Question

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July \(16,1945 .\) What percentage of the strontium- \(90(t_{1 / 2}=28.9\) years) originally produced . by that explosion still remains as of July \(16,2015 ?\)

Short answer

As of July 16, 2015, approximately 21.3% of the strontium-90 from the first atomic explosion still remains.

Step-by-step solution

Calculate the number of years since the detonation

First, we need to determine how long it has been since the detonation in 1945. Given the problem states that it is July 16, 2015, we simply subtract 1945 from 2015 to find the number of years that have passed: \(2015 - 1945 = 70\) years.

Calculate the number of half-lives

Next, we need to find the number of half-lives that have occurred during the 70 years. The half-life of strontium-90 is given as 28.9 years. We divide the number of years passed by the half-life to find out how many half-lives have occurred: \( \frac{70}{28.9} \approx 2.42 \) half-lives.

Calculate the remaining percentage of strontium-90

Each half-life reduces the remaining amount of material by half. To find the percentage of the original amount still remaining, we calculate \( \frac{1}{2}^{2.42}\). This value is approximately \( 0.213 \), or \( 21.3\% \) of the original strontium-90. Therefore, as of July 16, 2015, approximately 21.3% of the strontium-90 from the first atomic explosion still remains.

Key concepts

Understanding Strontium-90

Strontium-90 is a radioactive isotope characterized by its half-life of 28.9 years. It's a byproduct of nuclear fission, commonly found in waste from nuclear reactors and fallout from nuclear explosions. When discussing strontium-90, it's crucial to recognize its radioactive nature and the implications for the environment and human health.

To understand its impact, one must know that strontium-90 behaves like calcium when inside the human body, potentially affecting bone health and increasing cancer risks. Its slow decay rate means it remains active for extended periods, which is why calculating its remaining percentage after several decades, like in the Alamogordo atomic explosion, is demonstrative of its persistent presence.

Radioactive Decay and Its Calculations

Radioactive decay is the process through which unstable atomic nuclei lose energy by emitting radiation. For elements like strontium-90, this process can be quantified using the concept of a half-life, which is the time it takes for half of a radioactive substance to decay. Calculating the remaining amount after a period involves knowing the total time elapsed and dividing it by the half-life to get the number of half-lives that have occurred, a pivotal step in determining what fraction still persists.

To calculate the remaining percentage of a radioactive element, you raise the number 0.5 (indicating half) to the power of the number of half-lives elapsed. Complex calculations can be simplified using logarithms, but the basic concept reinforces the exponential nature of the decay process.

The Consequences of an Atomic Explosion

An atomic explosion results from the sudden, uncontrollable release of nuclear energy, usually following nuclear fission or fusion. The first detonation in 1945 demonstrated the destructive power of such an event. The explosion produces an intense blast, significant heat, and a plethora of radioactive isotopes, including strontium-90. The aftermath involves not just immediate destruction but also long-term environmental contaminations, like that of strontium-90, which can linger and influence ecosystems and health for decades.

The significance of assessing remaining radioactive materials years after an explosion cannot be overstated. It aids in understanding the long-term impact on affected areas, assisting in cleanup and health impact mitigation strategies crucial for restoring safety and monitoring radioactive decay to prevent future risks.