The correct answer is option 3: Phosphorus. Phosphorus is an essential mineral that is required by the human body for the hardening of bones and teeth. It plays a crucial role in the formation and maintenance of the skeletal system.

Option 1: Iodine is not directly involved in the hardening of bones and teeth. Instead, iodine is necessary for the production of thyroid hormones, which regulate the body`s metabolism.

Option 2: Iron is important for the production of red blood cells and the transportation of oxygen throughout the body. It does not contribute directly to the hardening of bones and teeth.

Option 4: Potassium is an electrolyte that helps to maintain proper fluid balance and nerve function in the body. While it is important for overall health, it is not directly involved in the hardening of bones and teeth.

In conclusion, while all of these elements are important for various bodily functions, it is phosphorus that is specifically required for the hardening of bones and teeth.