Radioactive Decay II
Syllabus Reference:
–6.2 – Radioactive Decay
–12.2 – Nuclear Physics
Isotope Stability
Small nuclei when N = Z
Larger nuclei need more neutrons
Too many or too few = unstable
 radioactive decay
Decay Series
When an isotope decays into
another that is also radioactive, a
series can occur.
Allows us to find some isotopes in
nature that ordinarily wouldn’t be
there.
HalfHalf-life, rate of decay
Radioactive decay is random
– Can’t predict individually, can as a whole.
The number of parent nuclei in a sample and the
number of decays per second (activity) decreases
exponentially with time.
HalfHalf-life = the time it takes for half the parent
isotope in a given sample to decay.
– Or the time in which there is a 50% chance of decay.
– Or the time for activity to decrease by 50%
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Practice
Iodine 131 decays with a halfhalf-life of
approximately 8 days. If a sample of
Iodine 131 has an initial mass of 100 g,
how much of the isotope will remain after
24 days?
– 12.5 g
A sample of phosphorousphosphorous-90 (T1/2 = 14
days) has a mass of 7.5 g. Some time
later, only 1.88 g of the original isotope
remains. How many days have passed?
– 28 days
Decay Constant
The Decay Constant (λ
(λ) is the ratio
between the number of nuclei decaying
per unit time and the total number of nuclei
of the original isotope
 (ΔN/Δ
N/Δt)/N =λ
=λ
Activity of a sample = (Δ
(ΔN/Δ
N/Δt) = -λN
 Determined by λ and N
Radioactive Decay Law
N = N0e-λt
– Using calculus from activity definition
– N = activity remaining
– N0 = original activity
– t = time over which decay has occurred
1 Becquerel (Bq
(Bq)) = 1 event/s
T1/2 = ln2/λ
ln2/λ
– From above equation
Practice
24 Na
11
undergoes β decay with a halfhalf-life
of about 15 hours.
A) What is the decay constant for sodiumsodium-24?
B) If the initial activity of a sample is 3.6 x 103
Bq,
Bq, what will its activity be after 6 hours?
A) 1.28 x 10-5 s-1
B) 2.73 x 103 Bq
Radioactive Dating
14C
dating
– T1/2 of 5730 years
– Useful up to ~60,000 years
– Other isotopes for older dating, 238U
(4.5 x 109 T1/2) for rocks
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Detection of Radiation
Schematic drawing of a photomultiplier tube
(from scintillator)
Geiger counter or GeigerGeiger-Muller tube
Scintillation counter
Cloud chamber
Bubble chamber
Photocathode
Photons eject
electrons via
photoelectric effect
Each incident
electron ejects
about 4 new
electrons at each
dynode stage
“Multiplied” signal
comes out here
Vacuum inside
tube
An applied voltage
difference between
dynodes makes
electrons accelerate
from stage to stage
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