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Diapositiva 1F.V. Frazzoli
Terni 7Marzo 2008
• energy - electron-volt 1 electron-volt = kinetic energy of an electron when
moving through potential difference of 1 Volt; • 1 eV = 1.6 × 10-19 Joules • 1 kW•hr = 3.6 × 106 Joules = 2.25 × 1025 eV • 1 MeV = 106 eV
• mass - eV/c2
• proton mass = 938 MeV/c2
• neutron mass = 939.6 MeV/c2
• amu = 1.66 x 10-27kg • amu = 931.494 MeV/c2
About Units
• Proton – Charge = 1 elementary charge e = 1.602 x 10-19 C – Mass = 1.673 x 10-27 kg = 938.27 MeV/c2 =1.007825 u
= 1836 me – spin ½, magnetic moment 2.79 e/2mp
• Neutron – Charge = 0 – Mass = 1.675 x 10-27 kg = 939.6 MeV/c2 = 1.008665 u =
1839 me – spin ½, magnetic moment -1.9 e/2mn
Properties of Nucleons
XA Z
• X: Chemical symbol of the element • Z : Atomic number = number of protons in nucleus • A: Mass Number = Z+N
• N: Number of neutrons in nucleus Example:
» Mass number is 27 » Atomic number is 13 » Contains 13 protons » Contains 14 (27 – 13) neutrons
Al27 13
Beta- Decay AZ A(Z+1) + e- + an anti-neutrino
• A neutron has converted into a proton, electron and an anti-neutrino.
Beta+ Decay AZ A(Z-1) + e+ + a neutrino
• A proton has converted into a neutron, positron and a neutrino.
Electron Capture AZ + e- A(Z-1) + a neutrino
• A proton and an electron have converted into a neutron and a neutrino.
~ 99 44
• Number of protons is conserved. • Number of neutrons is conserved.
• Gamma Emission AZ* AZ + γ
• An excited nucleus loses energy by emitting a photon.
HePbPo 4 2
• decay constant λ: probability of decay per unit time
• Rate of decay ∝ number N of nuclei
• Solution of diff. equation (N0 = nb. of nuclei at t=0)
• Mean life τ = 1/ λ
Law of radioactive decay .
• The decay curve follows the equation – N = No e- λt
• The half-life is also a useful parameter – The half-life is defined as the
time it takes for half of any given number of radioactive nuclei to decay
Decay Curve λλ
0.6932ln 21 ==T
Radioactive Decay Paths
• It has a single bound state with a binding energy of 2.22463 ± 0.00004 MeV, which is measured with
- the formation reactions
- or inverse reaction
γ dn p +→+
ΔE = Nuclear binding energy = mc2
1 proton 1.00728 u 1 neutron 1.00866 u mass of deuterium:2.01355 u
________ mass of parts: 2.01594 u missing mass 0.00239 u
The photon released in forming deuterium has an energy of 2.225 MeV, equivalent to the 0.00239 u
PH320 APPLIED NUCLEAR PHYSICS PH320 APPLIED NUCLEAR PHYSICS –– PartPart 1 1 –– INTERACTIONS INTERACTIONS 17
~0.025eV THERMAL ~1eV EPITHERMAL ~1keV SLOW 100 keV – 100 MeV FAST >100 MeV HIGH ENERGY
They are called thermal because they
are in thermal equilibrium with their
surroundings
Neutrons are classified in vague groups depending on their kinetic energy
1 keV 10 keV 100 keV 1 MeV 10 MeV
Fission
• Units: cm2
• Describes the theoretical “size” that an atom presents, like a target, to be hit by an approaching neutron
• Frequently reported in “barns” • 1 barn = 10-24 cm2
H1 σ (n,el) σ (n,γ)
Reaction Rate (R)
σ (n,f) fertile isotopes Th232, U238
Prompt Fission Neutron Energy Spectrum for Thermal Fission of Uranium-235
Delayed neutron emission
σ (n,f) U235, σ (n,γ) U235
ν: number of neutrons per fission η: number of neutrons in fission per neutron absorbed
3.04 2.58 2.51
Fast (>0.5 MeV)
2.93 2.49 2.42
JMeVQ
0.00450.0010.66σa (barns)
4.710.643.8σs (barns)
fission neutrons
Water H2O
Kinetic Energy of Fission Products 167 MeV Energy of Fission Neutrons 5 “ Instantaneous Gamma-rays Energy 5 “ Capture Gamma-rays Energy 10 “ Beta Particles From Fission Products 7 “ Gamma-rays from Fission Products 6 “
_________ 200 MeV
Recoverable Energy from Fission
Neutron cycle in reactor
Follow the fate of a neutron from one generation to the next with conditional probabilities of various loss mechanisms.
