Question

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July 16, 1945 . What percentage of the strontium- \(90\left(t_{1 / 2}=28.9\right.\) years) originally produced by that explosion still remains as of July 16,2013 ?

Short answer

As of July 16, 2013, approximately \(19.5\%\) of the strontium-\(90\) originally produced in the first atomic explosion still remains.

Step-by-step solution

Determine the time elapsed

Calculate the time elapsed since the first atomic explosion by subtracting the explosion date from the given date, which is July 16, 2013. Initial date: July 16, 1945 Final date: July 16, 2013 Time elapsed = 2013 - 1945 = 68 years

Calculate the number of half-lives

Find how many half-lives have occurred in the elapsed time period. Given half-life (t1/2) of strontium-90: 28.9 years Time elapsed: 68 years Number of half-lives = Time elapsed / Half-life = 68 / 28.9 ≈ 2.354

Use the half-life formula

Use the formula for remaining percentage of a substance after n half-lives: Remaining percentage = \((0.5)^n\) * 100%, where n is the number of half-lives. In this case, n ≈ 2.354 Remaining percentage of strontium-90 = \((0.5)^{2.354}\) * 100% ≈ 19.5% So, as of July 16, 2013, approximately 19.5% of the strontium-90 originally produced still remains.

Key concepts

Radioactive Decay

Radioactive decay is a fundamental process in nuclear chemistry, where an unstable atomic nucleus loses energy by emitting radiation. This process transforms the original element into a different element or a different isotope. In essence, it's nature's way of breaking down unstable atoms into more stable ones.
The decay of radioactive materials occurs at a constant rate, known as the decay rate, which is unique for each radioactive isotope. The process continues until a stable isotope is formed. During decay, radiation is emitted, which can be in the form of particles like alpha (α) and beta (β) particles, or electromagnetic waves such as gamma (γ) rays. This emitted radiation is what makes radioactive materials useful but also potentially harmful. Understanding radioactive decay is crucial for harnessing nuclear energy, medical applications like cancer treatment, and understanding the age of archeological and geological samples.

Half-life Calculations

Half-life is the time it takes for half of a given amount of a radioactive substance to decay. This is a key concept to determine how quickly a substance loses its radioactivity. Calculating half-life is essential in various fields such as medicine, physics, and environmental science.To find out how much of a radioactive element remains after a certain period, you can use the half-life formula: \[\text{Remaining Amount} = \left(0.5\right)^n \times \text{Initial Amount}\]where \(n\) is the number of half-lives that have passed. For instance, if the half-life of strontium-90 is 28.9 years, and 68 years have passed, you divide the elapsed time by the half-life to find \(n\). Applying the formula, you determine the remaining percentage of the substance.

Strontium-90

Strontium-90 is a radioactive isotope with a half-life of about 28.9 years. It is produced during the fission of uranium and plutonium in nuclear reactors and atomic bombs. Due to its long half-life, strontium-90 remains in the environment for many years, which is a cause of concern. This isotope is chemically similar to calcium, which means it can be easily absorbed by living organisms through bones and teeth. Because of this, strontium-90 poses health risks, particularly increasing the risk of bone cancer and leukemia. Monitoring and understanding the behavior of strontium-90 is vital for assessing its environmental impact and potential health hazards.

Atomic Bomb Testing

The detonation of atomic bombs during tests results in the production of various radioactive materials, including isotopes like strontium-90. These tests took place primarily in the mid-20th century, with the first bomb being detonated in New Mexico in 1945. Such tests were important for understanding nuclear weaponry during and after World War II. Unfortunately, atomic bomb testing has left behind a legacy of radioactive contamination, which persists even decades later. Isotopes from these tests can have long half-lives, causing them to remain hazardous to the environment and human health long after the initial explosion. Efforts have been made globally to ban further atmospheric nuclear tests through treaties, aiming to reduce radioactive pollution and its long-term effects. Understanding the historical and environmental context of these tests is essential for addressing contemporary radioactive contamination.