Final answer:
The element that reacts most vigorously with water to produce hydrogen gas is potassium (K).
Step-by-step explanation:
Based on our knowledge of periodic trends, we can predict that the element that reacts most vigorously with water to produce hydrogen gas is potassium (K).
As we move down Group 1 of the periodic table, from lithium to francium, reactivity with water increases. Potassium is located just below sodium, making it more reactive and capable of producing hydrogen gas and heat when it reacts with water.
Therefore, the correct answer is C) Francium (Fr) from the given options.