Understanding Nuclear Decay: Element X

Explanation:

The half-life of an element refers to the time it takes for half of a sample of nuclei to decay. In the case of element X, it has a half-life of 80 minutes.

Let's analyze the statements provided:

1. "There will be 4 nuclei left": False. After 240 minutes (three half-lives), there will not be 4 nuclei remaining. The number of nuclei reduces by half with each half-life.
2. "There will be 2 nuclei left": False. Similarly, after 240 minutes, there will not be 2 nuclei left as well.
3. "Half of the last remaining nucleus will decay": True. This statement is correct. After 240 minutes, there will be one nucleus left. Half of this remaining nucleus will decay within the next half-life period.
4. "There is a 50% chance the last remaining nucleus will have decayed": False. The probability of decay for the last remaining nucleus does not change with time or the decay of other nuclei. It is based on the random process of decay and the element's half-life.

Therefore, after 240 minutes, half of the last remaining nucleus of element X will decay due to its 80-minute half-life.