If it takes 45 days for 80.0 mg of a particular radioactive isotope to decay to 10.0 mg what is its half-life?
To find the half-life of a radioactive isotope, you need to understand the concept of half-life. The half-life is the time it takes for half of the substance to decay.
In this case, you are given that it takes 45 days for 80.0 mg to decay to 10.0 mg. Let's break down the problem:
Start with the initial amount of the isotope: 80.0 mg.
After one half-life, half of the isotope decays, so you are left with: 80.0 mg / 2 = 40.0 mg.
Similarly, after the second half-life, you are left with: 40.0 mg / 2 = 20.0 mg.
And after the third half-life: 20.0 mg / 2 = 10.0 mg.
You can see that it takes 3 half-lives for 80.0 mg to decay to 10.0 mg. Therefore, the half-life of this radioactive isotope is 3 times the given time of 45 days.
To calculate the half-life specifically, multiply the given time by 1/3:
45 days × 1/3 = 15 days.
So, the half-life of this particular radioactive isotope is 15 days.