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

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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

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Content

Activity Units Decay Constant Half-Life Law of Radioactive Decay Mean Life

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Overview

Radioactive decay principles and pertinent terms will be discussed

Units to measure radioactive decay will be defined

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1 Bq = 1 disintegration per second

Activity

The amount of a radionuclide present

SI unit is the becquerel (Bq)

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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

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Units

Curie (Ci) = 3.7 x 1010 dps

Becquerel (Bq) = 1 dps

1 Ci = 3.7 x 1010 Bq

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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

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The Decay Constant is denoted by

NOTE: has units of

Typically or sec-1 or “per second”

Decay Constant

1time

1sec

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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

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The relationship between half-life and decay constant is:

Half-Life and Decay Constant

T½ = 0.693

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Half-Life

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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

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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.

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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

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Differential Equation for Radioactive Decay

= -N(t)dNdt

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Radioactive Decay Equation

N(t) = No e -t

This equation is known as the law of radioactive decay

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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

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Radioactive Decay

The amount of activity decayed away after “n” half-lives is given by

A(t)Ao

1 -

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The amount of activity A(t) remaining after “n” half-lives is given by

Radioactive Decay

A(t)Ao

12n

=

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Mean Life

TM = 1.44 T1/2

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Radioactive Decay

Activity (A)

Bq

or

disintegrations

time

time (t)

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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

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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

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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

-

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Substituting and 0 for t

= Aoe - ()

-- e - (0)

-

= Ao-

- 1-

0

= +Ao

0 1

Area Under the Decay Curve

= Ao

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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

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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

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but ln(2) = 0.6931

= ln (2)

T½

Mean Life & Decay Constant

= 1.44 T½ = Tm1

= 0.693

T½

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Tm = 1.44 T½

TmT½

Activity (A)

Bq

or

disintegration

time

time (t)

½Ao

Ao

Mean Life

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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

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A radionuclide has a half life of 10 days. What is the mean life?

Sample Problem

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Solution to Sample Problem

Mean Life = 1.44 T1/2

= 1.44 x 10 days

= 14.4 days

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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

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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)