Radiation and its detection
Physics 123
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Lecture XXII
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Binding energy per nucleon
Fusion
Fission
Too many protons
Electrostatic repulsion
Most tightly woven nuclei
in the middle of the Mendeleev’s table
Energetically most favorable place
Not enough nucleons to
build up strong force
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Isotopes
• Same chemical element
(Z=Np) can have different
number of neutrons –isotopes:
• Carbon Z=66 p, but it can
have
• 5n: 11C, 6n: 12C, 7n: 13C,
8n: 14C, 9n: 15C, 10n: 16C
• Only 12C is stable (98.9% of C
on Earth)
• Unstable isotopes
radioactively decay
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Radiation
• Types of radioactive particles:
–
–
–
–
a – radiation (He nuclei = 2p+2n, charge = +2e);
b – radiation (this is just an electron, charge = -e);
g – radiation (these are photons, charge=0)
Neutrons (charge=0)
• Sources of radiation
– Naturally radioactive elements (e.g. plutonuium,
uranium…),
– Induced radiation (by bombarding with energetic
particles),
– Human activity (nuclear power plants, X-rays)
– Cosmic rays (atmosphere shields most of it)
– Atomic bomb
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a-radiation
•

•
•
•
•

226
88Ra
222
86Rn+a
a-particle – nucleus of He = 2p+2n
Z decreases by 2 when a-particle is emitted, A decreases by 4
Why not just p’s and n’s separately?
Because of binding energy m(a)<2m(p)+2m(n)
Why not then larger nuclei?
a-particle is the most “tightly bound” nucleus. Just like atoms
nuclei have energy shells
– Protons and neutrons are fermions like electron – Pauli exclusion principle
works as well
– In the ground state we can have 2p (spin up, spin down) and 2n (spin up,
spin down)
– Protons and neutrons are not identical particles (e.g. different electric
charge), so Pauli principle does not apply to a proton and neutron
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a-radiation
• If this decay is energetically
favored why does not it
happen immediately?
• Tunneling through a barrier
• Probability depends
exponentially on the thickness
of the barrier
T e
 2GL
2m(U 0  E )
,G 
2
h
• That is why lifetimes of
radiation materials differ by
many orders of magnitude
1ms-1010 years
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b-decay
• 146C147N+e-+ne
• In b-decay nucleus charge (Z) changes by +1, while mass (and A)
essentially stays the same: me<<mp, mn<< me (though not zero!!!
as the book says; the book is old, new discoveries were made)
• Electron is not one of the “atomic orbital” electrons, it was
created in the neutron decay:
np+e+ne
• Neutrino has no electric charge and does not participate in strong
interactions – its chances of interaction with matter are rather low
– was not detected until 1956
• Its existence was predicted by Pauli in 1930 based on energy
conservation in b-decays
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b+ -decay
• 1910Ne199Fe+e++ne
• In b+ -decay nucleus charge (Z) changes by -1,
• e+ - is a positron – antipartner of an electron
• Positrons don’t live long, when matter meets antimatter
they annihilate. There are plenty of atomic electrons to
annihilate with
e-+e+ gg
• Electron capture (from innermost shell – K-shell):
7 Be+e-7 Li+n
4
3
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g-decay
 g-rays are just very energetic photons (keV, MeV)
• Because nuclei energy is much larger than atomic
energy, the spacing between energy levels is
larger as well (though space-wise nucleus is much
smaller than atom), hence photons emitted in
nuclear transitions are a lot more energetic
• Charge and mass stays the same in this transition
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Radioactive decay law
• Nuclei decay is a random
process, number of particles
DN decaying in interval of
time Dt is proportional to the
total number of particles:
DN= -lNDt
 Differential equation
dN
 lN
dt
 lt
N  N 0e
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Rate of decay
• Number of particles
decaying per unit of time:
dN
  l N 0 e  lt
dt
dN
(t  0)  lN 0
dt
dN  dN  lt

