Energy used to charge nerve cells A nerve cell is shaped...

Energy used to charge nerve cells A nerve cell is shaped like a cylinder. The membrane wall of the cylinder has $\mathrm{a}+0.07$ -V potential difference from the inside to the outside of the wall. To help maintain this potential difference, sodium ions are pumped from inside the cell to the outside. For a typical cell, $10^{9}$ ions are pumped each second. (a) Determine the change in chemical energy each second required to produce this increase in electric potential energy. (b) If there are roughly $7 \times 10^{11}$ of these cells in the body, how much chemical energy is used in pumping sodium ions each second? (c) Estimate the fraction of a person's metabolic rate used to pump these ions.

Transcript

00:01 Hello students in this question we are provided that there is the energy used to charge a nerve cell okay, so a nerve cell is shaped like a cylinder so a nerve cell has to be charged it has a membrane wall the potential of the membrane wall is 0 .07 volts and the the we need to maintain this potential difference so that sodium ions are are supposed to be a pumped from inside of the cell to the outside so inside to outside it has to be pumped so for a typical cell 10 to the power nine ions are pumped every second so what is the first one so a determine the change in chemical energy so chemical energy can be calculated by delta delta e delta e can be calculated as equal to q times delta v okay okay where delta v is the potential difference and q is the charge so for given that the potential difference is 0 .07 volts and we have one sodium ion that is one electron which is equal to 1 .6 into 10 to the power minus 19 so that is positive charge so it's positive so we can calculate delta e so delta e will be equal to one electron so that is 1 .6 times 10 to the power minus 19 positron times delta is 0 .07 so that will give you a value of value of 1 .12 times 10 to the power minus 20 joules that will be the chem change in chemical potential energy chemical energy to produce the increase in electric potential energy right that is the first question now going to the second question if the body has 7 times 10 to the power 11 of these cells in the body the total change in chemical energy for pumping sodium ions each second can be calculated by multiplying the this is the number so multiplying the the total so number the total change in chemical energy total delta will be equal to 1 .1 2 times 10 to the power minus 20 times 7 times 10.

02:42 To the power 11 cells so that will give you a total energy total change in chemical energy of 7 .84 times 10 to the power minus 9 joules a minus 9 joules so that will be the total energy for pumping sodium ions each second now going to the third part to estimate fraction of personal metabolic rate to pump so to estimate the fraction of metabolic rate we need to compare the total change in chemical energy used in pumping sodium ions in each second with the metabolic rate so metabolic rate of the person varies depend upon a upon person to person so average we can estimate it is 70 watts 70 watts at rest okay so for one watt is equal to 1 jule 1 jule per second right so 1 watt is equal to 1 jude per second.

03:53 So we can use the fraction of metabolic rate...

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