Final answer:
With equal Na+ concentrations inside and outside the cell and the membrane voltage set to the Nernst potential for Na+, little to no Na+ movement would occur since this represents an equilibrium state between concentration and electrical gradients.
Step-by-step explanation:
If the concentration of Na+ outside and inside the cell are both 100 mmol/liter and you set a membrane voltage of 58 millivolts using a voltage clamp, measuring membrane current with Na+ being the only ion crossing the membrane, you would expect to see little to no movement of Na+ ions. This is because the membrane voltage equals the Nernst potential for Na+, which is the voltage at which there is no net flow of ions across the membrane due to equilibrium between the concentration gradient and the electrical gradient.
Typically, the resting potential inside a neuron cell membrane is about -70 mV due to differing ion concentrations on either side, creating an electrical charge difference. However, when Na+ channels open, positively charged sodium ions rush into the cell, reducing this charge difference in a process called depolarization. If the concentration of Na+ was higher outside the cell, the ions would move into the cell following the concentration gradient until the electrical charge inside the cell increases, potentially reaching as high as +30 mV, and causing further depolarization.