91Ó°ÊÓ

Potassium ion diameter$=0.30nm$

Current$=1.8\mathrm{pA}$

The current is the charge that goes through a circuit per unit of time. Consequently, when time $t$comes, the charge will be:

role="math" localid="1649137054592" $q=It$

Here, charge is a multiple of the elementary charge,

$q=ne$

Modify the expression,

role="math" localid="1649134772412" $ne=It$

The equation for find the number of charges,

$n=\left(\frac{It}{e}\right)$

Substitute the values,

$n=\frac{{\displaystyle 1.8·{10}^{-12}·{10}^{-3}}}{{\displaystyle 1.6·{10}^{-19}}}$

$n=11250.$

Hence, the number potassium ions will pass through if the ion channel opens for$1.0ms$is$11250.$

Potassium ion diameter

Current$1.8pA$

Density is calculated by dividing the current flow by the cross-sectional area at which it flows, which in our situation is a circle.

So, we have

$J=\frac{I}{A}=\frac{4I}{\mathrm{Ï€}{D}^2}$

Substitute the values,

role="math" localid="1649137777099" $J=\left(\frac{4×1.8×{10}^{-12}A}{\mathrm{π}×{\left(3×{10}^{-10}m\right)}^2}\right)$

$=2.55×{10}^7\mathrm{A}/{\mathrm{m}}^2$

Hence, the current density in the ion channel is$2.55×{10}^7\mathrm{A}/{\mathrm{m}}^2$.