Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Question
**Tools:**
- \( x10^y \)
In the problem, you are required to use the concept of half-life to determine the initial amount of the radioactive isotope. Given that you presently have 77.1 grams of \(^{32}\text{P}\) and knowing its half-life, you can utilize the exponential decay formula to back-calculate the original quantity from 7 days ago.
For the calculation, you can use the formula:
\[ N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}} \]
Where:
- \( N(t) \) is the remaining quantity of the isotope after time \( t \).
- \( N_0 \) is the initial quantity of the isotope.
- \( t \) is the elapsed time.
- \( T_{1/2} \) is the half-life of the isotope.
With these tools and information, you can compute the initial amount of \(^{32}\text{P}\) that was present 7 days ago.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f33cc2f-0221-41a8-a3a2-cc96bc7960a2%2Fb7d64ced-2a7c-466c-9780-f6f76737ad28%2Foligk5l_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
\(^{32}\text{P}\) is a radioactive isotope with a half-life of 14.3 days. If you currently have 77.1 g of \(^{32}\text{P}\), how much \(^{32}\text{P}\) was present 7.00 days ago?
**Answer Field:**
**Tools:**
- \( x10^y \)
In the problem, you are required to use the concept of half-life to determine the initial amount of the radioactive isotope. Given that you presently have 77.1 grams of \(^{32}\text{P}\) and knowing its half-life, you can utilize the exponential decay formula to back-calculate the original quantity from 7 days ago.
For the calculation, you can use the formula:
\[ N(t) = N_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}} \]
Where:
- \( N(t) \) is the remaining quantity of the isotope after time \( t \).
- \( N_0 \) is the initial quantity of the isotope.
- \( t \) is the elapsed time.
- \( T_{1/2} \) is the half-life of the isotope.
With these tools and information, you can compute the initial amount of \(^{32}\text{P}\) that was present 7 days ago.
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