 The half-life of a radioactive isotope is 11 seconds. Determine the fraction of undecayed nuclei after 5.5 seconds. Before I get into this, why don't you pause the video and give this one a try? Alright, hopefully we have given this a shot. Now, we know that the radioactive nuclei they decay exponentially. And this is how the decay looks like over time. We can say that initially there are n not number of radioactive nuclei. And the time it takes for this number to fall to its half, for 50% of the nuclei to decay, for it to become n not by 2, the time required is called a half-life. So this time right here is, this is one half-life. And the number of undecayed nuclei, which are still radioactive, they are n not by 2 at this point. If we add one more half-life, then we can see that the number of radioactive nuclei that remain is half of this number and that is n not divided by 4. So this is, this is 2 times the half-life. And similarly, if we add one more, if we add one more, then this is 3 times 3 half-lives and the number of undecayed nuclei at this point is n not divided by 8. So we can see that there is a pattern over here, a pattern between the number of half-lives and the number of undecayed nuclei. After one half-life, the number of undecayed nuclei are n not divided by 2. And after two half-lives, it is n not by 4. After three half-lives, it is n not by 8. So if we keep on writing half-lives, we can say that after n-th half-life, the number of undecayed nuclei would be n not divided by 2 to the power n. Because we can write 8 as 2 to the power 3, we can write 4 as 2 square and 2 to the power 1 is just 2. And the question is asking us to figure out the fraction of undecayed nuclei after 5.5 seconds, which is half of the half-life. Half-life is 11 seconds and 11 by 2 is 5.5. So the number of undecayed nuclei after half of half-life, that would be n not divided by 2 to the power 1 by 2. Or we can write this as n not divided by root 2. We can say that the number of undecayed nuclei after 5.5 seconds, let's call that n. This is equal to n not divided by root 2. And the fraction of undecayed nuclei, that would be the number that remains divided by the initial number of nuclei. So that would be n divided by n not. And this comes out to be equal to 1 by root 2.