Final answer:
If the sodium/potassium ATPase were turned off, the membrane potential would eventually become equal to zero, as the active transport that creates and maintains the ion concentration gradients essential for the resting membrane potential would no longer function.
Step-by-step explanation:
If the sodium/potassium ATPase were turned off, the membrane potential would eventually become equal to zero. The sodium/potassium ATPase is essential for maintaining the resting membrane potential of a neuron by actively transporting three Na⁺ ions out of the cell and two K⁺ ions into the cell. This creates a higher concentration of Na⁺ outside the cell and a higher concentration of K⁺ inside the cell. The difference in ion concentration across the cell membrane leads to the resting membrane potential, which is typically around -70 mV, with the inside of the cell being negatively charged relative to the outside.
K⁺ ions can leave the cell through channels that are open about 90% of the time, whereas Na⁺ channels are rarely open, further contributing to this charge difference. Without the activity of the sodium/potassium ATPase, there would be no active transport to maintain these concentration gradients, and the passive diffusion of ions would eventually lead to an equalization of ion concentrations on both sides of the membrane. This would result in a membrane potential that approaches zero, eliminating the charge difference across the membrane.