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What is the activity of a 28.3 µCi sample of carbon-14 in becquerels?

What is the activity of a 28.3 µCi sample of carbon-14 in becquerels?

Chemistry
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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### Calculation of Radioactive Activity #### Question What is the activity of a 28.3 µCi sample of carbon-14 in becquerels? #### Answer Box **activity:** _______________ Bq #### Explanation To convert the activity of a radioactive sample from microcuries (µCi) to becquerels (Bq), we can use the following conversion factors: - 1 µCi = 1 x 10^-6 Ci - 1 Ci (curie) = 3.7 x 10^10 Bq Let's perform the conversion step-by-step: 1. Convert microcuries to curies: \[ 28.3 \, \mu \text{Ci} = 28.3 \times 10^{-6} \, \text{Ci} \] 2. Convert curies to becquerels: \[ 28.3 \times 10^{-6} \, \text{Ci} \times 3.7 \times 10^{10} \, \text{Bq/Ci} \] 3. Simplify the expression: \[ = 28.3 \times 3.7 \times 10^4 \, \text{Bq} \] \[ = 104.71 \times 10^4 \, \text{Bq} \] \[ = 1.0471 \times 10^6 \, \text{Bq} \] So, the activity of a 28.3 µCi sample of carbon-14 is approximately \(1.047 \times 10^6\) Bq.
Transcribed Image Text:### Calculation of Radioactive Activity #### Question What is the activity of a 28.3 µCi sample of carbon-14 in becquerels? #### Answer Box **activity:** _______________ Bq #### Explanation To convert the activity of a radioactive sample from microcuries (µCi) to becquerels (Bq), we can use the following conversion factors: - 1 µCi = 1 x 10^-6 Ci - 1 Ci (curie) = 3.7 x 10^10 Bq Let's perform the conversion step-by-step: 1. Convert microcuries to curies: \[ 28.3 \, \mu \text{Ci} = 28.3 \times 10^{-6} \, \text{Ci} \] 2. Convert curies to becquerels: \[ 28.3 \times 10^{-6} \, \text{Ci} \times 3.7 \times 10^{10} \, \text{Bq/Ci} \] 3. Simplify the expression: \[ = 28.3 \times 3.7 \times 10^4 \, \text{Bq} \] \[ = 104.71 \times 10^4 \, \text{Bq} \] \[ = 1.0471 \times 10^6 \, \text{Bq} \] So, the activity of a 28.3 µCi sample of carbon-14 is approximately \(1.047 \times 10^6\) Bq.
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