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# Topic 4 - Sources of Radiation

## Decay Chains

### Serial Transformation

• Described by Bateman equations
• Secular
• Transient
• No equilbrium
• Mixtures of unrelated nuclides

### Decay schemes

• Fission fragment example
• 90Kr rapidly disappears
• 90Rb created and also disappears
• 90Sr present for extended period, while 90Y grows in
• Final product is stable

### Decay Equations

• Where
• Np is the # of atoms of parent
• Nd is the # atoms of daughter
• lp or d is the decay constant (ln2/T½ ) 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

• Half-life of parent is >>> daughter,
• Decrease of parent is negligible over observation period
• Example: 226Ra (half-life =1620 yr) decays to 226Rn (half-life 4.8 days).
• The observation period is so small relative to 1620 years that 1 gram of Ra-226 was used to define the unit of radioactivity - the Curie.
• When the half-life 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 half-life is of the order of the observation time and the daughter half-life is considerably shorter (but not negligibly shorter).
• Examples:
• 132Te (78 hours) decaying to 132I (2.3 hours)
• 113Sn decaying to 113mIn (1.7 hours)
• 99Mo parent - 99mTc

• Upper curve for 99mTc is the straight application of the Bateman equation.
• Lower curve: takes into account the fact that about 10% of the 99Mo decays go promptly to 99Tc
• 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 half-life is longer than the parent half-life, there is no equilibrium established between them. As the short-lived 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

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