Question

A current of $\mathbf{0}\mathbf{.300}\mathbf{A}$through your chest can send your heart into fibrillation, ruining the normal rhythm of heartbeat and disrupting the flow of blood (and thus oxygen) to your brain. If that current persists for$\mathbf{2.00}\mathbf{}\mathbf{min}$, how many conduction electrons pass through your chest?

Short answer

The number of conduction electrons passing through your chest is$2.25\times {10}^{20}$ .

Step-by-step solution

Stating the given data

1. The amount of current flowing in the chest,$\mathrm{I}=3.0\mathrm{A}$
2. The time till which the current persists is $\mathrm{t}=2.0\min \text{or}120\sec$.

Understanding the concept of Ampere’s law and quantisation of charges 

Using the formula of Ampere's law, we can get the net charge flowing in the conductor. Again, using the quantization concept, we can get the number of conduction electrons present in it.

Formula:

(i) The amount of current using the ampere’s law, $\mathrm{I}=\mathrm{qt}$.

(ii) The number of electrons present, $\mathrm{n}=\mathrm{q}/\mathrm{e}$.

Calculation of the conduction electrons 

Using the given data in equation (i), we can get the value of net charge flowing through the chest as follows:

$\begin{array}{c}\left|\mathrm{q}\right|=(0.3\mathrm{A})/(120\sec )\\ =36.0\mathrm{C}\end{array}$

This charge consists of n electrons (each of which has an absolute value of charge equal to e). Thus, using the value of net charge in equation (ii), we can get the number of conduction electrons as follows:

$\begin{array}{c}\mathrm{n}=\frac{36.0\mathrm{C}}{1.60\times {10}^{-19}\mathrm{C}}\\ =2.25\times {10}^{20}\end{array}$

Hence, the total of number of conduction electrons is $2.25\times {10}^{20}$.