Topic 4  Sources of Radiation
Decay Chains 


Serial Transformation
 Radioactive decay chains
 Described by Bateman equations
 Secular
 Transient
 No equilbrium
 Mixtures of unrelated nuclides
Decay schemes
 Fission fragment example
 ^{90}Kr rapidly disappears
 ^{90}Rb created and also disappears
 ^{90}Sr present for extended period, while ^{90}Y
grows in
 Final product is stable
Decay Equations
 Where
 N_{p} is the # of atoms of parent
 N_{d} is the # atoms of daughter
 l_{p or d} is the decay constant (ln2/T_{½} )
of parent or daughter
 The second term in the activity equation is just the residual daughter
product activity remaining from any that was present at t=0.
 This equation is simpler if we set this value to zero and just examine
the first term. The equation for activity of the daughter is known as
the Bateman equation
Secular Equilibrium
 Halflife of parent is >>> daughter,
 Decrease of parent is negligible over observation period
 Example: ^{226}Ra (halflife =1620 yr) decays to ^{226}Rn
(halflife 4.8 days).
 The observation period is so small relative to 1620 years that
1 gram of Ra226 was used to define the unit of radioactivity 
the Curie.
 When the halflife of parent is >>the daughter, the Bateman
Equation reduces to:
Secular Equilibrium
 The plot of parent and daughter activity in secular equilibrium is:
Transient Equilibrium
 When the parent halflife is of the order of the observation time
and the daughter halflife is considerably shorter (but not negligibly
shorter).
 Examples:
 ^{132}Te (78 hours) decaying to ^{132}I (2.3 hours)
 ^{113}Sn decaying to ^{113m}In (1.7 hours)
 ^{99}Mo parent  ^{99m}Tc
 Upper curve for ^{99m}Tc is the straight application of the
Bateman equation.
 Lower curve: takes into account the fact that about 10% of the ^{99}Mo
decays go promptly to ^{99}Tc
 Ratio of parent to daughter
Maximum Activity
 Use calculus to find the time at which the daughter reaches a maximum
No equilibrium
 When the daughter halflife is longer than the parent halflife,
there is no equilibrium established between them. As the shortlived
parent dies off, the activity of the daughter starts from zero, grows
to a maximum, then falls slowly at its own decay rate (the parent having
since died off and not able to influence daughter rate any further).
Mixed Sources
