Question

The small molecule cyclic AMP (cAMP) takes about 0.2 second to diffuse 10 µm, on average, in a cell. Suppose that cAMP is produced near the plasma membrane on one end of the cell; how long will it take for this cAMP to diffuse through the cytosol and reach the opposite end of a very large cell, on average? Assume that the cell is 200 µm in diameter.

(A) 4 seconds
(B) 16 seconds
(C) 80 seconds
(D) 200 seconds

Answer 1

It would take approximately 4 seconds for cyclic AMP (cAMP) to diffuse across a cell that is 200 µm in diameter, which represents answer choice (A).

Step-by-step explanation:

Given that cyclic AMP (cAMP) takes approximately 0.2 seconds to diffuse a distance of 10 µm in a cell, we can calculate the time it would take for cAMP to diffuse across a cell that is 200 µm in diameter. The time it takes for diffusion is proportional to the square of the distance because diffusion is a process that depends on the random motion of molecules. If it takes 0.2 seconds to diffuse 10 µm, we can set up a ratio to find the time it would take to diffuse 200 µm:

(0.2 seconds / 10 µm) = (x seconds / 200 µm)

Cross-multiplying and solving for 'x' gives:

x = (0.2 seconds * 200 µm) / 10 µm = 4 seconds

Therefore, on average, it would take 4 seconds for cAMP to diffuse from one end of a 200 µm cell to the other. This corresponds to answer choice (A).