AP Physics Questions on Radioactive Decay and Dating

📚 Quick Study Guide

• ⚛️ Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation.
• ⏱️ The rate of decay is characterized by the half-life ($T_{1/2}$), which is the time required for half of the radioactive nuclei to decay.
• 📝 The decay constant ($\lambda$) is related to the half-life by the equation: $\lambda = \frac{ln(2)}{T_{1/2}}$.
• 🧪 The number of radioactive nuclei remaining after time $t$ is given by: $N(t) = N_0e^{-\lambda t}$, where $N_0$ is the initial number of nuclei.
• 🌍 Radiocarbon dating uses the decay of carbon-14 to estimate the age of organic materials.
• 🦴 The age of a sample can be determined using: $t = \frac{ln(N_0/N(t))}{\lambda}$.
• ☢️ Common types of radioactive decay include alpha decay, beta decay, and gamma decay.

🧪 Practice Quiz

1. What type of decay involves the emission of a helium nucleus?
   1. Alpha decay
   2. Beta decay
   3. Gamma decay
   4. Neutron emission
2. The half-life of a radioactive isotope is 10 years. How much of the isotope will remain after 30 years?
   1. 1/2
   2. 1/4
   3. 1/8
   4. 1/16
3. What is the decay constant of a radioactive isotope with a half-life of 69.3 seconds?
   1. 0.1 s^-1
   2. 0.01 s^-1
   3. 1 s^-1
   4. 10 s^-1
4. A sample initially contains 1000 radioactive nuclei. After 1 hour, 250 nuclei remain. What is the half-life of the isotope?
   1. 15 minutes
   2. 30 minutes
   3. 45 minutes
   4. 2 hours
5. Which of the following is NOT a type of radioactive decay?
   1. Alpha decay
   2. Beta decay
   3. Gamma decay
   4. Delta decay
6. Carbon-14 dating is most effective for dating materials up to what age?
   1. 5,730 years
   2. 57,300 years
   3. 573,000 years
   4. 5,730,000 years
7. What particle is emitted during beta decay?
   1. Helium nucleus
   2. Electron or positron
   3. Photon
   4. Neutron