Question

Neurons are components of the nervous system of the body that transmit signals as electric impulses travel along their length. These impulses propagate when thecharge suddenly rushes into and then out of a part of the neuron called an axon. Measurements have shown that, during the inflow part of this cycle, approximately$\mathbf{5}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{11}}{\mathbf{Na}}^{\mathbf{+}}$ (sodium ions) per meter, each with charge $\mathbf{+}\mathbf{e}$, enter the axon. How many coulombs of charge enter the length of the axon during this process?

Short answer

The magnitude of charge entering the axon is 1.3nC.

Step-by-step solution

Step 1: Concept of electric charge.

An electric charge is an entity or a property of a particle that causes it to get influenced via experiencing a force when placed inside an electric or magnetic field.The charge due to electrons is mainly what is referred to as electric charge and one electron carries a charge of $1.6\times {10}^{-19}\mathrm{C}$. Like charges repel each other and unlike charges attract each other.

(b) Determination of the magnitude of charge entering the axon.

There is a finite charge carried by each ion when it enters the axon.

The total charge is calculated as,

$\mathrm{Q}=\mathrm{Ne}$ ….. (1)

Where N is the number of ions and e is the electric charge having the value.$1.6\times {10}^{-19}\mathrm{C}$

Calculate N by the given values,

$$\begin{gathered} \mathrm{N}=(\mathrm{no}.\mathrm{ofions}/\mathrm{length})(1.5\mathrm{cm}) \\ =\left(5.6\times {10}^{11}\mathrm{ions}/\mathrm{m}\right)\left(1.5\times {10}^{-2}\mathrm{m}\right) \\ =8.4\times {10}^9\mathrm{ions} \end{gathered}$$

Thus, the total charge according to equation (1) is,

$$\begin{gathered} \mathrm{Q}={\mathrm{N}}_{\mathrm{e}} \\ =\left(8.4\times {10}^9\right)\left(1.6\times {10}^{-19}\mathrm{C}\right) \\ =1.3\times {10}^{-9}\mathrm{C} \\ =1.3\mathrm{nC} \end{gathered}$$

Hence, the magnitude of charge entering the axon is 1.3 nC .