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Problem 43 Hard Difficulty

Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited $=$ nerve speed $\times$ pulse duration $=50.0 \mathrm{m} / \mathrm{s} \times 2.0 \times 10^{-3} \mathrm{s}=0.10$ $\mathrm{m}$ ). In the resting state, the outer surface of the axon wall is charged positively with $\mathrm{K}^{+}$ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure $\mathrm{P} 18.43$ . Model the axon as a parallel-plate capacitor and take $C=\kappa \epsilon_{0} A / d$ and $Q=C \Delta V$ to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness $d=1.0 \times 10^{-8} \mathrm{m},$ axon radius $r=1.0 \times 10^{1} \mu \mathrm{m},$ and cell-wall dielectric constant $\kappa=3.0$ . (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many $\mathrm{K}^{+}$ ions are on the outside of the axon assuming an initial potential difference of $7.0 \times 10^{-2} \mathrm{V}$ ? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge $e$ per squared $\left({\mathrm{Å}}^{2}\right) .$ An atom has a cross section of about $1 {\mathrm{Å}}^{2}$ $(1 Å$ $=10^{-10} \mathrm{m} )$. (b) How much positive charge must flow through the cell membrane to reach the excited state of $+3.0 \times 10^{-2} \mathrm{V}$ from the resting state of $-7.0 \times 10^{-2} \mathrm{V}$ ? How many sodium ions (Na^ $^{+} )$ is this? (c) If it takes 2.0 $\mathrm{ms}$ for the $\mathrm{Na}^{+}$ ions to enter the axon, what is the average current in the axon wall in this process? (d) How much energy does it take to raise the potential of the inner axon wall to $+3.0 \times 10^{-2} \mathrm{V},$ starting from the resting potential of $-7.0 \times 10^{-2} \mathrm{V}$ ?

Answer

a. no answer available
b. no answer available
c. no answer available
d. w=7 \cdot 5 \times 10^{-12} \mathrm{J}

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Video Transcript

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As we know that one equals to 1.6 months. Clever tennis for minus 19 column and won't pastrami close to tennis for minus 10 meter. So this will give us. So save my clothes too. What need you wanted by 219. Stop Old Square. So the show's then the child density is not large. In part B. We have to kill Claire the positive charge, which will jump through the Selman brand and the number of sodium lines. So we have to kill Clegg, allergic to end and to. So let's kill Claire to do. First, you two equals toe Siri to now setting the valleys into this equipment, we will get 1.67 months. Flower tennis ball right for out into three points element. Claritin is four minus two. World which is close to you, do equals two. Why 0.1 flower, Tell us about minus 10. Cool up. So now the total charge we must flow through the membrane is they'll take a week. Wall Street. You to mind asking one. Now sitting The wedding's off control. And if you want, we will right? 5.12 Collaborative. It's about minus 10 column minded. Soon I want to fly away. Then it's about minus nine clump. So what if this was 1.17 multiplied by? Tell us about minus nine column. So this with us there, the Q equals to 1.67 multiplied witness for minus nine column. But it can't be that Inez. I don't like your peoples, too. 1.7 multiply. We're doing a spot of minus nine now. Then Umberto finds will be and two equals. Two Don't actually wanted by now sitting the values we will get and two equals to 1.7 multiplied by 10. It's about minus nine. Columbia, wanted by 1.6 months, flowered in this bar minus 90. So here we can right there 1.67 for more accuracy. So this saw this with us and do equals two 1.1 to play tennis party tonight. So these are the Kepler. Any plus signs. In parts of this question, we need to find the current in exam wall. So the question is, I equal student. I can't be worried by Delta t now setting the world is into this question one born Soon I want to play tennis for minus nine. Sorry here six hours there 6 to 1 multiple opportunities for minus nine clumped. You wanted 2.1 club a tennis for ministry Second So the current Phoebe 0.3 million better here Millie equals tutors for minus trend in body. We need to kill played the energy required to raise the potential upto the given level, but is good. In order to calculate this current energy would be lined the former law cables to one by two. Siri to square. Now setting the well is into this equation. We will get cables to one by two into 1.67 months. Claritin respond when they said for art in tow, three points. You want to play tennis by minus two world old square. So this will give us the value for care is cables to 7.5 multiply our generous part minus Well, Jules. So end off the question. Thank you.

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