Summary
Lecture 40
N is the number of nuclei remaining after time t.
Radioactive decay law:
N = N0 e
N0 is the number of nuclei present at time t = 0.
λ is the decay constant (characteristic of the nuclide).
− λt
The half-life is the time it takes for half the nuclei in a given
sample to decay; it is related to the decay constant:
Nuclear Fusion
Dosimetry
Radiation Therapy
Nuclear Magnetic Resonance (NMR)
Elemental Particles
T1/ 2 =
Fission and fusion are processes that convert matter into energy.
Nuclear fission: the nuclei of certain
isotopes split when they absorb neutrons.
1
0
0.693
λ
ΔE = Δmc 2
235
141
92
1
n + 92
U → 236
92 U → 56 Ba + 36 Kr + 30 n
The difference in mass, or energy, between the original uranium nucleus and
the fission fragments is about 8.5 MeV - 7.6 MeV = 0.9 MeV.
Since there are 236 nucleons of uranium involved in each fission, the total
energy released per fission is: E = (0.9 MeV / nucleon)(236 nucleons) ≈ 200 MeV
Chain reaction: the neutrons that are released during fission can strike other
nuclei and cause them to split (is observed in nuclear fission reaction).
Physics 112, Spring 2010, Apr 28, Lecture 40
Physics 112, Spring 2010, Apr 28, Lecture 40
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Critical Mass
Hydrogen Nucleus
The hydrogen nucleus consists of
What is the meaning of the term "critical mass"?
1) a single proton
2) a single neutron
3) one proton and one neutron
4) one proton and two neutrons
1) this refers to the mass of the "critical" elements in a reactor, i.e., the uranium
or plutonium
2) this refers to the minimum amount of fissionable material required to sustain a
chain reaction
3) this is the amount of mass needed to make a power reactor economically
feasible
4) this is the material which is just on the verge of becoming radioactive
Half-Life
Chain Reaction
What happens to the half-life of a radioactive substance as it decays?
A chain reaction can occur
1) it remains constant
2) it increases
3) it decreases
4) it could do any of these
Physics 112, Spring 2010, Apr 28, Lecture 40
1) in any uranium core
2) when critical mass of uranium or plutonium is reached
3) in any plutonium core
4) in any material under specific conditions
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Nuclear Fusion
Nuclear Fusion
Nuclear fusion: The combining of two nuclei to form a larger nucleus.
Hydrogen-1 and hydrogen-2 nuclei fuse to form a nucleus of helium-3.
+
+
+
+ +
+
γ
+
One of the simplest fusion reaction involves the production of deuterium from
1
2
a proton and a neutron:
1 H + n →1 H + γ
1. The initial rest mass (measured in atomic mass units, u):
1.007825 u + 1.008665 u = 2.016490 u
energy
2. The mass difference:
(5.49 MeV)
hydrogen
deuterium
(hydrogen isotope)
Possible fusion for reactors:
H + 21 H→31 H +11 H
(4.03 MeV)
2
1
H + 21 H→ 23 He + n
(3.27 MeV)
2
1
H + 31 H→ 42 He + n
(17.59 MeV)
2
1
2.014102 u is the mass of deuterium, 21H
helium-3
(helium isotope)
1
1
2.016490 u − 2.014102 u = 0.002388 u
H
3. Energy released in this reaction:
Hydrogen
2
1
H
Deuterium
3
1
H
Tritium
Physics 112, Spring 2010, Apr 28, Lecture 40
Energy related to one
atomic mass unit:
Uranium
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Fusion Reactor
Development in fusion reactors has been going on for decades.
“Thermonuclear bomb”, or “hydrogen
bomb” is the most destructive weapons
ever developed.
A fission process, or
atomic bomb is used
to create the
required temperature
and pressure for
fusion to occur.
T ≈ 108 K
Joint European Tokamak (JET)
Explosive
The atomic bomb uses an uncontrolled
chain reaction to release enormous
amounts of energy in a very short
period of time; usually formed into a
sphere of critical mass.
(1.67262×10−27 kg )(3 ×108 m / s) 2
= 931.5 MeV
1.6 ×10−19 J / eV
(Δm)c 2 = (0.002388 u )(931.5 MeV / u ) = 2.22 MeV
Nuclear and Thermonuclear Bombs
Nuclear fission releases a lot of energy;
about 200 MeV is released in the fission
of a single uranium nucleus; chemical
combustion releases about 10 eV per
molecule.
Nuclear weapons
are in a range of 10100 kilotons of TNT
(trinitrotoluene).
E = mc2 =
Two conditions must be met:
- high temperatures;
- high plasma density.
Thermonuclear weapons have been
built that are as powerful as 100
megatons, 100 000 000 kg.
Physics 112, Spring 2010, Apr 28, Lecture 40
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There is great promise!
A cheap, clean energy source that
could meet the world’s energy need.