Fission neutron
239 93 Np β ν−+ +
23.5min
2.35 d
24110 yr
233 91Pa β ν−+ +
27.0 d
159200 yr
2 1
Characteristics of spent fuel
• Highly radioactive – Emits very strong radiation – needs shielding – Emits heat – needs cooling – Contains many different nuclides – with very
different half life (seconds to millions of years)
• Contains valuable material (U, Pu)
Composition of a PWR assembly
Fresh Fuel
Spent Fuel
Uranium (4% 235U) : 500 kg
Uranium (0,9% 235U) : 475 kg Pu : 5kg FP : 20 kg recyclables
480 Kg U238+20 Kg U235
470.7 Kg U238+4.3 Kg U235
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
10 100 1 000 10 000 100 000 1 000 000
Time (years)
Po te
nt ia
Light glass (FP)
* as if incorporated, per tonnes of heavy metal
Partitioning & Transmutation • P&T is a potential HLW
management strategy to process the waste by partitioning specific hazardous elements or nuclides and then transmuting them into less hazardous forms
• P&T aims to reduce the radiotoxicity of disposed waste or reduce the duration for which the waste represents a threat to the environment
Transmutation technologies under investigation:
• neutron flux in a fast reactor • neutron flux in a thermal reactor • fast sub-critical reactor coupled
to a particle accelerator
Principi fisici dell’energia nucleare
n-p and p-p interactions
Neutron Economy Equation
Terni 7Marzo 2008
• energy - electron-volt 1 electron-volt = kinetic energy of an electron when
moving through potential difference of 1 Volt; • 1 eV = 1.6 × 10-19 Joules • 1 kW•hr = 3.6 × 106 Joules = 2.25 × 1025 eV • 1 MeV = 106 eV
• mass - eV/c2
• proton mass = 938 MeV/c2
• neutron mass = 939.6 MeV/c2
• amu = 1.66 x 10-27kg • amu = 931.494 MeV/c2
About Units
• Proton – Charge = 1 elementary charge e = 1.602 x 10-19 C – Mass = 1.673 x 10-27 kg = 938.27 MeV/c2 =1.007825 u
= 1836 me – spin ½, magnetic moment 2.79 e/2mp
• Neutron – Charge = 0 – Mass = 1.675 x 10-27 kg = 939.6 MeV/c2 = 1.008665 u =
1839 me – spin ½, magnetic moment -1.9 e/2mn
Properties of Nucleons
XA Z
• X: Chemical symbol of the element • Z : Atomic number = number of protons in nucleus • A: Mass Number = Z+N
• N: Number of neutrons in nucleus Example:
» Mass number is 27 » Atomic number is 13 » Contains 13 protons » Contains 14 (27 – 13) neutrons
Al27 13
Beta- Decay AZ A(Z+1) + e- + an anti-neutrino
• A neutron has converted into a proton, electron and an anti-neutrino.
Beta+ Decay AZ A(Z-1) + e+ + a neutrino
• A proton has converted into a neutron, positron and a neutrino.
Electron Capture AZ + e- A(Z-1) + a neutrino
• A proton and an electron have converted into a neutron and a neutrino.
~ 99 44
• Number of protons is conserved. • Number of neutrons is conserved.
• Gamma Emission AZ* AZ + γ
• An excited nucleus loses energy by emitting a photon.
HePbPo 4 2
• decay constant λ: probability of decay per unit time
• Rate of decay ∝ number N of nuclei
• Solution of diff. equation (N0 = nb. of nuclei at t=0)
• Mean life τ = 1/ λ
Law of radioactive decay .
