Giving cells actively \"pump\" positive sodium ions (Na^+) from inside the cell

Question

Giving cells actively "pump" positive sodium ions (Na^+) from inside the cell to outside the cell. This process is referred to as pumping because work must done on the ions to move them from the negatively charged inner surface of the membrane to the positively charged outer surface. Assume that the electric potential is 0.080 V higher outside the cell than inside the cell, and that the cell membrane is 0.09 mu m thick. (It is estimated that as much as 0% of the energy we consume in a resting state is used in operating this sodium pump.") (a) Calculate the work that must be done to move one sodium ion from inside the cell to outside? (b) If the thickness of the cell membrane is increased, does your answer to part (a) increase, decrease, or stay the same? stay the same decrease increase

Explanation / Answer

Potential difference = deltaV = 0.08 V ; thickness = .09 um

a)we know that the amount of workdone required will be:

W = q deltaV

q in this case will be positive e,

q = 1.6 x 10^-19

W = 1.6 x 10^-19 x 0.08 = 1.28 x 10^-20 J

Hence, W = 1.28 x 10^-20 J

b)stay the same

As we have seen that the thickess is not used for calculating the required work done.

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