Question

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

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

Step-by-step solution

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.

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

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

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.

Key concepts

Half-Life Calculation

In understanding radioactive decay, the concept of half-life is crucial. Half-life refers to the time it takes for half of a sample of a radioactive material to decay. This doesn't mean that all atoms decay after a half-life, but rather that half of the atoms will have transformed into different elements or isotopes. This process is exponential, which means the same proportion of the substance decays over each equal time period corresponding to its half-life.

For example, if you start with 100 grams of a radioactive substance with a half-life of 10 years, only 50 grams would remain after 10 years. After another 10 years (totaling 20 years), just 25 grams would remain. Calculating the remaining percentage of a radioactive substance can be done using a simple formula:

• Remaining percentage = \(100 \times \left(\frac{1}{2}\right)^n\), where \(n\) is the number of half-lives.

Let's scrub through the numbers: if 72 years have elapsed for strontium-90 with a half-life of 28.9 years, the number of half-lives that have passed is approximately 2.49. Using the formula:

• Remaining percentage = \(100 \times \left(\frac{1}{2}\right)^{2.49} \approx 17.33\%\),

which means roughly 17.33% of the original sample is still present.

Nuclear Chemistry

Nuclear chemistry is the study of the nucleus of the atom and the changes it can undergo. Unlike other areas of chemistry, nuclear chemistry focuses on the forces within the atom rather than the interactions between different atoms. In nuclear reactions, the nucleus's protons and neutrons are rearranged, leading to a transformation. This can result in changes in the atomic number, creating a new element, or even energy release in the form of radiation.

There are a few different types of radiation produced in nuclear reactions:

• Alpha radiation: Consists of two protons and two neutrons. It's relatively heavy and doesn't travel far through air.
• Beta radiation: Consists of electrons or positrons. It has a moderate ability to penetrate materials.
• Gamma radiation: Highly penetrating electromagnetic radiation and requires dense materials to be blocked effectively.

Radioactive decay, which releases this radiation, is part of why nuclear chemistry is important in fields like medicine for cancer treatment, energy production in nuclear reactors, and environmental science.

Strontium-90 Decay

Strontium-90 (\(^{90}\text{Sr}\)) is a particularly significant isotope in the study of nuclear chemistry. This radioactive isotope is a byproduct of nuclear fission found in nuclear fallout, such as the first atomic explosion in Alamogordo mentioned in the problem.

One of the critical concerns with strontium-90 is its biological impact. Because it chemically imitates calcium, strontium-90 can accumulate in bones and bone marrow of living organisms. This can damage bone cells and potentially lead to bone cancer or leukemia over prolonged exposure.

Its long half-life of 28.9 years means it remains a threat long after initial exposure, emphasizing the importance of understanding and managing radioactive materials. Knowing the remaining percentage of strontium-90 from an event (like the Alamogordo explosion) helps determine potential risks and required remediation actions to minimize its environmental impact.