if you start with 100mg of radioactive material that has a half life of one hour, how many mg's of radioactive material would you have in 10.2284952 hours?
x=100(.5)^(10.2284952)
x=.083352
To calculate the amount of radioactive material remaining after a certain time, we need to use the half-life formula: Remaining Amount = Initial Amount × (1/2)^(time / half-life).
In this case, the initial amount of radioactive material is 100mg, and the half-life is one hour. We want to find out the remaining amount after 10.2284952 hours.
Let's plug the values into the formula and calculate the result step-by-step:
1. Calculate the number of half-lives: time / half-life = 10.2284952 / 1 = 10.2284952
In this case, the time in hours is equal to the number of half-lives because the half-life is one hour.
2. Apply the formula: Remaining Amount = Initial Amount × (1/2)^(number of half-lives)
Remaining Amount = 100mg × (1/2)^10.2284952
Now, let's calculate it using a calculator or a math software:
Remaining Amount ≈ 100mg × (1/2)^10.2284952
≈ 100mg × 0.000462659
The approximate value of the remaining amount of radioactive material after 10.2284952 hours is 0.0462659mg.