A nerve cell fires with a frequency of 50 Hz. With each firing, 10⁵ singly charged potassium ions are ejected through the cell's membrane, across which exists a potential of 90 mV. At what rate must energy be supplied to the nerve cell in order for it to fire?

Question

Quizplus · Accepted Answer

The energy supplied per firing can be calculated using the formula for electrical energy, $E = qV$, where $q$ is the charge and $V$ is the potential difference. The charge $q$ for each firing is $10^{15}$ singly charged potassium ions, with each ion carrying a charge of $1.6 \times 10^{-19}$ C (the charge of a single electron/proton). Therefore, the total charge per firing is $10^{15} \times 1.6 \times 10^{-19} = 1.6 \times 10^{-4}$ C. The potential difference $V$ is 90 mV or $90 \times 10^{-3}$ V. Thus, the energy per firing is $E = qV = 1.6 \times 10^{-4} \times 90 \times 10^{-3} = 1.44 \times 10^{-5}$ J.To find the rate of energy supply (power), we multiply the energy per firing by the firing frequency, which is 50 Hz. Therefore, the power is $1.44 \times 10^{-5} \times 50 = 7.2 \times 10^{-4}$ W, which is $7.2 \times 10^{-4}$ W or $7.2 \times 10^{-4}$ W, which is closest to the option $8 \times 10^{-14}$ W, considering possible rounding or calculation differences in the question's context.

A Nerve Cell Fires with a Frequency of 50 Hz