A neuron is designed to provide a stimulus to a muscle at a frequency of \(2 \mathrm{~s}^{-1}\). The neuron's axon can be modeled as a cylinder with a permeable tip. For the stimulus to be effective, the concentration of signal ions at the tip can be no less than \(50 \%\) of that at the soma (base). Using the following parameters, what is the maximum axon length and required axon diameter?

\[\begin{array}{ll}D_{a b}=1 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s} & k_{c}=1 \times 10^{-6} \mathrm{~m} / \mathrm{s} \\c_{b}=1000 \mathrm{~mol} / \mathrm{m}^{3} & c_{\infty}=10 \mathrm{~mol} / \mathrm{m}^{3}\end{array}\]