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The neurons of giant squids, for example, consist of axons with very large radii, which allows the squid to react very quickly when confronted with a predator. Assuming no change in the resistivities or membrane thickness of the axon, by what factor must the radius of the axon increase such that the speed of the pulse increases by a factor of 10

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Answer:

100

Explanation:

[tex]\rho_m[/tex] = Resistivity of axon

r = Radius of axon

t = Thickness of the membrane

[tex]\rho_a[/tex] = Resistivity of the axoplasm

Speed of pulse is given by

[tex]v=\sqrt{\dfrac{\rho_mrt}{2\rho_a}}[/tex]

So, radius is given by

[tex]r=\dfrac{2\rho_a}{\rho_mt}v^2[/tex]

If radius is increased by a factor of 10 new radius will be

[tex]r_2=\dfrac{2\rho_a}{\rho_mt}(10v)^2\\\Rightarrow r_2=100\dfrac{2\rho_a}{\rho_mt}v^2\\\Rightarrow r_2=100r[/tex]

So, The radius will increase by a factor of 100.

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