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Passage of Radiation Through Matter
Measurement of Radiation: Dosimetry
Radiation: α- and β-particles, γ-waves, X-rays, protons, neutrons and other
particles.
Alpha, beta, and gamma radiation have different ability to penetrate matter.
Aluminum
Lead
Lead
Because radiation produces ionization of the atoms, it can cause considerable
damage to any material, particularly to biological tissue.
1. Alpha (α)
Radiation can also be used to treat certain diseases, particularly cancer.
2. Beta (β)
We need to measure radiation.
Dosimetry: quantification of the amount, or dose, of radiation.
3. Gamma (γ)
1. Source activity: how many disintegration occur per second.
2. Absorbed dose or exposure (effect of radiation on the absorbing material).
Some amount of radiation will pass the material, some can
cause considerable damage, particularly to biological tissue.
3. Radiation damage to biological organism.
How radiation will damage biological organism?
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Physics 112, Spring 2010, Apr 28, Lecture 40
Source Activity
Absorbed Dose or Exposure
The strength of a source can be specify at a given time by stating the source activity.
Exposure or absorbed dose (effect of radiation on the absorbing material).
Source activity: how many disintegration occur per second.
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The earliest unit of dosage was the roentgen (R):
1 .6 × 10 12 ion pairs per gram of dry air at standard conditions
The unit is the curie (Ci)*:
1 Ci = 3.70 ×1010 disintegrations per second
Current definition for roentgen: the amount of X- or γ- radiation that deposits
0 .878 × 10 −2 J of energy per kg of air
* The activity of one gram of radium.
The SI unit is the becquerel (Bq):
The rad: the amount of radiation that deposits energy at a rate of 1x10-2 J/kg in any
absorbing material.
1 Bq = 1 disintegrations per second
The SI unit for absorbed dose is the gray (Gy):
The gray and rad are physical units of dose: the energy deposited per unit mass.
Commercial suppliers specify source activity at a given time:
However, they are not the most meaningful units for measuring the biological damage
produce by radiation.
ΔN
0.693
N
= λN =
T1/ 2
Δt
Physics 112, Spring 2010, Apr 28, Lecture 40
1 Gy = 1J / kg = 100 rad
Equal doses of different types of radiation cause different amount of damage.
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Radiation Damage to Biological Organism
Radiation Therapy
1. Somatic damage refers to any part of the body except the reproductive cells.
2. Genetic damage refers to damage to reproductive sells, causing mutation.
Quality factor (QF)
Relative biological effectiveness (RBE)
Effective dose (rem) = dose (rad) × QF (rem is rad equivalent man).
SI units: Effective dose (in Sv) = dose (Gy) × QF (Sv is sievert).
1 Gy = 100 rad
and
1 Sv = 100 rem
50 rem (or 50 Sv) of fast neutrons does the same
biological damage as 50 rem (or 50 Sv) of γ -rays.
In the USA, the natural radioactive background
averages 0.3 rem (~300 mrem) .
A short dose of 1000 rem (10 Sv) is nearly
always fatal.
Physics 112, Spring 2010, Apr 28, Lecture 40
Collimated gamma-ray detector
for scanning over a patient.
Radiation source rotating so
that the beam always passes
through the diseased tissue but
minimizing the dose in the rest
of the body.
From X-ray medical exams the average person
receives ~60 mrem per year.
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Nuclear Magnetic Resonance (NMR)
Nuclear Magnetic Resonance in Research
Effect of magnetic field on nucleus.
NMR signal(s)
from the atom
nucleus in (a)
one or (b) two
different local
environments
Magnetic field: 9.4 T
A nucleus in a magnetic field can have its
spin either parallel (spin-up) or antiparallel
(spin-down) to the field.
(a)
(b)
Bexternal is the magnetic field produced by a magnet.
Blocal
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Physics 112, Spring 2010, Apr 28, Lecture 40
is the magnetic field produced by electrons
around NMR nuclei.
Resonance frequency in kHz or ppm
The magnetic field splits the
energy levels of nucleus
slightly; the energy difference is
proportional to the magnetic
field.
4-mm rotor
Bexternal
hf = ΔE = γBtotal
hf = γ ( Bexternal + Blocal )
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2.5-mm rotor
NMR spectrometer: Bruker
Biospin DSX-400.
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Radiation Dosage
Elementary Particles: Classification
Sources of elementary particles: cosmic rays and high-energy accelerators.
All of the following are units used to describe radiation dosage in humans
except
1) curie
2) sievert
3) rem
4) RBE
Fermilab at Batavia,
Illinois.
Effective Dose of Radiation in Human Body
The interior of the
tunnel of the main
accelerator at
Femilab.
A unit that measures the effective dose of radiation in a human is the
1) curie
2) RBE
3) rad
4) rem
To explain some experiments, a new particle was considered and named by E. Fermi the neutrino (“little neutral one”).
Physics 112, Spring 2010, Apr 28, Lecture 40
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