Question

The concentration of \[{K^ + }\] ions in the interior and exterior of a Nerve cell are $500$ \[mM\] and $25$ $mM$ respectively. The electrical potential (in volt) that exists across the membrane is: \[[lo{g_{10}}2 = 0.3,2.303{\text{ }}RT/F = 0.06]\] (Given answer be multiplying with $1000$)

Answer 1

Hint: We need to remember that the electrical potential is decided by concentration gradients of charged particles across the membrane and by membrane permeability to every sort of ion. In a resulting neuron, there are concentration gradients over the membrane for sodium ion and potassium ion. Ions move downward their gradients via channels, resulting in a separation of charge that makes the electric potential.

Complete step by step answer:
As we know that the neuron is the basic cell unit of the nervous system. Neurons are available in a variance of shapes and sizes, there are over a billion within the body.
The resting neuron features a voltage over its membrane called an electric potential, or just the resting membrane potential. Note that the charge is also because the concentration gradients influence this distribution.
The Nernst equation, at the concentration and charge forces working on a specific ion to ascertain if that ion is in passive equilibrium.
Given, Equilibrium potential for an ion $\left( E \right)$ is adequate to the universal gas constant times absolutely the temperature divided by the charge on that ion by Faraday’s constant, this obtained quantity is multiplied by the log of the concentration ration inside and exterior of the membrane is:
Given, the concentration of \[{K^ + }\] ion in interior of a Nerve cell is $500$ \[mM\]
Exterior of a nerve cell is $25$ $mM$
\[[lo{g_{10}}2 = 0.3,2.303{\text{ }}RT/F = 0.06]\]
$E = \dfrac{{0.06}}{1}\log \dfrac{{{{[{K^ + }]}_{exterior}}}}{{{{[{K^ + }]}_{interior}}}}$
Now we can substitute the given values we get,
$E = \dfrac{{0.06}}{1}\log \dfrac{{25}}{{500}}$
On simplification we get,
$E = - 0.0780$
Given answer be multiplying with $1000$
So,
$( - 0.0780) \times 1000 = - 78$
The electrical potential (in volt) that exists across the membrane is $ - 78$.

Note:
We need to remember that the equilibrium potential for potassium is negative in some species, this suggests that the inside of the cell would need to be $ - 70$ to $ - 75$ , so as to stop the external movement of potassium given these concentration gradients. The resting membrane potential is close but not just like the \[{K^ + }\] ion equilibrium potential in neurons. Neuron resting membrane potentials in under physiological conditions are somewhat less negative than the \[{K^ + }\] equilibrium potential.