Physics Honors/AP 1 and 2

Homework

# Physics 30: 8-13 Half-Lives and Decay Rates

## Homework

Text Reading: Giancoli, Physics - Principles with Applications, Chapter 30, Sections 8 to 13

##### Study Points
• 30:8 The most common expression for radioactivity is by half-life: the amount of time for half of the available radioactive isotope atoms to decay. This rule follows an exonential law: ΔN/Δt = (ΔN/Δt)0e-λt. When N = N0/2, this law reduces to N0/2 = N0e-λT), where tfrac12; = 0.693/λ where λ is the decay constant.
• 30:9 The level of activity is inverse to the length of the half-life: long half-lives indicate low activity or fewer radioactive events per unit time.
• 30:10 Radioactive isotopes often decay to radioactive isotopes, creating a cascade of events called a decay series. Many series have multiple paths, or steps where several different decay events are possible.
• 30:11 Radioactive dating is used to determine the age of material by comparing the current proportions of radioactive isotopes to the products its decay series against assumptions of the conditions under which the material formed. These assumptions must be checked against independent criteria to prevent circular reasoning.
• 30:12 Because the uncertainty principle tells us that energy conservation can be violated by ΔE for a time Δt (about h/2π), a particle in the right state can tunnel from its nuclear position to a free state. The length of this tunnel controls the rate of decay.
• 30:13 Radiation can be detected and measured with a Geiger counter, a scntillation conter, a semiconductor, cloud chambers, bubble chambers, and wire drift chambers.

### Key Equations

PrincipleEquationVariables
Decay Rate ΔN: decays
Δt: period of time
λ: decay constant for isotope
Radioactive Decay Law R: rate at interval Δt
Δ: number of events
λ: decay constant
R0: Initial decay rate at t=0
Half-life T: period for half of isotope nuclei to decay
λ: decay constant for isotope

### Web Lecture

Read the following weblecture before chat: Half-Lives

### Study Activity

Use the McGrawHill Radioactive Lab to determine the halflife of an element. Follow the lab instructions and watch the short video, then perform the observations needed to complete the lab.

### Chat Preparation Activities

• Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
• Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

### Chapter Quiz

• Required: Complete the Mastery exercise with a passing score of 85% or better.
• Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

### Lab Work

If you want lab credit for this course, you must complete at least 12 labs (honors course) or 18 labs (AP students). One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!