Xenon-124 has the longest half-life of 1.8 x 1022 years. Assuming that xenon-124 was created 12 billion years ago calculate the current ratio of xenon-124 present in the universe.
Xenon-124 has the longest half-life of 1.8 x 1022 years. Assuming that xenon-124 was created 12 billion years ago calculate the current ratio of xenon-124 present in the universe.
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![**Understanding Xenon-124 and Its Half-Life**
Xenon-124 has the longest half-life of 1.8 × 10^22 years. Assuming that xenon-124 was created 12 billion years ago, calculate the current ratio of xenon-124 present in the universe.
To solve this problem, we need to apply the concept of half-life, which tells us how long it takes for half of a radioactive substance to decay. Here's a step-by-step explanation of the process:
1. **Initial Amount**: Consider the initial amount of xenon-124 when it was formed.
2. **Elapsed Time**: The time elapsed since its creation is 12 billion years.
3. **Calculate Decay**:
- Use the formula for radioactive decay:
\[
N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}}
\]
where:
- \( N(t) \) is the remaining amount after time \( t \).
- \( N_0 \) is the initial amount.
- \( t \) is the elapsed time (12 billion years or \( 12 \times 10^9 \) years).
- \( t_{1/2} \) is the half-life (1.8 × 10^22 years).
4. **Calculate the Current Ratio**:
- Substitute the values into the decay formula to find \( N(t) \).
- The result will give the ratio of the remaining xenon-124 to the initial amount, indicating how much xenon-124 exists now compared to when it was formed.
This calculation will provide insight into the longevity and persistence of elements like xenon-124 in the universe.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18a542a1-0899-4ebe-acd6-685d74e53e0e%2F487171a7-9632-4e49-a66d-e075f9f16e53%2F502gz9a_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Xenon-124 and Its Half-Life**
Xenon-124 has the longest half-life of 1.8 × 10^22 years. Assuming that xenon-124 was created 12 billion years ago, calculate the current ratio of xenon-124 present in the universe.
To solve this problem, we need to apply the concept of half-life, which tells us how long it takes for half of a radioactive substance to decay. Here's a step-by-step explanation of the process:
1. **Initial Amount**: Consider the initial amount of xenon-124 when it was formed.
2. **Elapsed Time**: The time elapsed since its creation is 12 billion years.
3. **Calculate Decay**:
- Use the formula for radioactive decay:
\[
N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}}
\]
where:
- \( N(t) \) is the remaining amount after time \( t \).
- \( N_0 \) is the initial amount.
- \( t \) is the elapsed time (12 billion years or \( 12 \times 10^9 \) years).
- \( t_{1/2} \) is the half-life (1.8 × 10^22 years).
4. **Calculate the Current Ratio**:
- Substitute the values into the decay formula to find \( N(t) \).
- The result will give the ratio of the remaining xenon-124 to the initial amount, indicating how much xenon-124 exists now compared to when it was formed.
This calculation will provide insight into the longevity and persistence of elements like xenon-124 in the universe.
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