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.

33 dys