Physics and Engineering of Radiation Detection

1.3. Radioactivity and Radioactive Decay 11

α-decay: Qα=(MX−MY−Mα)c^2

β-decay: Qβ=(MX−MY)c^2

HereMstands for atomic mass, which means thatMαis the mass of the helium
atom and not the helium nucleus as in case of equation 1.3.A.

Example:

Determine if actinium-225 can decay throughαas well asβmodes.

Solution:

Theαdecay reaction for actinium-225 can be written as

225

89 Ac→

221

87 Fr+

4

2 He.

TheQ-value, in terms ofatomic masses, for this reaction is

Qα =(MAc−MFr−Mα) 931. 502

= (225. 023229 − 221. 014254 − 4 .002603) 931. 502

=5. 93 MeV.

If actinium went throughβdecay, the decay equation would be written as

225

89 Ac→

225

90 Th+e,

with aQ-value, in terms ofatomic masses,givenby

Qβ =(MAc−MTh) 931. 502

= (225. 023229 − 225 .023951) 931. 502

= − 0. 67 MeV.

Since theQ-value is positive forαdecay therefore we can say with confidence

that actinium-225 can emitαparticles. On the other hand a negativeQ-value

forβdecay indicates that this isotope can not decay through electron emission.

1.3.B TheDecayEquation.......................

Radioactive decay is a random process and has been observed to follow Poisson
distribution (see chapter on statistics). What this essentially means is that the rate
of decay of radioactive nuclei in a large sample depends only on the number of
decaying nuclei in the sample. Mathematically this can be written as

dN

dt

∝−N

or

dN

dt

= −λdN. (1.3.12)

HeredN represents the number of radioactive nuclei in the sample in the time
windowdt.λdis a proportionality constant generally referred to in the literature as