Final answer:
The half-life of a radioactive element cannot be determined from the emission of one alpha particle per second without additional information. The emission rate per second does not provide enough data to accurately calculate the half-life for any given element.
Step-by-step explanation:
The question you're asking relates to the concept of half-life, which is the time it takes for half of a radioactive sample to decay. If the radioactive element emits an alpha particle per second at an instant, it does not directly determine the half-life without additional information. To find out the half-life, you would need to know either the initial quantity of the substance and the remaining quantity after a certain time or be given a specific relationship between emission rate and half-life for that element.
According to your question, the answer choices provided don't correspond directly to the emission rate of one alpha particle per second—they rather seem to suggest fixed durations. However, as no specific element is mentioned nor is there enough information given, it isn't possible to accurately answer the question. An emission of one alpha particle per second could correspond to many different half-lives depending on the element and the total number of atoms present.