Final answer:
The sodium-potassium pump is the structure that moves sodium and potassium ions across the semipermeable membrane of cells, using ATP to drive the ions against their concentration gradients.
Step-by-step explanation:
The structure responsible for the sodium and potassium ions switching places across the semipermeable membrane is known as the sodium-potassium pump. This pump is critical for maintaining the electrochemical gradient across the cell membrane. Operating through active transport and powered by ATP, the sodium-potassium pump moves three sodium ions out of the cell and two potassium ions into the cell, each against its concentration gradient. The action of the pump is essential for a variety of cellular functions, including generating action potentials in nerve cells.