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A radioactive isotope has a half life of 60.2 minutes. How longwill it take for the radiation from a 325 pCi sample to decrease to41 pCi?...

Question

A radioactive isotope has a half life of 60.2 minutes. How longwill it take for the radiation from a 325 pCi sample to decrease to41 pCi?

A radioactive isotope has a half life of 60.2 minutes. How long will it take for the radiation from a 325 pCi sample to decrease to 41 pCi?



Answers

232 Ra has a half-life of 11.4 d. How long would it take for the radioactivity associated with a sample of $^{232} \mathrm{Ra}$ to decrease to $1 \%$ of its current value?

Hey, guys. So in this question were given that the radioactive ice to phosphorus 32 has 1/2 life of 14.3 days and were asked to find how long it will take this sample to lose 99% of its radio activity. So the first thing I'm going to do is use Thehuffingtonpost Asian for first order reaction to find my rate constant. So that is my half life Equalling 0.693 over K. I'll solve for K. So that gives me 0.693 over my half life. And I can go ahead and just plug in my half life into this equation. And when I do that, I get that my half life is or my K value is 0.485 in verse days as my unit. Now that I have this, I can go ahead and use my integrated rate law equation for first order reaction to find the concentration or the time. Excuse me. So my rate law equation is the natural log of a Sebti is equal to the natural log of my initial concentration minus Katie. I'm gonna go ahead and solve for Katie by adding it over to the left side. And I'm going to go ahead and subtract the natural log of Ace empty over to the right side. And when I do that by law algorithm rules, I get this expression. With this, I console for tea. So T is going to be equal to one over, okay, times the natural log of our concentrations. And with this, I can go ahead and plug in my value. So for my k value, that's what we just found earlier. So that's one over. Uh, excuse me, guys. 0.485 days in verse, times the natural log of my initial concentration, which is 100% so as a decimal distress one over the concentration at the time that we want. So if 99% of the phosphorus 32 decomposes, that means we're left with 1% and 1% as a decimal is 0.1 Plugging this into our calculator, we find that the time it takes to decompose 99% of the radioactive phosphorus is 95 days. And this is our final answer

Question here does us that the half life off story um 2. 34 is equal to 24.1 days and then were asked the time it's going to take for the mask off 84.5. Milly grants off story um 2 34 to decay to give a mass off 20.9 milligrams. The initial mass I am not is supposed to be 84.5 mg, and the final mass at Time T, which can be denoted as empty in sub D, is equal to 20.9 mg. So using this information, we can calculate the time it will take for the decay reaction Docker and reduce the mass to 20.9 mg city is equal toe the time that it has been all the time we need to calculate, and this will be equal to negative behalf divided by 0.693 Mhm. Multiply that by the natural, log off the mass at Time T, and we have to divide that by the mass at time zero or the initial mass. If we substitute for these, that would look like this and because we are substituting the half life in the units off days. The final answer that we get by substituting values to this equation 40 is going to be in the units off days, and then we simplify this. But given the answer 48 point six days and this is how long it is going to take for the mass off story, um 2 34 to drop to 20.9 mg, starting from 84 point 5 mg.

Question. 69. The half life of trillion is 12.3 years. How long will it take for 7/8 of the sample to decay? Half life is the time it takes were half a radioactive material to disintegrate by radioactive decay processes. So that means that if you initially start off with a certain amount after 1/2 life, you'll have half assed much. After a second half life, you'll have 1/4 after 1/3 we'll have an eighth and so on. So in this question, it says that we're have 7/8 decayed, which means that we'll have an eighth remaining. So that's 12 3/2 lives, and we know that 1/2 life is 12.3 years, so the time port to decay will be three times 12.3 or 36.9 years.

Half life is defined as the time it takes were half a sample of a radioactive material to decay to form a more stable substance. So if, for example, you start off with an initial amount after 1/2 life, we would have half that amount. After a second half life, we would have 1/4 after 1/3 we would haven't eight remaining and so on. So if you know the half life and you know the amount remaining or how much has decayed, you can predict how long it would take. So if we know, for example, that the halfway of a certain isotopes is 12.3 years and we want to know, how long does it take to have it? 7/8 decayed. So if seven it's was decayed, that means that 1/8 remains, which means that it's taken one to 3/2 lives. So we have 3/2 lives and everyone half life has a time of 12.3 years. We multiply three by 12.3. 36.9 years has passed


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