Radioactive Decay

1. You know that radioactive decay occurs when there are too many protons or neutrons in the nucleus of an atom. The nucleus changes through the process known as decay where disintegrations occur
1. Disintegrations are measures in time
2. Usually expressed in disintegrations per second or minute (dps or dpm).
3. These disintegrations is/are the emitting of radiation from atom (alpha, beta, gamma)
2. Measurement of radioactive decay
1. A curie (Ci) is a unit of radioactive decay and can be expressed as 3.7 x 10¹⁰ dps or 2.2 x 10¹²
dpm
2. The following table shows further examples of disintegrations per minute and second
3. SI unit is bequerel (Bq), which is another unit of measurement
1. 1 Bq = 1 dps
2. From the table below note the correlation between Bq and Ci



Ci	dps	dpm	Bq
1 Ci	3.7 x 1010	2.2 x 1012	37 GBq
1 mCi	3.7 x 107	2.2 x 109	37 MBq
1 μCi	3.7 x 104	2.2 x 106	37 kBq



4. Additional appreciation is to understand the placement of the prefixes as defined below
   

Prefixes

Application

Tera (T) = 10 12 Giga (G) = 109 Mega (M) = 10 6 kilo (k) = 103 hecto (h) = 102 deca (da) = 101 deci (di) = 10-1 centi (c) = 10-2 milli (m) = 10-3 micro (:) = 10-6 nano (n) = 10-9 pico (p) = 10-12 femto (f) = 10-15 atto (a) = 10-18

As an example most technologists apply Ci when measure a radioactive dose.  Example 25 mCi of 99mTcMDP.  How does one convert this to Bq?  First Approach 1 mCi = 3.7 x 107 dps x 25 (mCi) = 9.25 x 108 dps Looking over at the prefixes for 106 = Mega therefore the MBq value is 925 Second Approach From the chart above if 1 mCi = 37 MBq then 25 x 37 =925 MBq.  Applying the above chart maybe more efficient when calculating or converting Ci to Bq and visa versa.



5. Suggestion - To convert Ci to Bq apply the following
   1. 1 Ci = 37 GBq
   2. 1 mCi = 37 MBq
   3. 1 :Ci = 37 kBq
   4. Questions
      1. 18.7 mCi = _____ MBq
      
      
      
      
      2. 121.5 :Ci - _____ kBq
      
      
      
      
6. Suggestion - To convert Bq to Ci apply the following
   1. 1 GBq = 2.7 x 10^-2 Ci or 2.7 x 10¹ mCi
   2. 1 MBq = 2.7 x 10^-2 mCi or 2.7 x 10¹ :Ci
   3. 1 kBq = 2.7 x 10^-2 :Ci
   4. 1 Bq = 2.7 x 10^-11 Ci
   5. Questions
      1. 288 MBq = _____ mCi
      
      
      
      
      2. 710 kBq = _____ :Ci
      
      
3. Physical half-life (T_p)
1. This is the physical decay of a radionuclide
2. It is defined as the time in which it takes a number of atoms to disintegrate to ½ the original amount
3. The rate of decay remains constant and cannot be altered, even with the application of temperature, pressure, or chemical interaction
4. As a radionuclide decays over time fewer of the original atoms remain. This remaining fraction of atoms, that decay per unit time, is known as the decay constant (λ)
1. The larger the λ per unit time the shorter the half-life (T_½)
2. This has an inverse relationship
3. While the literature refers to λ as being “constant” in reality it is a statistical value, which means that there maybe a slight variation in the decay time
4. Refer to the chart below an note that the y-axis represents the number of radioatoms and the x-axis represents the number of T_½

5. The decay formula can be expressed in the following formula


1. A_t = number of atoms at a certain point in time
2. A_o = number of atoms originally present
3. e = base of the natural logarithm, 2.718
4. λ decay constant
5. t = time
6. Expanding “– (λt)” the formula can be re-written. Note 0.693 is the natural log of 2

Let’s apply the decay formula to see how this works!

Question: You have 250 μCi of ¹²³I. How much activity remains in 24 hours?

First calculate "e^-λt" using a scientific calculator enter the data below

1. (2), (ln), (x), (t), (/), (T1/2) (-/+), (=), (Inv), and (ln);
2. Where 2 ln = 0.693;
3. Which is multiplied by t (time) = 24 hours;
4. That is then divided the T1/2 of the radiopharmaceutical = 13 hours;
5. Then in order to make it a negative decay select your -/+ key;
6. Inverse of the exponent;
7. e^-λt = 0.278;
8. This is multiplied by N_o (250 μCi); and
9. N_t = 69.5 μCi
10. To use a programmable calculator the following buttons would have to selected:

    

11. Entering your data is different and the correct sequence is displayed above
4. On a rare occasion you might need to solve time.  That is how much time has passed during the decay process.  To do this you must know  original activity and the current activity.  Several points need to be made
   1. When calculating the natural log the ratio places A_t in the numerator and A_o in the denominator
   2. The radionuclide must be known and in this case we are using ^99mTc.  This means that the the half-life is set to 6 hrs
   3. As an example, initially you had 271 mCi of 99mTc and after a period of time there was 37.5 mCi remaining. How much time has passed between the two readings?
   4. The formula is solve below

