The half-life of indium-111, a radioisotope used in studying the distribution of white blood cells, is t1/2 = 2.805 days. What is the decay constant of 111In?

Video transcript

Hey folks, welcome back. So here we have Mercury 203 is a synthetic radio isotope of mercury that undergoes beta decade to thallium 203. The half life of mercury is 23 and has been found. So it has been found to be 46.60. So that's the half life of mercury. We need to calculate the value of DK constant or the rate constant, which is K. Right? So we know that all of the radioactive processes are going to proceed in the first order fashion, first order and we actually have half life. So the half life of first order is a very easy equation. It is just half life Equals two Ln of A line of two divided by that rate constant or their decay constant. Right? So a line of two is obviously just a constant because you're going to get a number when you plug that into the calculator, half life is given to us. It is 46.6 days. And now we just need to solve for K. So let's go ahead and solve for K. So it's going to be a one of two over the half life. Okay, so let's go ahead and plug in numbers. So we have a lot of two, I'm just going to leave it as that and then half life is 46. days. Right? So that's days. So when you solve for that, when you put that into the calculator, K is going to equal to 1. Times 10 to the -2. And what are the units here? Well, here on the top, we don't have any units, but on the bottom we have days and days are on the denominator. So it's going to be days in verse right? Days To the -1. Power in verse. And that's exactly what they wanted. They wanted inverse days. So there is our answer right there. Very simple problem. Thank you so much for watching. I hope this was helpful. And we'll see you in the next video.