PH 103 Dr. Cecilia Vogel Lecture 23

Review Outline  Nuclei   decays  Radiation damage  Nuclear physics  exponential decay  decay constant  half-life

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 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-Life  This kind of behavior is exponential decay: N = # nuclei left at time t N o = initial # nuclei  = decay constant (not wavelength!)

Decay Constant  Decay Constant,  how fast it decays  higher, faster decay  inversely proportional to half-life

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.  BEWARE of 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  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  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 of t and t ½ are time units:  seconds, minutes, years, etc.  Units of are inverse time  Be consistent with your time units!!  N and N o are unitless numbers  or moles  Units of R and R o  1 decay/s = 1 Bq = 1 Bequerel (sometimes written as s -1 )  1 Ci = 1 Curie = 3.7X10 10 Bq