Radioactivity - Institute for Structure and Nuclear ... · Radioactivity Lecture 4 The Physics of...
Transcript of Radioactivity - Institute for Structure and Nuclear ... · Radioactivity Lecture 4 The Physics of...
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Radioactivity
Lecture 4 The Physics of radioactive Decay
and Nuclear Reaction
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Nature of Radiation
• Deflection in electric field • α radiation is positively charged • β radiation is negatively charged • γ radiation is neutral • Stopping in material • α radiation has small range and
large mass • β radiation has deep range and
small mass • γ radiation has largest range and
no mass – electromagnetic radiation
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Origin of Radiation • Radioactive decay of unstable nucleus
configuration (too many protons or too many neutrons) transitioning into a more stable form.
• What represents a stable or unstable isotope configuration
• Too many protons deflective Coulomb forces • Too many Neutrons reduce the strong binding
force • Too many nucleons cannot be bound together
by strong force • Too much deformation increases instability of
nucleus. • Heavy deformed nuclei will spontaneously
fission
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Radiation as Energy Release A nucleus emits radiation of certain energy (E=hν for gammas and E=Ekin for particles) to reach the lowest possible energy configuration!
2
21 mvEkin =
Energy release in gravitational potential
Energy release in nuclear potential
Particle decay to excited states with subsequent de-excitation by emission of gamma radiation
β-decay
γ-decay
γ-spectrum
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β- decay n ⇒ p+e-+ν
β+ decay p ⇒ n+e++ν
_
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Alpha Decay of the Nucleus
Occurs mainly for very heavy nuclei which are not stable against alpha emission
Alpha particle α = 4He
88226
86222
24Ra Rn He⇒ +
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Nucleus conversion through α-decay
Determine the end-product of the ‘yellow’ a-emitter: ZA
N ZA
NX X⇒ +−−
−24
2 α
Z
N
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Beta Decay of the Nucleus
β decay is the emission of an electron e- or positron e+ to convert a neutron to a proton or a proton to a neutron inside the nucleus 6 · e+ 7 · e+ +1 · e-
The β decay always converts along isobars
Too many neutrons
Too many protons
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Gamma Decay of Nucleus
excited states in nucleus
Excitation of nucleus with subsequent characteristic γ emission
Excited states correspond to vibration, rotation or quantum state excitation
Ex
γ emission l< 10-15 m
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Nucleus conversion through β+,--decay
ZA
N ZA
N
ZA
N ZA
N
X XX X
⇒ +
⇒ +− +
+
+ −−
1 1
1 1
β
βDetermine the end-product of the β+-emitter:
Determine the end-product of the β--emitter:
Z
N
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Energy in Nuclei According to Einstein’s formula, each nucleus with a certain mass m stores energy: E=mc2
Proton mp = 1.007596 · 1.66·10-24 g = 1.672·10-24 g Neutron mn = 1.008486 · 1.66·10-24 g = 1.674·10-24 g Carbon m12C = 12.00000 · 1.66·10-24 g = 1.992·10-23 g Lead m208Pb = 207.797665 · 1.66·10-24 g = 3.449·10-22 g Uranium m238U = 238.050783 · 1.66·10-24 g = 3.952·10-22 g
1 amu=1/12(m12C)=1.66 · 10-24 g Breaking up nuclei into their constituents requires energy
www.nndc.bnl.gov/chart/reCenter.jsp?z=42&n=53
http://amdc.impcas.ac.cn/web/masseval.html
http://amdc.impcas.ac.cn/evaluation/data2012/data/mass.mas12http://www.nndc.bnl.gov/chart/reCenter.jsp?z=42&n=53http://amdc.impcas.ac.cn/web/masseval.html
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Some unavoidable unit considerations
227
23
19
2
2
/49.9311066.11/300000
10022.6106022.11
11
cMeVkgamuskmc
particlesgAJeV
smkgJ
=⋅=
=⋅≡
⋅=
⋅=
−
−
http://en.wikipedia.org/wiki/Electronvolt
http://en.wikipedia.org/wiki/Electronvolthttp://en.wikipedia.org/wiki/Electronvolthttp://en.wikipedia.org/wiki/Electronvolthttp://en.wikipedia.org/wiki/Electronvolthttp://en.wikipedia.org/wiki/Electronvolt
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Nuclear binding energy
M · c2 < Z mp · c2 + N mn · c2
The mass difference is the binding energy B
The binding energy is the energy that needed to dissociate a nucleus into its single constituents. It is released when N neutrons and Z protons fusion together to form a nucleus with the mass number A!
