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3/2003 Rev 1 I.2.7 – slide 1 of 35
Session I.2.7
Part I Review of Fundamentals
Module 2 Basic Physics and MathematicsUsed in Radiation Protection
Session 7 Radioactive Decay
IAEA Post Graduate Educational CourseRadiation Protection and Safety of Radiation Sources
3/2003 Rev 1 I.2.7 – slide 2 of 35
Radioactive decay is the process by which unstable atoms transform themselves into new chemical elements
Students will learn about decay constants, activity, units, half-life, how to use the radioactive decay equation, and mean life
Introduction
3/2003 Rev 1 I.2.7 – slide 3 of 35
Content
Activity Units Decay Constant Half-Life Law of Radioactive Decay Mean Life
3/2003 Rev 1 I.2.7 – slide 4 of 35
Overview
Radioactive decay principles and pertinent terms will be discussed
Units to measure radioactive decay will be defined
3/2003 Rev 1 I.2.7 – slide 5 of 35
1 Bq = 1 disintegration per second
Activity
The amount of a radionuclide present
SI unit is the becquerel (Bq)
3/2003 Rev 1 I.2.7 – slide 6 of 35
Multiples & Prefixes (Activity)
Multiple Prefix Abbreviation1 ------- Bq
1,000,000 Mega (M) MBq
1,000,000,000 Giga (G) GBq
1,000,000,000,000 Tera (T) TBq
1 x 1015 Peta (P) PBq
3/2003 Rev 1 I.2.7 – slide 7 of 35
Units
Curie (Ci) = 3.7 x 1010 dps
Becquerel (Bq) = 1 dps
1 Ci = 3.7 x 1010 Bq
3/2003 Rev 1 I.2.7 – slide 8 of 35
Non-SI Units
Quantity Old Unit SI Unit Conversion
Activity curie (Ci) becquerel (Bq) 1 Ci=3.7 x 1010Bq
Absorbed
Dose rad gray (Gy) 1 rad = 0.01 Gy
Equivalent
Dose rem sievert (Sv) 1 rem = 0.01 Sv
3/2003 Rev 1 I.2.7 – slide 9 of 35
The Decay Constant is denoted by
NOTE: has units of
Typically or sec-1 or “per second”
Decay Constant
1time
1sec
3/2003 Rev 1 I.2.7 – slide 10 of 35
A = N
Where N is number of atoms in a sample and A is the activity of the sample.A has units of disintegrations per second (dps or Bq).
Activity
3/2003 Rev 1 I.2.7 – slide 11 of 35
The relationship between half-life and decay constant is:
Half-Life and Decay Constant
T½ = 0.693
3/2003 Rev 1 I.2.7 – slide 12 of 35
Half-Life
3/2003 Rev 1 I.2.7 – slide 13 of 35
Half-Life
Radionuclide Half-Life
Phosphorus-32 14.3 days
Iridium-192 74 days
Cobalt-60 5.25 years
Caesium-137 30 years
Carbon-14 5760 years
Uranium-238 4.5 x 109 years
3/2003 Rev 1 I.2.7 – slide 14 of 35
Sample Problem
A criticality accident occurs in an Uranium processing facility. 1019 fissions occur over a 17-hour period. Given that the fission yield for 131I is 0.03 and its half-life is 8 days, calculate the 131I activity at the end of the accident. Neglect 131I decay during the accident.
