The half-life of ²³²Th is 1.4⨉10¹⁰ yr. Find the number of disintegrations per hour emitted by 1.0 mol of ²³²Th.

Video transcript

Hello. Everyone in this video we're gonna calculate for the number of disintegration per hour. Irradiated by 1.55 moles of this right here. So we want to go ahead and remember that whenever dealing with radioactive and nuclear decay of isotopes, we're going to follow the first order kinetics and the half life of a first order reaction is given to us by will T half for half life is the natural log of two divided by Cape and rearranging this equation. Then we can have K. Equaling to the L. N. The natural log of two divided by the time. Alright, so going head to plug in. My numerical values are given from the problem. So you have K equaling again too. Our 0.693 divided by 4.33 times 10 to the 10 year. Then thou give me my value for kate as 1.6005 times 10 to the negative 11 year to the negative ones. Something that's not given to us but we should know is that one mole is equal to 6.022 times 10 to the 23rd. Alright, so for our rate it's equal to K. Times. And so plugging in mind american values. Then we can have the rate equaling two. Our case we just offer over here being 1.6005 times 10 to the negative 11 Course we have the unit being here to the - multiplying by right over here. So does have 6.22 times 10 to 23rd. And that will give us the rate of 9.63, 8 times 10 to the 12. All right now, finally calculating for the number of disintegration per hour. So we can say rate is equal to 9.63, 8 times 10 to the 12. They will go ahead and convert our years in two days. So for every one year There is about 3, 65.25 days and going from days to hours of one day Per 24 hours. So putting that into my calculator, I'll get the value of 1.10 times 10 to the nine. And right here is going to be my final answer for this question. Thank you all so much for watching.