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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
PH 103

Dr. Cecilia Vogel

Lecture 23

review
Review
  • Nuclei
    • a, b ,g decays
    • Radiation damage

Outline

  • Nuclear physics
    • exponential decay
    • decay constant
    • half-life
how quickly decay occurs
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
half life
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.
half life1
Half-Life
  • This kind of behavior is exponential decay:
  • N = # nuclei left at time t
  • No = initial # nuclei
  • l = decay constant
    • (not wavelength!)
decay constant
Decay Constant
  • Decay Constant, l
    • how fast it decays
      • higher l, faster decay
    • inversely proportional to half-life
where to find the info
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.
working backward
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:
decay rate
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.
units
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