Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 38: Problem 49

The table below lists reported levels of iodine- 131 contamination in milk in three 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? $$\begin{array}{lcc} \hline & \multicolumn{2}{c} {\text { Level }(\mathrm{B} q / \mathrm{L})} \\ \hline \text { Country } & \text { Reported } & \text { Safety Guideline } \\ \hline \text { Poland } & 2000 & 1000 \\ \text { Austria } & 1500 & 370 \\ \text { Germany } & 1184 & 500 \\ \hline \end{array}$$

Short Answer

Expert verified
The duration for the iodine-131 levels in milk to decline to a safe level by the respective standards is approximately; Poland: 8.04 days, Austria: 16.24 days and Germany: 10.05 days.

Step by step solution

01

Calculating Half-life for Poland

Firstly, monitor the ratio of the reported level to the safety guideline level for Poland. The ratio is \( \frac{2000}{1000} = 2 \). Given that half life is time it takes for substance to reduce by half, we know it takes one half-life, or 8.04 days, for Poland's iodine-131 levels to drop to the safety guideline.
02

Calculating Half-life for Austria

Next, do the same for Austria. The ratio here is \( \frac{1500}{370} \approx 4.05 \). This is greater than 2, but less than 4, hence, it would take more than one half-life but less than two. To approach it mathematically, take the logarithm base 2 of the ratio, which will reveal the number of half-lives. In this case, \(\log_2 {4.05} \approx 2.02\), so it would take approximately 2.02 half-lives, or \(2.02 * 8.04 \approx 16.24\) days to reach the safety guideline level.
03

Calculating Half-life for Germany

Lastly, for Germany, the ratio is \( \frac{1184}{500} = 2.37 \). Again, this indicates the number of half-lives needed is somewhere between 1 and 2. Using the logarithm base 2, we get \(\log_2 {2.37} \approx 1.25\), so it would take approximately 1.25 half-lives, or \(1.25 * 8.04 \approx 10.05\) days to reach the safety guideline level.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Nickel-65 beta decays by electron emission with decay constant \(\lambda=0.275 \mathrm{h}^{-1} .\) (a) Identify the daughter nucleus. (b) In a sample of initially pure \(\mathrm{Ni}-65,\) find the time when there are twice as many daughter nuclei as parents.

Beta decay by positron emission is soon followed by a pair of 511 -keV gamma rays. Why?

The power output of the fission reactions at Oklo was 10 to \(100 \mathrm{kW} .\) If at some point that power had been sufficient to boil away the water at the reaction site, the chain reaction would have a. ceased. b. continued, but more slowly. c. been unaffected. d. sped up.

How many half-lives will it take for the activity of a radioactive sample to diminish to \(10 \%\) of its original level?

You're assessing the safety of an airport bomb-detection system in which neutron activation of the stable nitrogen isotope \(\frac{15}{7} \mathrm{N}\) turns it into unstable \(^{\text {is }}\) N. The \(N\) - 16 decays by beta emission with 7.13-s half-life. How long after activation will the \(\mathrm{N}-16\) activity have dropped by a factor of 1 million?
See all solutions

Recommended explanations on Physics Textbooks

Kinematics Physics

Read Explanation

Solid State Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Fluids

Read Explanation

Electromagnetism

Read Explanation

Force

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free