Juliet started working with a radioactive substance. In 1997, she started with 200 g. When she measured again in 2002, she had 100 g left. In 2007, she had 50 g.
| Radioactive isotope | Half-life |
|---|---|
| Rubidium-91 | 58.4 seconds |
| lodine-131 | 8 days |
| Cobalt-60 | 5 years |
| Carbon-14 | 5730 years |
| Cesium-135 | $2.3 \times 10^6$ years |
| Uranium-238 | $4.5 \times 10^9$ years |
Which substance is she most likely measuring?
A. rubidium-91
B. iodine-131
C. cobalt-60
D. carbon-14
Answer (2)
Calculate the time it takes for the substance to reduce to half its amount: 5 years.
Compare the calculated half-life with the half-lives of the substances in the table.
Identify the substance in the table whose half-life is closest to the calculated half-life: Cobalt-60.
Conclude that the radioactive substance Juliet is most likely measuring is Cobalt-60: co ba lt − 60 .
Explanation
Analyzing the Radioactive Decay Let's analyze the decay of the radioactive substance Juliet is working with. We know the initial amount in 1997 was 200g, in 2002 it was 100g, and in 2007 it was 50g. We need to determine the half-life of this substance and compare it to the provided table to identify the most likely isotope.
Calculating the Half-Life First, let's calculate the time it takes for the substance to reduce to half its amount. From 1997 to 2002, it took 5 years (2002 - 1997 = 5) for the substance to decay from 200g to 100g. This means the half-life is approximately 5 years. To confirm, let's check the decay from 2002 to 2007. Again, it took 5 years (2007 - 2002 = 5) for the substance to decay from 100g to 50g. This further confirms that the half-life is 5 years.
Comparing with the Table Now, we compare the calculated half-life (5 years) to the half-lives of the substances listed in the table:
Rubidium-91: 58.4 seconds
Iodine-131: 8 days
Cobalt-60: 5 years
Carbon-14: 5730 years
Cesium-135: 2.3 × 1 0 6 years
Uranium-238: 4.5 × 1 0 9 years
We can see that Cobalt-60 has a half-life of 5 years, which perfectly matches our calculated half-life.
Conclusion Therefore, the radioactive substance Juliet is most likely measuring is Cobalt-60.
Examples
Radioactive decay and half-life are crucial concepts in various fields, including medicine and archaeology. For instance, in medicine, radioactive isotopes with specific half-lives are used for diagnostic imaging and cancer treatment. Understanding half-life helps doctors determine the appropriate dosage and timing of these treatments. In archaeology, carbon-14 dating, which relies on the half-life of carbon-14, is used to determine the age of ancient artifacts and fossils. By measuring the remaining amount of carbon-14 in a sample, archaeologists can estimate when the organism died, providing valuable insights into past civilizations and ecosystems.
Juliet is most likely measuring Cobalt-60, which has a half-life of 5 years, matching her findings of a decrease in mass over time. In 5 years, the substance reduces from 200 g to 100 g, and again from 100 g to 50 g, confirming the half-life. This fits perfectly with the half-life data provided.
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