 e
dt  dt  0
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Half-life
• Half-life – period of time
T1/2 in which the number
of particles decreases by a
factor of 2: N=N0/2
N  N 0 e  lT1 / 2
N 0 / 2  N 0 e lT1 / 2
lT1 / 2
2
lT1/ 2  ln 2
e
T1/ 2 
ln 2
l
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
0.693
l
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Radioactive dating
• The majority of carbon atoms are 126C, but small
fraction (1.3x10-12) is radioactive isotope 146C (half-life
5730 yr)
• This ratio in atmosphere is constant for many thousand
years
• Carbon is absorbed by living organisms in CO2 during
the life process, after death it remains fixed
• The age of remains can be determined by the ratio of
14 C to 12 C
6
6
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Example of radioactive dating
• An animal bone fragment has carbon mass 200g. It
registers an activity of 16 decays/s. What is the age of
the bone?
 200 g 
(1.3 10 12 )  1.3 1013
N ( C )  6.02 10 atoms
 12 g 
0.693
l
 3.83 10 12 s 1
5730 yr  365  24  60  60
dN
(t  0)  lN 0  3.83 10 12 s 1 1.3 1013  50s 1
dt
 dN / dt 0  50
lt
e 

 3.125

 (dN / dt )  16
14
0 6
t
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l
23
ln( 3.125)  2.98 1011 s  9400 yr
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Decay series
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Detection of radiation
• Different types of radiation interact differently with
matter (=atomic structures)
• Charged particles ionize atoms – ionizing radiation
• Photons can also ionize atoms + Compton effect +pair
production
• Alpha particles and neutrons can displace nuclei from
crystal structure + interact with nuclei strongly
• Radiation dose = amount of energy deposited per kg of
mass
– 1 rad = 10-2J/kg
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Magnetic force on moving charge
• Charged particles bend in magnetic
field, there charge to momentum ratio
can be determined from the radius of
curvature
• Magnetic force = Centripetal force
F=qvB
• Centripetal acceleration
a=v2/R
• Newton’s second law
F=ma
qvB=mv2/R
mv
R
qB
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In experiments B is known,
q=e most of the time,
Measure R- measure mv
For aXXII
given v measure m – magnetic
Lecture
17
spectrometer
Detection of radiation
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p-n diode
• The current flows through p-n junction if electrons have vacancies to jump to,
it does not flow in the opposite direction
• When ionizing particle goes through p-n diode it produces e-hole pairs –
current starts flowing – detect the particle with high position precision
P-type +++
vacancies +++
+
+++
----n-type
electrons ---
P-type +++
+++
+++
--+
n-type -----
current
Electron
flow
Reverse bias
Forward bias
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No
current
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Radiation effect on humans
• Effects on humans are different from different types of radiation  quality
factor (QF):
– QF(g) = QF(b) = 1; QF(a) = 20.
– Effective dose (in rem) = dose (in rad) x QF
• Levels of radiation
•
•
•
•
Natural background 0.36 rem /year
Medical X-ray 0.040 rem /year
US recommended upper limit 0.5 rem/year
Radiation workers ~ 5rem /year
• Radiation damage in biological organisms – alteration in DNA
– Somatic (any part of body, but reproductive)
• First affect the blood cells (shortest regeneration time)
• Can lead to cancer (by altering the DNA)
– Genetic (reproductive organs)
• Leads to mutations, smaller dose is harmful
• Rate matters
• Short dose of 1000rem is fatal
• 400 rem over short period of time – 50% fatal
• 400 rem over several weeks usually not fatal
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Radiation in medicine
• Radiation therapy
– Focus radiation on cancer cells (kill the bad guys)
• Medical imaging
– Use radioactive isotopes to tag molecules
– PET (positron emission tomography):
– e++e-=2g
– Photons travel in a
straight line –
easy to find their source
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