3/2003 Rev 1 I.2.7 – slide 15 of 35
Solution to Sample Problem
Activity = N = x
x ( 1019 x 0.03) = 3 x 1011 Bq 131I
0.6938 days
1
86,400 sec day-1
3/2003 Rev 1 I.2.7 – slide 16 of 35
Differential Equation for Radioactive Decay
= -N(t)dNdt
3/2003 Rev 1 I.2.7 – slide 17 of 35
Radioactive Decay Equation
N(t) = No e -t
This equation is known as the law of radioactive decay
3/2003 Rev 1 I.2.7 – slide 18 of 35
Expressing the equation in terms of activity:
Radioactive Decay Equation
N(t) = No e-t
A(t) = Ao e- t
where A(t) = activity at any time t
and Ao = the initial activity at time t = 0
or
3/2003 Rev 1 I.2.7 – slide 19 of 35
Radioactive Decay
The amount of activity decayed away after “n” half-lives is given by
A(t)Ao
1 -
3/2003 Rev 1 I.2.7 – slide 20 of 35
The amount of activity A(t) remaining after “n” half-lives is given by
Radioactive Decay
A(t)Ao
12n
=
3/2003 Rev 1 I.2.7 – slide 21 of 35
Mean Life
TM = 1.44 T1/2
3/2003 Rev 1 I.2.7 – slide 22 of 35
Radioactive Decay
Activity (A)
Bq
or
disintegrations
time
time (t)
3/2003 Rev 1 I.2.7 – slide 23 of 35
Example
The area under the curve is speed x time or(50 km/hr) x 1 hr = 50 kilometers
Speed (s)
kph
or
kilometers
hour
time (hours) 1
50
A Vehicle Traveling at Constant Speed
3/2003 Rev 1 I.2.7 – slide 24 of 35
Example
The area under the curve is (speed x time)/2
or(50 kph x 1 hr)/2 = 25 kilometers
Speed (s)
kph
or
kilometers
hour
time (hours) 1
50
A Decelerating Vehicle
3/2003 Rev 1 I.2.7 – slide 25 of 35
Area Under the Decay Curve
A = Ao e - t
0
A dt = Ao e - t dt0
= Ao e - t dt 0
= Ao
0
e - t
-
3/2003 Rev 1 I.2.7 – slide 26 of 35
Substituting and 0 for t
= Aoe - ()
-- e - (0)
-
= Ao-
- 1-
0
= +Ao
0 1
Area Under the Decay Curve
= Ao
3/2003 Rev 1 I.2.7 – slide 27 of 35
Half-Life
However, when t = T½, the activity decreases to ½ of the original value:
At = Ao e - t or At
Ao
= e - t
At
Ao
=½Ao
Ao
= ½
½ = e - T½
3/2003 Rev 1 I.2.7 – slide 28 of 35
Take the natural logarithm of both sides
ln (½) = -T½
1
=ln (½)
-T½Regrouping terms yields
But ln (½) = - ln (2) so:1
=- ln (2)
-T½
ln (2)
T½=
Half-Life & Decay Constant
ln (½) = ln (e )- T½
3/2003 Rev 1 I.2.7 – slide 29 of 35
but ln(2) = 0.6931
= ln (2)
T½
Mean Life & Decay Constant
= 1.44 T½ = Tm1
= 0.693
T½
3/2003 Rev 1 I.2.7 – slide 30 of 35
Tm = 1.44 T½
TmT½
Activity (A)
Bq
or
disintegration
time
time (t)
½Ao
Ao
Mean Life
3/2003 Rev 1 I.2.7 – slide 31 of 35
Activity (A)
Bq
or
disintegration
time
time (t)Tm
½Ao
Ao
Remember the equation A = N
the total # of atoms N = Ao/ = AoTm
Mean Life
3/2003 Rev 1 I.2.7 – slide 32 of 35
A radionuclide has a half life of 10 days. What is the mean life?
Sample Problem
3/2003 Rev 1 I.2.7 – slide 33 of 35
Solution to Sample Problem
Mean Life = 1.44 T1/2
= 1.44 x 10 days
= 14.4 days
3/2003 Rev 1 I.2.7 – slide 34 of 35
Summary
Activity defined and units discussed
Decay constant defined
Half-life defined - relationship to decay constant
Radioactive decay equation derived
Mean life derived - relationship to half-life
3/2003 Rev 1 I.2.7 – slide 35 of 35
Where to Get More Information
Cember, H., Johnson, T. E., Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2008)
Martin, A., Harbison, S. A., Beach, K., Cole, P., An Introduction to Radiation Protection, 6th Edition, Hodder Arnold, London (2012)
Jelley, N. A., Fundamentals of Nuclear Physics, Cambridge University Press, Cambridge (1990)
Firestone, R.B., Baglin, C.M., Frank-Chu, S.Y., Eds., Table of Isotopes (8th Edition, 1999 update), Wiley,
New York (1999)