Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this is 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?
3 days
10 days
13 days
33 days
decaying to 10% takes
log0.10/log0.5 = 3.32 half-lives
So, A's half-life is 33/3.32 = 9.94 days
B's half-life is 43/3.32 = 12.95 days
Looks like (a) is the answer
The two expressions below have the same value when rounded to the nearest hundredth.
mc013-1.jpg
What is the approximate value of mc013-2.jpg to the nearest hundredth?
To find the approximate difference in the half-lives of the isotopes, we first need to understand what half-life means.
The half-life of a radioactive substance is the time it takes for half of the original amount to decay. In this case, we are told that both isotopes decay to 10% of their original amounts.
Isotope A decays to 10% of its original amount in 33 days, so we can say that its half-life is approximately 33 days.
Isotope B decays to 10% of its original amount in 43 days, so its half-life is approximately 43 days.
Now, to find the difference in their half-lives, we subtract the shorter half-life from the longer half-life:
43 days - 33 days = 10 days
Therefore, the approximate difference in the half-lives of the isotopes is 10 days.
So, the correct answer is:
10 days.