39mg radioactive with 1/2 life is decay total in 2.5 years. How many mg it remain if half of the amount is decay in 2 years?
Thank you!
To find out how much radioactive material remains after a certain amount of time, we can use the formula for radioactive decay:
A = A₀ * (1/2)^(t / t₁/₂)
Where:
A is the amount of material remaining after time t
A₀ is the initial amount of material
t is the elapsed time
t₁/₂ is the half-life of the material
In this case, we know that the initial amount of material is 39 mg, the half-life is 2.5 years, and half of the amount decays in 2 years. We want to find the amount remaining after 2 years.
Let's calculate it step by step:
1. Find the fraction of the initial amount that decays in 2 years:
fraction_decayed = (1/2)^(2 / 2.5)
2. Calculate the amount remaining after 2 years:
amount_remaining = 39 * fraction_decayed
Now, let's plug in the values and calculate the result:
fraction_decayed = (1/2)^(2 / 2.5)
= (1/2)^(0.8)
≈ 0.630957
amount_remaining = 39 * 0.630957
≈ 24.57 mg
Therefore, approximately 24.57 mg of the radioactive material will remain after 2 years.
I hope this helps! Let me know if you have any further questions.