Czarcasm

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Does repolarization happen because this pump put sodium in the extracellular fluid and potassium into the intracellular fluid?
Well, that's part of the reason. After threshold is reached for the AP and hits +30 mV, at that point VG Na+ Channels close and VG K+ opens, allows intracellular potassium to leave the cell, repolarizing it in the process. VG K+ Channel begins to close around -70mV but because this process occurs slowly, it overshoots to -90 mV slightly, losing a few more K+ ions. This undershoot is known as hyperpolarization. From here, the Na/K+ pump helps re-establish the appropriate RMP and the proper concentration gradients within the cell.
 
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DrDreams

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You should understand that the natural tendency of sodium is to move inside of the cell because of the electrochemical gradient. The natural tendency of potassium is to flow out of the cell. I don't know if this helps you, but it had helped me.