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What is the half-life of an isotope that decays to 25% of its original activity in 60.3 h?half-life:...

Question

What is the half-life of an isotope that decays to 25% of its original activity in 60.3 h?half-life:

What is the half-life of an isotope that decays to 25% of its original activity in 60.3 h? half-life:



Answers

Calculate the half-life of a radioisotope if it decays to $12.5 \%$ of its radioactivity in 12 years.

Solving this problem. So here I can devalue t half multiplication, three is equal to five foward on further simplification. I can die T. How is equal to five powered by three which is equal to 1.667 Harvard. Now the value of lambda is equal to 0.693 by T. Have which is equal to 0.693. Bye 1.667 which is equal to 0.415 per Harvard. Now the value of anti can be written at 0.9 multiplication and not also in this problem I can write the value of anti which is equal to and not into the power minus lambda T. On solving further. I can write 0.9 and not is equal to and not into the power minus lambda T. On. Further simplification I can write a value of minus Lamberti is equal to long 0.9. On solving it further I can write the value of T. Is equal to minus long, 0.9 x 0.415. So finally I get the is equal to 0.25 hours as evidence.

So this problem we're doing for treaty you have life. Africam, please. Une is good point tree tree years and the time is it good to five years? You have to person tasty care. In this time period, this process will first find first find the cake posted for can be found based formula her life physical too Mitt log failing to do added by Okay, constant Where did take Constant is weaker. Cool Ellen two divided by half. Life is 1.3 three years and it's all this we get constant is equally cool. Is it a point 0562? Have you This is the your critical Esther for chicken. No initial number look like in prevalence it by musical to and not in the mud off you. Clear remaining after 20 Jim presented by and standing We can really But in a formula one is going to in order before minus lend rt the hope of playing percentage off clay did which is a cuckoo weekly. I the kid do a good bye. You shouldn't today Mystic live 100 Let me play. Medicaid is a quick Oh, you shouldn't roughly play minus breath Play a 90 off 20 right? Like you should never deployed by 100. Makes all this get friction to go toe one minus and the very by in north into I'm gig 11 has been is a good Nord. We keep our minus Linda, you are right in order. We're deeply 100 So we'll get local friction. Secret to one minus you keep on minus you, Nimda. Good. Very sexual values. We get one minus a key power minus zero point. Little 562 12 year. I will stick my way. Five years into this whole with 1100 When we saw this we get a fraction is a cool de for 15% is the answer 70 program.

Okay, Here's an application of half life We're talking about treaty. Um, and we have our half life formula here. So what we're going to do is substitute numbers into that formula and solve for the amount of Time T that it would take for 25% of the treaty. Um, to decompose. Okay, so we don't know how much we're starting with, so it doesn't really matter. We can just choose the amount we're starting with. I'm going to choose a not equals one. And so how much are we ending with? Well, if we want 25% of it to decompose, that means we still have 75% of it, So a would be 750.75 So I'm going to use those numbers and substitute them into my equation. And I get 0.75 equals one times two raised to the power negative t over 12.4, because 12 point pours the half life. So we're substituting that in for a tch. Now we're solving this equation for tea so we can divide both sides of the equation by one. That doesn't really do anything for us. That's why I chose a one because it would be so simple to work with. Next we can take the log of both sides. I'll go ahead and use the natural log. So the natural log of 0.75 equals the natural log of two to the negative T over 12.4. Now we can take this exponents and move it out to the front according to the power rule. So what we have at this point is natural log of 0.0.75 equals the opposite of tea, divided by 12.4 times natural log of two. And her goal is to get tea by itself. So there's three things we need to d'oh. We need to multiply both sides by 12.4. We need to divide both sides by natural log too. And we need to multiply both sides by a negative and we can do all those at once. So that will give us negative 12.4 times in natural log of 0.75 divided by the natural log of two equals t. Now, naturally, you're not gonna talk about time in that way. You're probably going to want an approximate answer. So we typed that whole thing into the calculator, being very careful with parentheses. Depending on your calculator, you may need more or less, and I end up with approximately 5.1465 and the units on that would be years. So that's how many years it would take to have 25% of it decomposed.

Yes, probably that human the number of nuclear initially present is equal to 50 1000 nuclear. And the number of Ukraine after 2.5 hours is equal to 20,000 588. And the time total time spent is equal to 2.5 hours. We're asked to find the half life. Did I get through with him? His initial number of place. 50 1000. She's in north. Then after one half life there will be 25 1000. You play which is not do it by two and after two half lives you can say that in both left will be and not do it by four which is equal to 12,500 nebulae. So you can see it pete number of. Uh huh. Lives alone is equal to two. Well we can find half life by the very in total time with number a half lives which is to it's absolutely believes these 2.5 hours. You had way too. When we saw this we get half life is equal to 1.25 course. This is the answer to this question. Thank you for what you do


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