Nerve signals in the body occur when a small voltage, called an action potential, is applied across the membrane of a cell. When this action potential is applied across a region of the cell membrane called an ion channel, current in the form of moving potassium ions will be established across the cell. If, during an action potential, a single ion channel with a resistance of 1.8 GΩ, is opened for 0.6 ms, approximately 90000 singly-ionized potassium ions travel through the channel during this time. What was the voltage of the action potential? You can approximate the ion channel to be Ohmic.

V = 43.2 mV

Explanation:

If we can approximate the ion channel to be Ohmic, this means that  we can apply Ohm's Law to get the voltage of the action potential, as follows:

       

The definition of electric current, is the rate of change of the charge, i.e., the amount of total charge crossing a given area, perpendicular to the flow of charge carriers, per unit time.If we know that approximately 90000 single ionized potassium ions travel through the channel during 0.6 mseg, we can find the value of the current.The charge represented by 90000 single ionized potassium ions, is the same as 90000 positive elementary charges, equal to 1.6*10⁻¹⁹ C each (as the potassium single ionized carries a +1 e charge).So, total charge is just the product of 90000 by 1.6*10⁻¹⁹ C:

       

        ⇒

Replacing the values of I and R in (1), we get:

Pe = 1/2k(x)^2  and .05n/m = .05x10^-9m = x