# Ionic Potentials across Cell Membranes

## Homework Statement

In its resting state, the membrane surrounding a neuron is permeable to potassium ions but not permeable to sodium ions. Thus, positive K ions can flow through the membrane in an attempt to equalize K concentration, but Na ions cannot. This leads to an excess of Na ions outside of the cell. If the space outside the cell is defined as zero electric potential, then the electric potential of the interior of the cell is negative. This resting potential is typically about -80 \rm mV. A schematic of this situation is shown in the figure.

Image 1 http://session.masteringphysics.com/problemAsset/1011446/22/1011446A.jpg

Image 2 http://session.masteringphysics.com/problemAsset/1011446/22/1011446B.jpg

There are 4 parts to this question.

A) Question: During the resting phase, what is the electric potential energy of a typical Na ion outside of the cell?
Answer: 0 meV B) Question: During the resting phase, what is the electrical potential energy of a typical K ion inside of the cell?
Answer: -80meV C) :uhh: During depolarization, what is the work done (by the electric field) on the first few Na ions that enter the cell?
The answer is one of the following:
-40 {\rm meV}
+40 {\rm meV}
-80 {\rm meV}
+80 {\rm meV}
-120 {\rm meV}
+120 {\rm meV}
0 {\rm meV}

D) :uhh: During repolarization, what is the work done (by the electric field) on the first few K ions that exit the cell?
The answer is one of the following:
-40 {\rm meV}
+40 {\rm meV}
-80 {\rm meV}
+80 {\rm meV}
-120 {\rm meV}
+120 {\rm meV}
0 {\rm meV}

## Homework Equations

There are 4 parts to this question. I already answered parts A and B, but can't figure out Parts C and D
How do I find the magnitude?
How do I figure out the sign?

## The Attempt at a Solution

The work done on a force is positive if the force and displacement are parallel, but negative if they are in opposite directions. For this problem, the magnitude of the work done is equal to the change in the ions electric potential energy.
I thought for part C the answer was either +40 or -40, but I tried those answers and they were wrong. I thought the magnitude was 40 because of a change from 0 to 40 meV so I'm confused on what the change is.
For part C and D, I do not know the magnitude or the sign of the answer.
Where is the force? I am having trouble figuring out where the force is in relation to the displacement, so I don't know if the answers are positive or negative.
How do I find the magnitude?
How do I figure out the sign?

## Answers and Replies

The work done on an object is equal to the magnitude of the object’s change in energy. The energy is the potential energy. For depolarization, the difference in potential energy can only be the initial values because nothing else has occurred yet--->-80meV inside and 0 outside => delta U= 80meV=magnitude of work. The sign is dependent on whether the object is moving in the direction of the force. It is positive, since in an effort to reach equilibrium the Na ions are rushing in, so they are going with the force.