The membrane that surrounds a certain type of living cell has a surface area of

Question

The membrane that surrounds a certain type of living cell has a surface area of 4.70 x 10^-9 m^2 and a thickness of 9.60 x 10^-9 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 4.60. (a) The potential on the outer surface of the membrane is + 58.2 mV greater than that on the inside surface. How much charge resides on the outer surface? (b) If the charge in part (a) is due to K+ ions (charge +e), how many such ions are present on the outer surface?

Explanation / Answer

a)

we have potential formula V = E / K X d

but we know that E = /0

then

V = / K 0 X d

but = Q / A

= V X K X 0 / d

Q = A X (V X K X 0 / d )

= 4.7 X 10-9 X ( 58.2 X 10-3 X 4.60 X 8.85/10-12 / 9.6 X 10-9 )

=4.7 X 10-9 X ( 2369.322 X 10-15 / 9.6 X 10-9 )

= 4.7 X 10-9 X 246.80 X 10-6

= 1159.98 X 10-15 C

or

= 1.159 X 10-12 C

b)the charge of each electron or K+ ion is 1.60 X 10-19

so the total number of ions is = 1.159 X 10-12 / 1.60 X 10-19

= 0.72 X 107

= 7.2 X 106 ions are present on the outer surface.

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