Answer:
0.268
Step-by-step explanation:
If you want to know how much of a radioactive substance is left after some time, you need to use some fancy math and some weird symbols. First, you need to know the decay constant (λ), which tells you how fast the stuff is disappearing. Then, you need to know the half-life (T1/2), which tells you how long it takes for half of the stuff to go poof. The formula to find out how much stuff is left is:
N = N0 ⋅ e − λt
where:
N = the amount of stuff left after time t N0 = the amount of stuff you started with λ = the decay constant t = the time that passed e = some number that nobody knows (just kidding, it's about 2.718)
For example, let's say you have some krypton-85, which is a radioactive gas that glows green. You have 100 grams of it and you want to know how much is left after 25 years. The half-life of krypton-85 is 10.76 years, so you can find the decay constant using this formula:
λ = ln 2 / T1/2
where:
ln 2 = natural log of 2 (about 0.693) T1/2 = half-life
So, you plug in the numbers and get:
λ = ln 2 / 10.76 λ ≈ 0.0644 year−1
Now you can use this value to find out how much krypton-85 is left using the first formula:
N/N0 = e − λt N/N0 = e − (0.0644)(25) N/N0 ≈ 0.268
This means that after 25 years, you have about 26.8% of krypton-85 left, or about 26.8 grams. The rest has turned into something else, probably something boring like argon or oxygen. The answer is 0.268.