The capacity of a unit area of the cell membrane of a nerve cell is 1 μF / cm2. One square micrometer contains 75 channels

The capacity of a unit area of the cell membrane of a nerve cell is 1 μF / cm2. One square micrometer contains 75 channels for the transport of sodium ions across the membrane. The charge of one ion is 1.6 * 10-19 Cl. How many sodium ions need to be passed through one sodium channel for the potential difference between the outer and inner surfaces of the membrane to change by 100 mV?

Consider a capacitor with an area of 1 cm².
1 cm² = 100,000,000 µm².
Number of channels in an area of 1 cm²:
n = 100,000,000 µm² * 75 channels / µm² = 75 * 10⁸ channels.
The relationship between capacitance C, voltage U and charge Q:
CU = Q.
The charge Q is equal to the number of ions N multiplied by the charge of the ion q:
CU = Nq.
N ions must pass through 1 cm² to reach 0.1 V:
N = CU / q.
We divide the number of ions by the number of channels:
n = N / (75 * 10⁸) = CU / (q₁ * 75 * 10⁸) = (10⁻⁶ F * 0.1 V) / (1.6 * 10⁻¹⁹ Cl * 75 * 10⁸) = 83.

Answer: about 83 ions need to be passed through 1 channel.