• On the left is the calculation and on the right are the buttons that you would select on a programmable calculator
• Numbers and buttons on the right are color coded
5. In yet another application you might have to calculate is to determine the T_1/2 of the radionuclide
1. When calculating the natural log note that you must determine the fraction of the remaining radionuclide.  This is done by placing At in the numerator and Ao in the denominator. 
2. The amount of time transpired is 2 hours
3. As an example, the technologist started with 226 mCi and after two hours only 197.4 mCi remains. What is the half-life of the radionuclide in question?
4. Solve for the formula in red
• On the left is the calculation and on the right are the buttons that you would select on a programmable calculator
• Numbers and buttons on the right are color coded

6. Average or mean life expectancy
1. Not all radioactive atoms decay at the same time
2. Using the λ a formula can express the average mean expectancy of the radioactive atom
3. It should also be noted that the average or mean decay is not equal to one half-life since at one half-life the activity level has only decreases by 50%



Available at this link;  http://www.hse.ubc.ca/rad/Calc/calcframe.htm is a calculator used for determining radioactive decay.  For T_1/2 and t keep them in the same time units.

7. Biological half-life (T_b)
1. This is the time it takes the body to eliminate ½ of the radioactive material
2. It has nothing to do with T_p, however, it is related to T_p (more on that in a moment)
3. Methods in which the body eliminates a radioactive compound would include: urine, feces, perspiration, and/or exhalation
4. When related to the T_p the biological effects of a radioactive compound is limited if the T_b is very short (even when the T_p is very long)
8. Effective half-life (T_e)
1. When combining the T_p and T_b the result is T_e
2. Will allow you to calculate amount of radiation absorbed by the body or even a specific organ
3. If T_p and T_b are known then the following formula can be used to calculate T_e

4. If T_pand T_eare known then this formula can be used to calculate T_b


Radiopharmaceutical	Biological Half-Life
99mTc-MDP	3 Hours
99mTc-RBC (ultra-tag)	63.7 Hours
99mTc-sulfur colloid	24 Hours
Sodium 131Iodide	80 Days
111In-octreotide	5.2 Hours
201Tl-choride	3.1 Days +/- 0.7 Day

5. Consider the following radioactive compounds and calculate thier T_p
1. ^99mTcMDP




2. ¹³¹I




3. ^99mTc sulfur colloid




6. Consider the following questions
   1. Can T_e= T_p?
   2. Can T_e= T_b
   3. Can T_b= T_p? See Abstract
   4. Clue - When evaluating these relationships remember that decay is always exponential?
9. Now it's time to look at Decay Schemes
1. What is a decay scheme? It allows us to look at specific information in a decay process. Specifically it identifies the parent radionuclide, the daughter radionuclide, type of radiation emitted, energy levels of the emitted particles and/or gamma-rays
2. This is all done in diagram format
3. First let us considered the general diagram or layout




1. From the above diagram note the initial horizontal line represents the parent radioatom
2. The arrow represents the change in Z value, where an angle to the left is a loss of Z (or proton) and the angle to the right is a gain of Z (or proton)
3. Arrow going straight down identifies gamma emission (note: no change is Z)
4. Also note that alpha, beta, electron capture, and gamma is identified in the above diagram
4. Now let’s look at a specific application


1. From the above diagram ¹²⁵I is diagramed
1. This proton rich radioatom captures an inner shell electron
2. Proton converts to a neutron
3. 35 keV gamma is released by the nucleus
4. T_½ is also identified

2. Now let us look at ¹³¹I
1. This neutron rich atom converts a neutron to a proton
2. β^- particle is ejected from the nucleus with an energy of 970 keV (consider the issue of 1/3 beta max)
3. At this point the radioatom still has energy left over from the decay process and a second horizontal line is drawn
4. Then a gamma-ray is emitted with an energy level of 364 keV
5. T_½ is also identified



3. How about positron decay
1. This proton rich atom converts a proton to a neutron
2. Releases a Beta plus particle
3. Annihilation reaction occurs (not seen in decay scheme)
4. Electron Capture will low level P-ray being produced
5. ¹⁸F decays to stable Oxygen

 


6. The last decay scheme we are going ton look at is ⁹⁹Mo
1. First note that ⁹⁹Mo has a 66 hour half-life
2. It decays by beta minus and emits seven β^- particles (only five shown)
3. Note to all the gamma emissions there is actually a total of 29
4. How many isomeric states are there?
5. Can you find the ^99mTc we use for tagging?
6. ^99mTc half-life is 6.02 hours and it decays to ⁹⁹Tc
7. ⁹⁹Tc has a 2.1 x 10⁵ yrs half-life
8. ⁹⁹Tc decays to ⁹⁹Ru and emits a 2402 keV β^- particle

Last but not least here is some homework for you all to work on.  It's due at our next lecture. 

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