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Problem 55 Medium Difficulty

The table below lists reported levels of iodine- 131 contamination in milk in four countries affected by the 1986 Chernobyl accident, along with each country's safety guideline. Given I-131's half-life of 8.04 days, how long did each country have to wait for I-131 levels to decline to a level deemed safe by its standards?
$$\begin{array}{lcc}\text { Country } & \text { Reported } & \text { Safety Guideline } \\\hline \text { Poland } & 2000 & 1000 \\\text { Austria } & 1500 & 370 \\\text { Germany } & 1184 & 500 \\\text { Romania } & 2900 & 185 \\\hline\end{array}$$

Answer

Poland: t = 8.04 d , Austria: t = 16.2 d , Germany: t = 10.0 d , Romania: t = 31.9 d

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Top Physics 103 Educators
LB
Liev B.

Numerade Educator

Farnaz M.

Simon Fraser University

Zachary M.

Hope College

Aspen F.

University of Sheffield

Video Transcript

All right. So Question 55 is related to the radiation content of milk in surrounding countries from around Chernobyl, Brother, you know, of course, it was the trend dramatic nuclear power plant incident which the radiation across countries that were near it at the time. So this neo this question deals with reported higher creation values and milk offended that they're allowed to sell at the time. That's question asks, based on the reported values for the radiation content of the milk, How long must we wait in order for the radiation level to be deemed safe in order to sell? So how long will take from the relation level to go from the reporter that you, here down to the safety guidelines value, um, so that the sample that were kicked that we care about here is I want 31. We're told that has 1/2 life of 8.4 days to determine the time from each of these points, we can simply to start with her typical t K equation. So the scenario are and not is our initial radiation values of mass media reported to call him, and our safety guideline is the radiation out at a given time, which is here again by em. So if you want to solve for time here we take the natural longer than the both signs. After we divide by and not just be cooperative native landed t is we're given half life. I'm going to replace Lambda with Ellen of to two divided by the half life and also going to rearrange this equation to solve for the time. What kind of two steps and one so that native son carries through breathed natural longer than of this radiation ratio and over and not multiplied by the half. Life divided by natural longer than two does the equation I use for each of these different countries, Morgan and is the final round final radiation value and not is the initial radiation value. So I'm going to use this equation. I am mo plug in the values because it's fairly straightforward, I think from here, But I will provide the answers. Of course. So, um, I'm gonna write about that Such to the time for Poland. The time for Austria, the time required for Germany and the time for Romania eso I can play these values in. However, for Poland, I don't really need to, because if he notes that that reported value and is exactly twice the safety guidelines value, that means we need the radiation level in Poland to decrease by a factor of two, which is exactly what 1/2 life is, the amount of time required flat Tooker is simply just 1/2 life. So no one calculation required for pulling because it is simply just whatever happened in the half light is of the sample. I will play nice with rest, though. So by performing this calculation again of this equation, using my values in the table and the half life provided the amount of time required for Austria would be 16.2 days. Timeline for Jimmy would be 10.0 days, 10.0 day. There's thing. And finally, for Romania, where has decreased the most. We expected to be the longest time frame, which it is, which is 31.9 games. So there you go

Carleton University
Top Physics 103 Educators
LB
Liev B.

Numerade Educator

Farnaz M.

Simon Fraser University

Zachary M.

Hope College

Aspen F.

University of Sheffield