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 x 10^17 electrons.

Step-by-step solution

Identify the given information

We are given a current of \(5.00 \mathrm{~mA}\) (or \(5.00 \times 10^{-3} \mathrm{~A}\)) and a time of \(10.0 \mathrm{~s}\). The charge of a single electron is \(1.60 \times 10^{-19} \mathrm{~C}\).

Calculate the total charge

Using the formula \(Q = I \times t\), where \(Q\) is the total charge, \(I\) is the current, and \(t\) is the time, we can calculate the total charge that flows during the given time period: \(Q = (5.00 \times 10^{-3} \mathrm{~A}) \times (10.0 \mathrm{~s}) = 5.00 \times 10^{-2} \mathrm{~C}\)

Calculate the number of electrons

Knowing the charge of a single electron (\(1.60 \times 10^{-19} \mathrm{~C}\)) and the total charge that flows during the given time (\(5.00 \times 10^{-2} \mathrm{~C}\)), we can find the number of electrons by dividing the total charge by the charge of one electron: \(N = \frac{5.00 \times 10^{-2} \mathrm{~C}}{1.60 \times 10^{-19} \mathrm{~C}}\)

Solve for N

Now, divide the total charge by the charge of one electron to determine the number of electrons: \(N = \frac{5.00 \times 10^{-2} \mathrm{~C}}{1.60 \times 10^{-19} \mathrm{~C}} \approx 3.13 \times 10^{17}\) electrons So, approximately \(3.13 \times 10^{17}\) electrons flow through your skin when exposed to a current of \(5.00 \mathrm{~mA}\) for \(10.0 \mathrm{~s}\).