a) The charge on the outer surface is ![1.2\cdot 10^{-12} C](https://tex.z-dn.net/?f=1.2%5Ccdot%2010%5E%7B-12%7D%20C)
b) The number of ions is ![7.5\cdot 10^6](https://tex.z-dn.net/?f=7.5%5Ccdot%2010%5E6)
Explanation:
a)
The membrane behaves as a parallel plate capacitor, whose capacity is given by the equation
![C=\frac{k\epsilon_0 A}{d}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7Bk%5Cepsilon_0%20A%7D%7Bd%7D)
where
k = 4.3 is the dielectric constant
is the vacuum permittivity
is the surface area
is the distance between the two plates
Substituting,
![C=\frac{(4.3)(8.85\cdot 10^{-12})(5.1\cdot 10^{-9})}{1.4\cdot 10^{-8}}=1.4\cdot 10^{-11} F](https://tex.z-dn.net/?f=C%3D%5Cfrac%7B%284.3%29%288.85%5Ccdot%2010%5E%7B-12%7D%29%285.1%5Ccdot%2010%5E%7B-9%7D%29%7D%7B1.4%5Ccdot%2010%5E%7B-8%7D%7D%3D1.4%5Ccdot%2010%5E%7B-11%7D%20F)
The capacity of the membrane is related to the potential difference between the two surfaces by
![C=\frac{Q}{\Delta V}](https://tex.z-dn.net/?f=C%3D%5Cfrac%7BQ%7D%7B%5CDelta%20V%7D)
where here we have
Q = excess charge on one surface
is the potential difference between the two surfaces
Solving for Q, we find
![Q=C\Delta V=(1.4\cdot 10^{-11})(0.0855)=1.2\cdot 10^{-12} C](https://tex.z-dn.net/?f=Q%3DC%5CDelta%20V%3D%281.4%5Ccdot%2010%5E%7B-11%7D%29%280.0855%29%3D1.2%5Ccdot%2010%5E%7B-12%7D%20C)
b)
We said that the net charge on the outer surface is
![Q=1.2\cdot 10^{-12} C](https://tex.z-dn.net/?f=Q%3D1.2%5Ccdot%2010%5E%7B-12%7D%20C)
The charge of one K+ ions is equal to the electron charge
![+e=1.6\cdot 10^{-19} C](https://tex.z-dn.net/?f=%2Be%3D1.6%5Ccdot%2010%5E%7B-19%7D%20C)
Therefore, the number of ions on the outer surface can be found by dividing the total charge by the charge of a single ion:
![N=\frac{Q}{e}=\frac{1.2\cdot 10^{-12}}{1.6\cdot 10^{-19}}=7.5\cdot 10^6](https://tex.z-dn.net/?f=N%3D%5Cfrac%7BQ%7D%7Be%7D%3D%5Cfrac%7B1.2%5Ccdot%2010%5E%7B-12%7D%7D%7B1.6%5Ccdot%2010%5E%7B-19%7D%7D%3D7.5%5Ccdot%2010%5E6)
Learn more about capacity:
brainly.com/question/10427437
brainly.com/question/8892837
brainly.com/question/9617400
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