Answer :
it would take approximately 33 minutes for 300 grams of Element X to decay to 80 grams.
To find the time it takes for 300 grams of Element X to decay to 80 grams, we need to use the half-life of the element, which is 11 minutes.
First, we need to find the number of half-lives it takes for the amount of Element X to decay from 300 grams to 80 grams.
To do this, we can use the formula:
N = N₀(1/2)^n
where N is the final amount of the element, N₀ is the initial amount, and n is the number of half-lives.
Plugging in the values, we get:
80 g = 300 g(1/2)^n
Solving for n, we get:
n = log₂(300/80) ≈ 2.24
Since we cannot have a fraction of a half-life, we round up to the nearest whole number, which is 3.
Now that we know it takes 3 half-lives for the element to decay from 300 grams to 80 grams, we can calculate the time it takes by multiplying the half-life by the number of half-lives:
Time = (11 minutes) * 3 ≈ 33 minutes
Therefore, it would take approximately 33 minutes for 300 grams of Element X to decay to 80 grams.
