Question

If originally there were X atoms of radioactive isotope present and now there are only X/8 atoms, how many half-lives have elapsed?

Answer 1

In radioactive decay, the number of radioactive atoms decreases by half for each half-life that passes. In this case, if originally there were X atoms and now there are only X/8 atoms, we can determine how many half-lives have elapsed by finding out how many times X needs to be divided by 2 to get X/8. Therefore, 3 half-lives have elapsed.

Step-by-step explanation:

In radioactive decay, the number of radioactive atoms decreases by half for each half-life that passes. In this case, if originally there were X atoms and now there are only X/8 atoms, we can determine how many half-lives have elapsed by finding out how many times X needs to be divided by 2 to get X/8.

Let's set up the equation: (X/2)n = X/8. We can simplify this equation to 2n = 8.

Taking the logarithm base 2 on both sides of the equation: n = log2 8 = 3.

Therefore, 3 half-lives have elapsed.