If the axo-membrane becomes more permeable to potassium ions.. Which onewould be true?

A. the inside of the membrane will become more positively charged.
B. the membrane will depolarize rapidly.
C. it will take a stimulus of larger magnitude to initiate an action potential.
D. the membrane will become hypopolarized.
E. the hyperpolarization at the end of the action potential will not occur.

In order to determine the correct answer, let's consider the consequence of an increase in potassium ion permeability.

When the axo-membrane becomes more permeable to potassium ions, it means that more potassium ions can pass through the membrane. Potassium ions have a net positive charge, so when they exit the neuron, they carry positive charge with them. This leads to an excess of positive charge leaving the inside of the neuron, making the inside of the membrane more negatively charged. Therefore, option A, "the inside of the membrane will become more positively charged," is incorrect.

Furthermore, an increase in potassium ion permeability would cause more potassium ions to leave the cell, leading to a decrease in the positive charge inside the neuron. This is known as hyperpolarization. Therefore, option D, "the membrane will become hypopolarized," is also incorrect.

Option B, "the membrane will depolarize rapidly," is not likely to occur because an increase in potassium ion permeability would result in the opposite effect, which is hyperpolarization.

Based on the above explanations, the correct answer is option C: "it will take a stimulus of larger magnitude to initiate an action potential." When the axo-membrane becomes more permeable to potassium ions, it counteracts the depolarizing effect of other ions, such as sodium, making it harder for the membrane to reach the threshold voltage required for an action potential to be generated. Thus, a stronger stimulus would be needed to meet the threshold.

Lastly, option E, "the hyperpolarization at the end of the action potential will not occur," is unrelated to the increased permeability of potassium ions. The hyperpolarization at the end of an action potential is primarily driven by the efflux of potassium ions, but it is not affected by the permeability changes during the action potential itself.

In summary, the correct answer is C: it will take a stimulus of larger magnitude to initiate an action potential.