Final answer:
Element X, with an initial mass of 220 grams and a half-life of 6 minutes, would take approximately 54 minutes to decay to 26 grams.
Step-by-step explanation:
In order to determine how long it will take for Element X to decay to 26 grams, we need to calculate the number of half-lives it will take to reach that amount.
The initial mass of Element X is 220 grams, and the half-life is 6 minutes.
First, we need to find the number of half-lives it takes for the mass to decrease from 220 grams to 26 grams:
220 grams / 26 grams = 8.46
Since we can't have a fractional number of half-lives, we need to round up to the nearest whole number, which is 9. Multiplying 6 minutes (the half-life) by 9 (the number of half-lives) gives us:
6 minutes * 9 = 54 minutes
Therefore, it would take approximately 54 minutes for Element X to decay to 26 grams.