Final answer:
If a neuron's membrane is only permeable to sodium ions, and sodium concentrations are equal on both sides, the membrane potential would be zero because no net movement of sodium ions would occur to create a charge difference.
Step-by-step explanation:
The resting membrane potential of a neuron is defined by the separation of charges across its plasma membrane, with the interior being negatively charged compared to the exterior. This potential is primarily the result of the different ion concentrations of sodium (Na+) and potassium (K+), as well as the selective permeability of the neuron's membrane to these ions. If the membrane is permeable only to sodium ions and the sodium concentrations are equal on both sides, then at rest, no net movement of sodium ions would occur, and there would be no charge difference across the membrane, resulting in a membrane potential of zero.
In a typical neuron, potassium ions (K+) largely contribute to the resting membrane potential as they are allowed to move more freely across the membrane than sodium ions. This movement, along with the function of the sodium-potassium pump, which exchanges three Na+ ions for two K+ ions at the cost of one ATP molecule, establishes the negative charge. Without this activity and with equal sodium concentrations, there would be no potential difference, making c (the resting membrane potential is zero) the correct answer for the scenario described.