⚛️ Topic Summary
Radioactive decay is a first-order kinetic process where the number of radioactive nuclei decreases over time. The rate of decay is proportional to the number of nuclei present. This relationship is described by a differential equation, allowing us to predict the amount of radioactive material remaining after a certain period.
Understanding the differential equation $ \frac{dN}{dt} = -\lambda N $ is crucial. Here, $N$ represents the number of radioactive nuclei, $t$ is time, and $\lambda$ is the decay constant, which is specific to each radioactive isotope. Solving this equation allows us to determine the half-life and predict the remaining quantity of a radioactive substance.
🧪 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Half-life |
A. The time it takes for half of the radioactive nuclei to decay. |
| 2. Decay constant |
B. The rate at which radioactive decay occurs, denoted by $ \lambda $. |
| 3. Radioactive decay |
C. The process by which an unstable atomic nucleus loses energy by emitting radiation. |
| 4. Differential equation |
D. An equation that relates a function with its derivatives. |
| 5. Isotope |
E. Variants of a chemical element which have different neutron numbers. |
📝 Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
Radioactive decay follows a first-order kinetics, meaning the rate of decay is proportional to the number of radioactive ________ present. The ________ equation describing this process is $ \frac{dN}{dt} = -\lambda N $, where $ \lambda $ is the ________. The time it takes for half of the substance to decay is called the ________. Different ________ have different decay constants.
🤔 Part C: Critical Thinking
Explain how the concept of half-life is useful in determining the age of ancient artifacts using carbon-14 dating.
