Physics 30: 8-13 Half-Lives and Decay Rates
Text Reading: Giancoli, Physics - Principles with Applications, Chapter 30, Sections 8 to 13
- 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.
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
||T: period for half of isotope nuclei to decay
λ: decay constant for isotope
Read the following weblecture before chat: Half-Lives
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.
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