1 HR SNM/VOICE CEU
 

A Tutorial by Stephen M. Karesh, PhD


Adapted for the Web by Stephen M. Karesh, PhD & Marsha Lipps CNMT


EQUILIBRIUM

Definition: Equilibrium is a condition established in a parent/daughter mixture when both parent and daughter are radioactive and when the daughter’s halflife is shorter than that of the parent. If the daughter’s half-life exceeds that of the parent, equilibrium will never be reached.
There are two types of equilibrium:

● Secular Equilibrium
● Transient Equilibrium

The basic difference between these two types of equilibrium is the following: during 10 half-lives of the daughter, essentially no parent decay takes place during secular equilibrium, but significant decay takes place during transient equilibrium.
There is a rule of thumb regarding how long it takes to reach equilibrium:

● Transient equilibrium is reached in ~4 t1/2 of daughter. For Tc-99m, predicted length of time is 24 hours; actual time to equilibrium is 23 hr.
● Secular equilibrium is reached in ~6 t1/2 of daughter.

SECULAR EQUILIBRIUM
Secular Equilibrium is a condition reached when the tphys of the parent is many times greater than the tphys of the daughter, e.g., 100-1000times greater or more. For example:

Ra226
------>
Rn222
1620 years
3.8 days

In this case, the ratio of half-life of parent to half-life of the daughter is >155,600. To keep things in perspective, during 10 half-lives of the daughter (38 days in the example above), decay of the parent is negligible. Decay of the parent is represented by the flat
line in the diagram below.

At the point at which activity of the parent and activity of the daughter become equal, equilibrium has been reached and the lines become parallel (as well as superimposed). The relationship between half-lives in secular equilibrium is:

apparent
 
physical
t
=
t
daughter
 
parent


This means that in the equilibrium mixture, the daughter appears to decay with the halflife of the parent. When the daughter is isolated from the mixture, it has its expected half-life. Perhaps the simplest explanation for their appearing to be equal is that the
daughter can’t decay until it is formed, and so the rate of formation of the daughter equals the rate of decay of the parent, which is very slow. Therefore the parent and daughter appear to have the same half-lives. In the case of the decay of Ra-226 to Rn-
222, the decay constant of the parent is 0.000001171day-1 (only 1 millionth decays per day).

TRANSIENT EQUILIBRIUM

Transient Equilibrium is a condition reached when the tphys of the parent is approximately 10 times greater than the tphys of the daughter. A classical example is theMo99/Tc99m Generator, where the ratio of the half-lives is 67 hr/6 hr = 11:1. During the
60 hr period representing 10 half-lives of Tc99m , almost 50% of the Mo99 has disappeared, as noted in diagram. This represents a very significant amount, unlike the negligible amount in secular equilibrium.

The relationship between Half-lives in transient equilibrium is the same as that in secular equilibrium:

apparent
 
physical
t
=
t
daughter
 
parent

There is a rule of thumb regarding how long it takes to reach equilibrium:
Transient equilibrium is reached in ~4 t1/2 of daughter.
For Tc-99m, predicted length of time is 24 hours; actual time to equilibrium is 23 hr.
Secular equilibrium is reached in ~6 t1/2 of daughter

CLINICALLY USEFUL GENERATORS

INDICATE WHETHER EACH GENERATOR LISTED BELOW IS IN TRANSIENT OR SECULAR EQUILIBRIUM
(CHECK YOUR ANSWERS USING THE ANSWER KEY BELOW)

 

 

 

 

 

 

 

 

 

 

ANSWER KEY


 

 

TUTORIAL NAVIGATION

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MO99

MISCELLANEOUS QUESTIONS.

 

 
   
June 25, 2010