Understanding Radionuclide Decay and Units of Activity, Study notes of Physics

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Decay Rates

10/25/

Radioactive Decay Decay (disintegration) is the process by which aradionuclide changes its number of neutrons and protonsfrom an unstable combination to a more stablecombination. Some people prefer to use the termtransformation rather than decay.E^ l^ i^ l d^

b t^ d^ it

d^ l^ t Examples include beta decay, positron decay, electroncapture and alpha decay.In radioactive decay, mass is always lost. This mass isconverted to energy and released. The released energy iscarried off by any charged particles and/or photons that areemitted (i.e., radiation).

Activity (A) The term “spontaneous” indicates that the transformationsare an inherent characteristic of the material and are notinduced by external forces (such as neutronbombardment).Because decay is a random process, it is impossible to sayi^ l^ h t th

ti it^ f^

l^ i^ ill b^ W precisely what the activity of a sample is, or will be. We canonly specify what the activity was. As such, the ICRUemploys the term "expectation value", i.e. the activity is thedecay rate we expect to have.

Units of Activity

Units of Activity - the curie (Ci)Multiples of the curie^ 1 curie (Ci)^

(^10) = 3.7 x 10dps

(^12) (2.22 x 10dpm) 1 millicurie (mCi)

(^7) = 3.7 x 10 dps

(^9) (2.22 x 10dpm) 1 i^ i^ ( Ci)

(^4) 3 7 10 d^

(^6) (2 22 10 d^

1 microcurie (uCi) = 3.7 x 10

4 dps^ (2.22 x 10

6 dpm) 1 nanocurie (nCi)

(^1) = 3.7 x 10dps

(^3) (2.22 x 10dpm) 1 picocurie (pCi)^

-2^ = 3.7 x 10 dps (2.22 dpm)

7

Units of Activity - the becquerel (Bq) The becquerel (Bq), named after Henri Becquerel whodiscovered radioactivity, is the basic unit of activity in theSysteme International (the SI system). Multiples of the becquerel^ 1 becquerel (Bq)

=^ 1 dpsq ( q)

p 1 kilobecquerel (kBq)

(^3) = 10 dps 1 megabecquerel (MBq)

(^6) = 10 dps 1 gigabecquerel (GBq)

(^9) = 10 dps 1 terabecquerel (TBq)

(^12) = 10 dps

Decay Constant

Decay Constant (

The decay constant, symbolized by the Greek letterlambda, can be described (not quite correctly) as thefraction of the atoms (or activity) of a radionuclide that isexpected to decay per unit time.e.g., a decay constant of 0.25 s

-1^ implies that 25% of the radionuclide's atoms (or activity) decay per secondradionuclide s atoms (or activity) decay per second.It can also be thought of as the proportionality constantbetween the number of atoms of a radionuclide and theactivity:

Decay Constant (

8 ) - examples

a. Calculate the decay constant of I-131 in days

-1^ :

Since the half-life of iodine-131 is 8.04 days This implies (incorrectly) that 8.62% of the activity decaysper day.

Decay Constant (

8 ) - examples

b. Calculate the decay constant of I-131 in hr

-1^ :

This implies (incorrectly) that 0 359% decays per hourThis implies (incorrectly) that 0.359% decays per hour.c. Calculate the decay constant of I-131 in y

-1^ :

This implies (incorrectly) that 3150% decays per year.

The Decay Constant is Immutable

(almost)

In general, the decay constant (or half-life) of a radionuclideis not affected by time, space, pressure, temperature,electromagnetic fields, etc.However, there are exceptions: the chemical form of thesample can affect the decay constant of radionuclides thatundergo electron capture and/or internal conversionundergo electron capture and/or internal conversion.This happens because the chemical bonds formed by anatom affect the availability of the electrons forcapture/conversion. For example, the decay constant ofBe-7 shows a 0.1% difference between beryllium metal andBeF. Tc-99m, which undergoes internal conversion in^2 nearly 100% of its decays (transitions), shows a 0.3%difference in decay constants between KTcO

and Tc^ S.^164 2

The Mean Life The mean (average) life of a radionuclide is calculated asfollows: J^ is the mean (average) life of the radionuclide (e g

hr)

J^ is the mean (average) life of the radionuclide (e.g., hr) 8 Is the decay constant of the radionuclide (e.g., hr

-1^ )

T is the half life of the radionuclide (e.g., hr)

The Decay Equation The following equation calculates the activity (A) for aspecified number of atoms of a radionuclide (N)

A^ =^8 N

The number of decays per unit time equals the fraction ofthe atoms decaying per unit time multiplied by the numberthe atoms decaying per unit time multiplied by the numberof atoms.Unfortunately, this equation is rarely of practical valuebecause the number of atoms is continually decreasing.

• The Decay Equation However, the next equations are useful because they tellus the number of atoms or activity of the radionuclide as afunction of time: Nis the number of atoms of a radionuclide at time tt Nis the number of atoms of a radionuclide at time zero^0 Ais the activity of a radionuclide at time tt Ais the activity of a radionuclide at time zero^0 e is the base of the natural log system, e = 2.