ASNT

PART 3 Radioactive Materials

High-energy photons that require no electrical power are available from samples of radioactive materials. Naturally occurring and manufactured (bombardment in or near nuclear reactors) radionu- clides all exhibit decay behavior. A sample of N nuclei decays at a rate of N λ where λ is the decay constant or probability of decay per unit time per nucleus (Kaplan 1955). This decay is expressed as s -1 and a decay rate of one decay or one disintegration per second is defined as 1 Bq. An older unit is the curie (1 Ci), defined as 3.7 × 10 10 × s –1 , ref lecting the activity or decay rate of a gram of radium 226. DECAY RATE AND HALF-LIFE In the case of a single radioactive nuclide, the probability that decay will occur during a time dt , therefore decreasing the number of nuclei present by dN , is proportional to the number of nuclei and a decay constant, λ , as shown in Equation 9: (Eq. 9) dN = − N λ dt Starting with an initial number of nuclei N 0 , integrating yields the equation relating the number of nuclei remaining at any time t :

The half-life of useful emitters remaining in a sample of decaying nuclei is simply the time necessary for decay of one-half of the sample, N = 1/2 N 0 .

1 2

N N 0

= e −λτ

=

(Eq. 11)

where τ is the half-life.

ln(2) λ

0.693 λ

(Eq. 12)

τ =

=

As the probability of decay increases, the half-life decreases (Figure 7).

100 120

0 20 40 60 80

Number of nuclei

0

20

40

60 Time (s)

80 100 120

−λ t

N = N 0 e

(Eq. 10)

Figure 7 Radioactive decay showing number of nuclei as a function of time; N 0 =100.

CHAPTER 2

48

Part 3