 Hello friends, this is Dheeraj from Centrum Academy. So today also I have taken up a question. This is a doubt which was asked by one of our students. So in case you also have any doubts, feel free to get in touch with us. So this question is from the radioactive chapter. So let's read the question first. A human body removes by waste, discharge, sweating, etc. And what is the radioactivity law? The law is that rate of decrease of a particular substance should be proportional to the number of substance that is present or the amount of substance that is there. So if I just treat it like a radioactive decay itself, I can say that dn by dt because of the body discharge is minus lambda times n. So this is due to what body does. Now what is written further is that there is a radioactive substance, technetium is the name of the element which is injected in some form in a human body. The body excretes half the amount in 24 hours. So basically the half life of how body removes this substance is given. Now since this is a radioactive substance, so it will have its own half life of disintegration. So that is given as 6 hours. So basically what is happening here is that this element, this radioactive element technetium, this is getting removed from the body by two different paths. One path is because of the radioactive decay. Let's call it as, let's represent it with a rate constant lambda 2. The another path is how body removes the waste. So that rate constant let us say is lambda 1. So the total rate at which this element is decreasing from the body will be because of what body does and what is happening because of the radioactive nature of the element. So you just have to add up both the rates and you arrive at the total rate of the depletion of this element from the body. So this is dn by dt is equal to lambda 1 plus lambda 2 times n. So now this equation is very similar to lambda times n where lambda is lambda 1 plus lambda 2. So basically you have a rate constant with equivalent rate constant of how body is removing plus because of the radioactive nature of this element. So I can write it down as lambda 1 plus lambda 2. Now lambda 1 can be written as 0.693 divided by 24 because the half life for lambda 1 process is 24 hours plus lambda 2 which is what 0.693 divided by 6 hours. So this is lambda equivalent. Now we need to find time after which the activity of this particular element decreases from 6 to 3. So we know that activity of an element is proportional to number of the elements. So if activity reduces to half the number of nucleus is also going by half. So in a way it is asking what is the half life of this particular reaction that is going on. So we know that lambda equivalent is this and half life for a process for which the rate constant is lambda is 0.693 divided by lambda. So t half will be this divided by lambda equivalent. So all you have to do is substitute it here and you will get the answer in terms of hours. That's how you approach this particular question. So I hope you have learned something today. In case you have any doubts feel free to get in touch with us. Thank you.