• The decay curve follows the equation – N = No e- λt
• The half-life is also a useful parameter – The half-life is defined as the
time it takes for half of any given number of radioactive nuclei to decay
Decay Curve λλ
0.6932ln 21 ==T
Radioactive Decay Paths
• It has a single bound state with a binding energy of 2.22463 ± 0.00004 MeV, which is measured with
- the formation reactions
- or inverse reaction
γ dn p +→+
ΔE = Nuclear binding energy = mc2
1 proton 1.00728 u 1 neutron 1.00866 u mass of deuterium:2.01355 u
________ mass of parts: 2.01594 u missing mass 0.00239 u
The photon released in forming deuterium has an energy of 2.225 MeV, equivalent to the 0.00239 u
PH320 APPLIED NUCLEAR PHYSICS PH320 APPLIED NUCLEAR PHYSICS –– PartPart 1 1 –– INTERACTIONS INTERACTIONS 17
~0.025eV THERMAL ~1eV EPITHERMAL ~1keV SLOW 100 keV – 100 MeV FAST >100 MeV HIGH ENERGY
They are called thermal because they
are in thermal equilibrium with their
surroundings
Neutrons are classified in vague groups depending on their kinetic energy
1 keV 10 keV 100 keV 1 MeV 10 MeV
Fission
• Units: cm2
• Describes the theoretical “size” that an atom presents, like a target, to be hit by an approaching neutron
• Frequently reported in “barns” • 1 barn = 10-24 cm2
H1 σ (n,el) σ (n,γ)
Reaction Rate (R)
σ (n,f) fertile isotopes Th232, U238
Prompt Fission Neutron Energy Spectrum for Thermal Fission of Uranium-235
Delayed neutron emission
σ (n,f) U235, σ (n,γ) U235
ν: number of neutrons per fission η: number of neutrons in fission per neutron absorbed
3.04 2.58 2.51
Fast (>0.5 MeV)
2.93 2.49 2.42
JMeVQ
0.00450.0010.66σa (barns)
4.710.643.8σs (barns)
fission neutrons
Water H2O
Kinetic Energy of Fission Products 167 MeV Energy of Fission Neutrons 5 “ Instantaneous Gamma-rays Energy 5 “ Capture Gamma-rays Energy 10 “ Beta Particles From Fission Products 7 “ Gamma-rays from Fission Products 6 “
_________ 200 MeV
Recoverable Energy from Fission
Neutron cycle in reactor
Follow the fate of a neutron from one generation to the next with conditional probabilities of various loss mechanisms.
Fission neutron
239 93 Np β ν−+ +
23.5min
2.35 d
24110 yr
233 91Pa β ν−+ +
27.0 d
159200 yr
2 1
Characteristics of spent fuel
• Highly radioactive – Emits very strong radiation – needs shielding – Emits heat – needs cooling – Contains many different nuclides – with very
different half life (seconds to millions of years)
• Contains valuable material (U, Pu)
Composition of a PWR assembly
Fresh Fuel
Spent Fuel
Uranium (4% 235U) : 500 kg
Uranium (0,9% 235U) : 475 kg Pu : 5kg FP : 20 kg recyclables
480 Kg U238+20 Kg U235
470.7 Kg U238+4.3 Kg U235
1E+00
1E+01
1E+02
1E+03
1E+04
1E+05
1E+06
1E+07
1E+08
1E+09
10 100 1 000 10 000 100 000 1 000 000
Time (years)
Po te
nt ia
Light glass (FP)
* as if incorporated, per tonnes of heavy metal
Partitioning & Transmutation • P&T is a potential HLW
management strategy to process the waste by partitioning specific hazardous elements or nuclides and then transmuting them into less hazardous forms
• P&T aims to reduce the radiotoxicity of disposed waste or reduce the duration for which the waste represents a threat to the environment
Transmutation technologies under investigation:
• neutron flux in a fast reactor • neutron flux in a thermal reactor • fast sub-critical reactor coupled
to a particle accelerator
Principi fisici dell’energia nucleare
n-p and p-p interactions
Neutron Economy Equation