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Chapter 19: Problem 37

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July \(16,1945 .\) What percentage of the strontium- 90\(\left(t_{1 / 2}=28.9 \text { years) originally produced }\right.\) by that explosion still remains as of July \(16,2017 ?\)

Short Answer

Expert verified
As of July 16, 2017, approximately 17.33% of the strontium-90 originally produced by the explosion still remains.

Step by step solution

01

Identifying given information

We are given the following information: - The explosion happened on July 16, 1945. - We want to find out the amount of strontium-90 remaining on July 16, 2017. - The half-life of strontium-90 is 28.9 years.
02

Calculate the elapsed time

We first need to find out how many years have passed since the explosion. To do this, we will subtract the explosion year from the target year: Elapsed time = 2017 - 1945 = 72 years
03

Calculate the number of half-lives

To find out how many half-lives have passed in 72 years, we will divide the elapsed time by the half-life of strontium-90: Number of half-lives = Elapsed time / Half-life of strontium-90 Number of half-lives = 72 years / 28.9 years ≈ 2.49
04

Calculate the remaining strontium-90

To find the percentage of the original strontium-90 that remains, we will use the formula: Remaining percentage = \(100 \times \left(\frac{1}{2}\right)^n\) where n is the number of half-lives. Remaining percentage = \(100 \times \left(\frac{1}{2}\right)^{2.49} \) Remaining percentage ≈ 17.33% As of July 16, 2017, approximately 17.33% of the strontium-90 originally produced by the explosion still remains.

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Most popular questions from this chapter

Many transuranium elements, such as plutonium-232 , have very short half- lives. (For \(^{232} \mathrm{Pu}\) , the half-life is 36 minutes.) However, some, like protactinium- 231 (half-life \(=3.34 \times 10^{4}\) years), have relatively long half-lives. Use the masses given in the following table to calculate the change in energy when 1 mole of \(^{232} \mathrm{Pu}\) nuclei and 1 mole of \(^{231} \mathrm{Pa}\) nuclei are each formed from their respective number of protons and neutrons. (Since the masses of \(^{232} \mathrm{Pu}\) and \(^{231} \mathrm{Pa}\) are atomic masses, they each include the mass of the electrons present. The mass of the nucleus will be the atomic mass minus the mass of the electrons.)

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