📚 Topic Summary
Radioactive decay is the process where an unstable atomic nucleus loses energy by emitting radiation. The activity of a radioactive substance refers to the rate at which these decays occur, usually measured in Becquerels (Bq) or Curies (Ci). The half-life is the time it takes for half of the radioactive atoms in a sample to decay. These two concepts are inversely related: a shorter half-life means a higher activity because the substance decays more quickly.
Mathematically, activity ($A$) is related to the number of radioactive nuclei ($N$) and the decay constant ($\lambda$) by the equation: $A = \lambda N$. The decay constant is related to the half-life ($t_{1/2}$) by: $\lambda = \frac{ln(2)}{t_{1/2}}$. Thus, a shorter half-life implies a larger decay constant and therefore a higher activity, given the same number of radioactive nuclei.
🧪 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Activity |
A. Time for half the nuclei to decay |
| 2. Half-Life |
B. The number of decays per second |
| 3. Decay Constant |
C. Probability of decay per unit time |
| 4. Becquerel (Bq) |
D. SI unit of radioactivity |
| 5. Radioactive Decay |
E. Process where an unstable nucleus emits radiation |
(Answers: 1-B, 2-A, 3-C, 4-D, 5-E)
☢️ Part B: Fill in the Blanks
Complete the following paragraph:
The _________ of a radioactive sample is inversely proportional to its _________. This means that if a substance has a very short _________, it will have a high _________ because it decays very rapidly. The relationship is quantified using the _________, which connects half-life and activity.
(Answers: activity, half-life, half-life, activity, decay constant)
🤔 Part C: Critical Thinking
Explain, in your own words, why isotopes with shorter half-lives are generally more dangerous than isotopes with longer half-lives.