Question

BIO Transmission of Nerve Impulses. Nerve cells transmit electric

signals through their long tubular axons. These signals propagate due to a

sudden rush of ${\mathbf{Na}}^{\mathbf{+}}$ions, each with charge $\mathbf{+}\mathbf{e}$, into the axon. Measurements

have revealed that typically about $\mathbf{5}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{11}}{\mathbf{Na}}^{\mathbf{+}}$ions enter each meter of the

axon during a time of . What is the current during this inflow of charge

in a meter of axon?

Short answer

The current during the inflow of charge in a meter of axon is$9\mu \mathrm{A}$.

Step-by-step solution

Define the current.

The charge per unit time is known as the current .

$I=\frac{Q}{t}$

Here, I is current in ampere$\left(\mathrm{A}\right)$, Q is charge in Columbus $\left(\mathrm{C}\right)$and t is time in sec

Determine current and direction of current.

Determine the current between the two electrodes as:

$$\begin{gathered} I=\frac{NQ}{t} \\ =\frac{\left(NumberofN{a}^{+}\right)\times \left|q\right|}{t} \end{gathered}$$

Substitute the values and solve as,

$$\begin{gathered} I=\frac{5\times {10}^{11}\times \left|-1.6\times \times {10}^{-19}\right|}{10\times {10}^{-3}} \\ =8.96\mu \mathrm{A} \\ \approx 9\mu \mathrm{A} \end{gathered}$$

Hence, current during the inflow of charge in a meter of axon is 8.96 $\mu \mathrm{A}$.