Final answer:
The flux of potassium across the membranes of rods in the dark is characterized by a greater potassium efflux compared to sodium influx, due to the sodium-potassium pump creating an electrochemical gradient favoring potassium outward movement and limited sodium inward flow.
Step-by-step explanation:
The statement that best describes the flux of potassium across the membranes of rods that are in the dark is that 'Potassium efflux is greater than sodium influx'. In the resting state, the neurons, including the rods in the retina, have a higher concentration of sodium outside of the cell, which tends to move inside due to the difference in concentration. Conversely, potassium is more concentrated inside the cell and moves out. This is facilitated by the sodium-potassium pump which actively transports three sodium ions out of the cell for every two potassium ions it pumps into the cell, resulting in a net negative charge inside the cell.
Since the interior is now more negatively charged, it adds to the electrochemical gradient that pulls sodium into the cell, while potassium tends to move out. Thus, in the resting state of rods that are in the darkness, the flux of potassium ions out of the cell is expected to be significant, in contrast to both the constrained influx of sodium and the negative membrane potential which inhibits the inward movement of positively charged sodium ions. Therefore, the correct answer is 'Potassium efflux is greater than sodium influx'.