Exercise 7.1 Part A The cytoplasm of a cell is a (moderately) conducting fluid,

Question

Exercise 7.1 Part A The cytoplasm of a cell is a (moderately) conducting fluid, surrounded by an insulating membrane, and embedded in a solution that is usually at least somewhat conducting. It can therefore be treated as a capacitor Assume the cell is spherical with a radius r = 10 m the cell membrane has an area A = 4m,2, and a thickness D 5 nm The capacitance should then be given by C = EA/D where the permittivity is given by ro with r, the dielectric constant, having a value of approximately 5, and E0 8.8542 × 10 12 F m 1 Calculate the capacitance of the cell membrane Express your answer to one significant figure. 3.495 10 12 Farad Submit My Answers Give Up Incorrect; Try Again; 3 attempts remaining, no points deducted Very close. Check the rounding and number of significant figures in your final answer Part B Calculate how many unipositive ions need to cross the cell membrane to give the interior a potential of 100 mV Express your answer to one significant figure. 2.18 10 unipositive ions Submit My Answers Give Up Incorrect; Try Again; 6 attempts remaining; no points deducted Very close. Check the rounding and number of significant figures in your final answer.

Explanation / Answer

(A) C = e0 er A / D

= (8.854 x 5 x 10^-12) (pi (10 x 10^-6)^2) / (5 x 10^-9)

C = 2.78 x 10^-12 F

(B) Q = C V

Q = (2.78 x 10^-12)(100 x 10^-3) =2.78 x 10^-13 C

n = Q/ e = (2.78 x 10^-13)/(1.6 x 10^-19) = 1.74 x 10^6

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