Half-Life
Decay Rates
 The number of particles
decaying in a short period of
time is proportional to the
number of particles.
N  lNt
 The decay constant is l.
 The decay rate or activity is
the rate of change.
• Activity decreases as time
increases
N
A
 lN
t
Measured Activity
 The SI unit of activity is the Becquerel (Bq).
• equals one decay/sec (s-1)
 The older unit is the curie (Ci).
•
•
•
•
Based on the decay of 226Ra
Once activity of one gram
Now defined by Bq
1 Ci = 3.7  1010 Bq
Half-Life
 The relationship for decay
gives rise to an exponential
relation.
• Decay constant is fixed for
a decay reaction
N
  l t
N
N  N 0 e  lt
 Decay is usually expressed
as a half-life.
• Time for half a sample to
decay
• Half-life constant for the
nucleus type
1
2
 e  lT
T
ln 2
l

0.693
l
Exponential Decay
 Half-life applies to each sample separately.
• This is exponential decay
Sample Size
 A source of 24Na is marked at
1.16 MBq. Find the number of
atoms of 24Na in the sample.
 Look up the half-life in a table.
• T = 15 h
• T = 5.4  104 s
 The activity is given in the
problem.
• Related to decay constant and
sample size
N
A
l
• Convert to half-life
N
A
l

AT
 9.0 1010
ln 2
Specific Activity
 Physical variables are often
 For a pure radionuclide:
normalized to the mass.
• Described as “specific”
lN
 Specific activity is the activity
6.02 10 23 l 4.17 10 23
SA 


m
M
MT
of a sample divided by the
mass.
• Units Bq g-1 or mCi g-1
• In solution expressed per unit
volume: pCi L-1
 Normal soil has a few pCi/g
 Drinking water has a
recommended limit of 5 pCi/L
of 226Ra + 228Ra.
Figure 29.08
14C
is a very rare isotope with a half-life of 5730 years.
In a living organism, the 14C activity is 0.25 Bq.
When the organism dies, the 14C exchange with the
environment stops.
14C starts decaying.
By measuring the 14C /12C ratio we can estimate the
age of the sample.
Excited States
 Nuclear decay can leave a
nucleus in an excited state.
• Many possible states may be
reached
• Lifetime typically 10-10 s
226
88
Ra
4.785 MeV
94.4%
a
5.5%
a
 Excess energy may be lost as
a photon or electron.
• Single gamma
• Series of gamma emissions
• Internal conversion beta
222
86
Rn
2.2%
0.186 MeV
3.3% b
0 MeV
Radiocarbon
 Carbon-14 (14C) is a
radioactive isotope.
14
C14 N  e 
14
N n C p
• Beta decay
• Half-life 5730 years
 Carbon-14 is produced in the
atmosphere by cosmic rays.
14
• Absorbed by organisms
• Stops at death
 Fraction of 14C to 12C
establishes the date of an
object.
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