📚 Topic Summary
The half-life of a radioactive substance is the time it takes for half of the atoms in a sample to decay. This decay occurs randomly, but the half-life provides a predictable average rate. The half-life is constant for a given isotope and is a fundamental property used in various applications, including radioactive dating and nuclear medicine.
The formula for calculating the remaining amount of a radioactive substance after a certain time is: $N(t) = N_0 e^{-\lambda t}$, where $N(t)$ is the amount remaining after time $t$, $N_0$ is the initial amount, $\lambda$ is the decay constant, and $e$ is the base of the natural logarithm (approximately 2.718).
🧪 Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. Half-life |
A. The number of nuclei remaining after a certain time. |
| 2. Decay constant |
B. The time it takes for half of the radioactive nuclei to decay. |
| 3. Initial amount |
C. A measure of how quickly a radioactive substance decays. |
| 4. Remaining amount |
D. The amount of the radioactive substance at the beginning. |
| 5. Radioactive decay |
E. The process by which an unstable atomic nucleus loses energy by emitting radiation. |
Answers:
- ⏱️ 1 - B
- 📉 2 - C
- ➕ 3 - D
- ➖ 4 - A
- ☢️ 5 - E
📝 Part B: Fill in the Blanks
Complete the following paragraph using the words provided: half-life, decay, constant, initial, remaining.
The __________ of a radioactive substance is the time it takes for half of the __________ atoms to undergo __________. The __________ amount refers to the starting quantity, and the amount left after a certain period is the __________ amount. The decay rate is __________ for a specific isotope.
Answers:
- ⏳ half-life
- ⚛️ initial
- 💥 decay
- ➕ initial
- ➖ remaining
- ♾️ constant
🤔 Part C: Critical Thinking
How does understanding half-life help in determining the age of ancient artifacts using carbon dating? Explain the process and its limitations.