Answer these questions to ensure you have a good understanding of half-life.
Carbon-14 has a half-life of 5,730 years. If you start with 100 grams of carbon-14, how many will you have in 5,730 years?
The half-life of hydrogen-3 is 12.3 years. If you start with 100 grams of hydrogen-3, how much will you have after 24.6 years?
The half-life of Calcium-47 is 3.91 x 105 seconds. A sample contains 4.11 x 1016 nuclei. What is the decay constant for this decay?
The half-life of Calcium-47 is 3.91 x 105 seconds. A sample contains 4.11 x 1016 nuclei. How much sample is left after 1.173 x 106 seconds?
| Your Responses | Sample Answers |
|---|---|
| After one half-life, or 5,730 years, you will have one-half your original sample. You will have half of 100 grams, or 50 grams. | |
| After 24.6 years, 2 half-lives will have passed. You will half of 100, which is 50, and then half of that again to end up with 25 grams. | |
| \(\mathsf{ 3.91 \times 10^{5} \text{ s} = \frac{0.693}{\lambda} }\) \(\mathsf{ \lambda = \frac{0.693}{3.91 \times 10^{5} \text{ s}} }\) \(\mathsf{ \lambda = 2.16 \times 10^{-6} \text{ s}^{-1} }\) |
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| 1.173 x 106 seconds is three half-lives: \(\mathsf{ \frac{4.11 \times 10^{16} \text{ nuclei}}{2} = 2.055 \times 10^{16} \text{ nuclei} }\) \(\mathsf{ \frac{2.055 \times 10^{16} \text{ nuclei}}{2} = 1.0275 \times 10^{16} \text{ nuclei} }\) \(\mathsf{ \frac{1.0275 \times 10^{16} \text{ nuclei}}{2} = 5.1375 \times 10^{15} \text{ nuclei} }\). |
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