a) The nerve cell does not look like our usual parallel plate capacitor, it look
ID: 1588065 • Letter: A
Question
a)
The nerve cell does not look like our usual parallel plate capacitor, it looks like a cylinder. But you can think of it as two parallel plates that have been rolled up. Below we show this model, thinking of the outside and inside of the membrane as the two plates.
The magnitude of the potential difference across the membrane in the resting state is about 80 mV. Which region is at the higher potential, the inside or the outside? What is the magnitude and direction of the electric field inside the membrane created by the ions just outside? Show your work.
b) In addition to the K and Cl ions stuck to the membrane, there are also Na ions inside the nerve cell. In its resting state, the nerve pumps Na ions, each a positive charge (+e), out of the cell, through the membrane, to the outside fluid. Does the nerve cell do positive or negative work on the Na ions during this transfer? Please briefly explain your reasoning.
c)
1. How much work is done against the electric field to carry one single Na ion across the membrane? Show your algebra and answer this question in electron volts (eV).
2. For each transfer of three sodium atoms the cell uses one molecule of its fuel called ATP. Each molecule of this fuel contains about 0.4 eV of energy. Compare these numbers to the answer you just got in part a - how efficient is this process? (2 points) (To convert: 1 eV = 1.6×10 J. )
Outside Membrane The Membrane Cl cl Ci c CI CI CI CI cl CI CI cI CI CI CI C CI cI CI C Axon SideExplanation / Answer
a) Because K "loses" an electron, and Cl receives an electron, they become: K+ and Cl-.
Thus, the potential is higher on K+ (outside) and lower on Cl-.(inside).
The electric field:
- magnitude: U=Ed --> E=U/d, U=potential difference between the 2 sides of the membrane.
- direction +sense: downward, from K+ to Cl-
b) The nerves do a negative work: W=-Fd (cos (alpha)=-1, with alpha=angle between the displacement vector, d, and E): F is also downward (Na+ is attracted to Cl-), and vector d is upward.
OBS: Bold letters means vectors.
c)
1. The work done by the nerves to transport the Na ion from - to + (from Cl- side to K+ side) is:
W--->+=qU=q(V--V+)=eU.
In eV: W=U=80 meV=80*10-3 eV (divide W by e=the charge of the electron).
c) The energy necessary to transport 3 Na ions is (in eV): W(3)=0.24 eV --> W(ATP)>W(3).
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