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Radioactive isotopes such as $^{32} \mathrm{P}$ are used to follow biological processes. The following radioactivity data (in relative radioactivity values) were collected for a sample containing $^{32} \mathrm{P}$ : $$\begin{array}{cc} \text { Time (days) } & \text { Relative Radioactivity } \\\hline 0 & 10.00 \\\hline 1 & 9.53 \\\hline 2 & 9.08 \\\hline 5 & 7.85 \\\hline 10 & 6.16 \\\hline 20 & 3.79 \\\hline\end{array}$$ a. Write the rate law for the decay of $^{32} \mathrm{P}$. b. Determine the value of the rate constant. c. Determine the half-life of $^{32} \mathrm{P}$. d. How many days does it take for $99 \%$ of a sample of $^{32} \mathrm{P}$ to decay?

And question 70. It discusses the synthetic radio isotope technetium, 99 which decays via beta mission. It is the most commonly used radioisotope for nuclear medicine. Data is provided below. It shows the disintegration rates per minute as a function of time per hour. We don't necessarily have to convert the time units to be the same units because all we're doing is determining the half life. The half life will be the time in hours when the disintegration rate in disintegration per minute, or whatever unit you choose is half of the initial rate. If it becomes half the initial rate, then half of the radio isotope has decayed. So we need to take the data that was provided and plot it and it is a little grainy here. But these are the values that were provided and they're plotted down below. We start at 1 80. Disintegration is for a minute. So the half life will be when we get to 90 disintegration per minute, which corresponds to this is six minutes down here, So the half life is six minutes.

Is a sub field of chemistry that deals with our radio activity and our nuclear processes and transformations within the nuclei. So here we're looking at our N 219. So this belongs to the decay series of uranium 235 and to 20. This belongs to the decay series of 2, 3, 2 thorium. So the alpha particle is a charge of plus two And a massive four Plus four units on a beta particle Has a charge of -1 and no mass. So the alpha emission decreases the mass number by four, and the beta emission has no effect on last number.

So I'm going to upload the gloves I made full of questions. Oh, so for the multiples of half life, Yeah. Oh, no. Good. Yeah. You can see that the initial amount ofthe raid and two twenty was stated to be assisting thousand and add a half life off fifty five point six, which will be some, very. Here you have eight thousand our terms presence, which is his only health, only initial amount. So in this actually makes you know that, indeed, at half life you have health off the original Amal tippin present and for the subsequent wants is the same. So you can see the graph is quite steep. Well, the so at fifty five men at the nest, half life you said you have eight hundred being reduced to four hundred at the other. They said, half life you have, it's not sand with four hundred there. Our original the amounts presence now is two hundred and save. So it will go on and go and go. And until because because there elements contains a specific amount so far, Toms. Yeah, it would go on until it gets too light. Zero hour Toms which pay the half life equation. It it is no feasible. But so for the next one for the nun. What a whole one look. You can see it's event different from the first one. I can't see on it. Fifty seconds. You have more than half off all you started with which desisting thousand are Tom's being present. So he told you that fifty seconds is that is not the half life to his. Well, when you Joe it Teo fifty five point six, which is the half life you would actually get to live eight hundred. And so this is how that graph for the nanoparticle help half lives would look like.

In this problem, the lifetime of emission of alpha particle is given by dirty. Which is equal to 3.8 23 It is Which on simplification I can write evaluate 3.8-3. Multiplication, 24 hour multiplication, 36/00. Which in solving I get devaluate (330) 307 0.2 seconds. Now I am just writing the high ginsburg uncertainty principle. So it can be written edge Daily multiplication, guilty. The approximately called two Agendas. So the value of them daily. The approximately equal to exodus by dirty. Which is approximately equal to catch by to buy Dirty. Which is equal to 6.62 more duplication 10 to the power minus 34 2 seconds. Bye two. Primary duplication DDT. Jiro 307.2 seconds. On simplification I get the value it 3.191. Multiplication 10 to the Power -40. You'll changing the unit. I just multiply and divide by this value which is equal to 1.99 Multiplication 10 to the power minus 21 e. B. The Rendon nucleus finite lifetime of the excited state is very high when compared it to the emitted alpha particle energy uncertainty.