Radioactive Decay

Section 8: RADIOACTIVE DECAY
In this section, we describe radioactivity - how unstable nuclei can decay - and the laws
governing radioactive decay.
Radioactive Decay
Naturally occurring radioactive nuclei undergo a combination of ?, ? and ? emission.
Artificially produced nuclei may also decay by spontaneous fission, neutron emission and even
proton and heavy-ion emission.
Any decay process is subject to the same basic law.
RADIOACTIVE DECAY LAW
The rate of decay (number of disintegrations per unit time) is proportional to N, the
number of radioactive nuclei in the sample dN/dt N (6.1)
The negative sign signifies that N is decreasing with time. is called the decay constant -
probability per unit time that a given radioactive nucleus will decay.
? Large rapid decay; small slow decay.
Equation (6.1) can be integrated to give N(t) = N0 exp( t) (6.2)
where N0 = number of radioactive nuclei at t = 0.
ACTIVITY AND HALF-LIFE
Activity: Number of disintegrations per unit time:
A(t) = N(t) = N0 exp( t) = A0 exp( t) (6.3)
This has the same exponential fall off with time as N(t).
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Time (sec)
Activity
BPA RADIOACTIVE DECAY
L8-2
Half-life: Time for half the radioactive nuclei in the sample to decay.
Substituting N0 = N0/2 and t = t1/2 into Eq. (6.2) gives t1/2 = ln2/ (6.4)
The figure above shows the activity of a sample decaying at a rate of exp(-t). The half-life of this
sample = ln2 ( 0.7 s).
DECAY CHAINS
When nuclei A decay into stable nuclei B, the number of each present at time t is
NA(t) = NA(0)e ?t and NB(t) = NA(0)(1 - e ?t) (6.5)
where only nuclei A are present initially.
The number of nuclei A (parent nuclei) decreases with time.
The number of nuclei B (daughter nuclei) increases from zero, initially, and approaches NA(0) as
t , i.e. all the parent nuclei eventually become daughter nuclei.
The total number of nuclei is constant: NA(t) + NB(t) = NA(0).
If nuclei B are also radioactive, the above equations do not apply, since, as nuclei B are
produced, they also decay. The daughter nuclei of B may also be radioactive and a decay chain is
set up: A B C etc.
We shall give a number of examples of decay chains in the next section.
TYPES OF RADIOACTIVE DECAY
The figure below shows how a variety of decay mechanisms transform an initial (parent) nucleus