular motions, assume that a lipid molecule is the size of a ping pong ball (4 cm diameter) and that the floor of your living room (6 m by 6 m) is covered wall to wall in a monolayer of balls. If two neighboring balls exchanged positions every 10^-7 seconds how fast would they be moving in km/h? How long would it take for a ball to move from one end of the room to another?


I am not sure where to begin with these and what type of equations to use. If anyone can at least help me begin thatd be greatly appreciated!
 
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Well at least part B is straightforward algebra. A ping-pong ball moves 4cm every 0.1us. What is that velocity in units of km/hr? At that speed, how long does it take for a ball to travel the 6m to go from wall-to-wall?

Then I guess you're supposed to use a similar analysis to check the numbers for the biological dimension case in part A. Does that help?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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