Final answer:
When ligand-gated sodium channels open, sodium ions enter the cell due to a high concentration gradient, leading to depolarization. The membrane potential shifts from -70 mV towards and beyond zero, reaching approximately +30 mV. Repolarization then ensues as potassium ions leave the cell, reestablishing the resting membrane potential.
Step-by-step explanation:
If a cell is at resting membrane potential and ligand-gated sodium channels open, there will be a net movement of sodium into the cell until various processes take place. Initially, because the concentration of Na+ is 10 times higher outside the cell, sodium ions will rush into the cell driven by the concentration gradient. This influx of sodium changes the membrane's voltage from a resting potential of around -70 mV to a more positive value, a process known as depolarization. Depolarization moves the membrane potential toward zero.
The movement of sodium into the cell will not stop when the membrane potential reaches zero due to the strong concentration gradient; it will continue until the membrane potential reaches approximately +30 mV. At this peak, voltage-gated potassium channels open and potassium ions leave the cell, which starts the process of repolarization, bringing the membrane potential back towards the resting state. After a brief period of hyperpolarization, where the membrane potential becomes slightly more negative than the resting state, it stabilizes at the resting potential due to the action of the sodium-potassium pump and the closure of potassium channels.