Question

A current of \(5.00 \mathrm{~mA}\) is enough to make your muscles twitch. Calculate how many electrons flow through your skin if you are exposed to such a current for \(10.0 \mathrm{~s}\).

Short answer

Answer: Approximately \(3.13 \times 10^{17}\) electrons.

Step-by-step solution

Convert the current to Coulombs per second

Given current, \(I = 5.00 \mathrm{~mA}\). To convert milliamperes (mA) to Amperes (A), divide by 1000: \(I = \frac{5.00}{1000} \mathrm{~A} = 0.005 \mathrm{~A}\)

Calculate the total charge that passed through the skin

Given time, \(t = 10.0 \mathrm{~s}\). We can calculate the total charge that passed through the skin using the formula \(Q = I \times t\), \(Q = 0.005 \mathrm{~A} \times 10.0 \mathrm{~s} = 0.05 \mathrm{~C}\)

Find the number of electrons

The charge of a single electron is approximately \(1.6 \times 10^{-19} \mathrm{~C}\). To find the number of electrons, divide the total charge by the charge of a single electron: \(n = \frac{0.05 \mathrm{~C}}{1.6 \times 10^{-19} \mathrm{~C}}\) \(n \approx 3.13 \times 10^{17}\) electrons So, approximately \(3.13 \times 10^{17}\) electrons flow through the skin when exposed to such a current for 10.0 s.