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PH 103

PH 103. Dr. Cecilia Vogel Lecture 23. Review. Nuclei a, b ,g decays Radiation damage. Outline. Nuclear physics exponential decay decay constant half-life. How Quickly Decay Occurs. As with all quantum processes it’s all probability.

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PH 103

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  1. PH 103 Dr. Cecilia Vogel Lecture 23

  2. Review • Nuclei • a, b ,g decays • Radiation damage Outline • Nuclear physics • exponential decay • decay constant • half-life

  3. How Quickly Decay Occurs • As with all quantum processes it’s all probability. • Cannot determine when a particular nucleus will decay, • just probability that it will have decayed in a certain time. • Can predict how many will decay in certain time, but not which ones. • for example can predict how long before half have decayed = half-life

  4. Half-Life • Half-life is • the time it takes for the number of radioactive nuclei to decrease by half. • After another half-life, half of what’s left will be gone. • Now only 1/4 left. • After another half-life, half of what’s left will be gone. • Now only 1/8 left. • etc • This kind of behavior is • exponential decay.

  5. Half-Life • This kind of behavior is exponential decay: • N = # nuclei left at time t • No = initial # nuclei • l = decay constant • (not wavelength!)

  6. Decay Constant • Decay Constant, l • how fast it decays • higher l, faster decay • inversely proportional to half-life

  7. Where to Find the Info • Appendix B, of course! • Find the isotope you’re interested in, • rightmost column holds half-lives. • If there’s nothing in that column, • it’s not radioactive. • BEWAREof units – they vary! • From the half-life, you can find the decay constant, • from the decay constant, you get decay as function of time.

  8. Working Backward • If you know the decay constant and the time, you can plug into exponential. • What if you need to calculate the decay constant or the time from N’s? • Solving decay eqn yields:

  9. Decay Rate • Another quantity of interest is • The number of nuclei that decay per unit time, called the decay rate • For each nucleus that decays • one emitted particle will be counted. • Decay rate = activity • Decay rate is also an exponential function of time.

  10. Units • Units of t and t½ are time units: • seconds, minutes, years, etc. • Units of l are inverse time • Be consistent with your time units!! • N and No are unitless numbers • or moles • Units of R and Ro • 1 decay/s = 1 Bq = 1 Bequerel (sometimes written as s-1) • 1 Ci = 1 Curie = 3.7X1010 Bq

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