The mass M of the nucleus is smaller than the mass of its proton and neutron constituents!
E=m·c2 N=3 neutrons
Z=3 protons
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Calculating the Nuclear Binding Energy
B = (Z · mp+ N · mn- M) · c2 Binding energy B of nucleus ( ) ( )( ) ( )
( )
( )nucleon
JA
CB
Jsmkg
smgsmg
smggg
cmmmCB Cnp
1212
112
112
821625
28232424
212
1017.1
10404.110404.110404.1/1091056.1
/10310992.110674.1610672.16
66 12
−
−−−−
−−−
⋅=
⋅=
⋅=
⋅=⋅⋅⋅=
=⋅⋅⋅−⋅⋅+⋅⋅=
⋅−⋅+⋅=
( ) ( )( ) ( )
( )
( )nucleon
JA
UB
Jsmkg
smgsmg
smggg
cmmmUB Unp
12238
102
102
721624
28222424
2238
10145.1
10725.210725.210725.2/1091003.3
/10310952.310674.114610672.192
14692 238
−
−−−−
−−−
⋅=
⋅=
⋅=
⋅=⋅⋅⋅=
=⋅⋅⋅−⋅⋅+⋅⋅=
⋅−⋅+⋅=
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Nuclear Potential and internal forces
( ) ( )
MeVaMeVaMeVaMeVaMeVaoddNZAoddNZAaevenNZAa
AZAaAZZaAaAaB
psymcsv
pp
symcsv
34;23;72.0;8.16;5.15
);(0);,();,(
21
3/43/4
23/13/2
=====
+==⋅−=⋅+=
+−
⋅−⋅−⋅⋅−⋅−⋅=
−−
−
δδδ
δ
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 1 MeV = 1.602·10-13 J
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2
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Nuclear Binding Energy Components
Mass number
1 MeV = 1.602·10-13 J
Binding energy normalized to mass number B/A B/A
(MeV
/nuc
leon
)
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Example: What is the binding energy of the oxygen isotope 18O?
mp= 1.007596 · 1.66 · 10-24 g mn= 1.008486 · 1.66 · 10-24 g
M(18O) = 17.99916 · 1.66 · 10-24 g
Z=8, N=10, A=18
Atomic Mass Unit: 1 amu=1/12(M12C)=1.66 · 10-24 g
B = (Z · mp+ N · mn- M) · c2 B(18O) = 1.382 · 105 keV = 2.21·10-11 J B(18O)/A=1.23·10-12 J
1g 18O contains 7.41·1011 J (W·s)
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Nuclear Decay Processes
A ⇒ B+b A(b)B
14C(β-ν)14N 234U(α)230Th
Decay energy is released in kinetic energy of emitted particles or in electromagnetic gamma radiation energy
( )
JeVMeVQ
MeVMeVMeVMeVQ
BBBQBBBQcmcmmQ
U
U
ThHeUUAbBd
AbBd
127
22
104.81025.55.52
5.52128.12755296.28325.1779
234
234
2304234234
−⋅=⋅==
=−+=
−+=−+=⋅−⋅+= JeV 19106.11 −⋅=
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Nuclear Reactions and Energy Release
a
A
Frederic Joliot and Irene Curie at Paris had observed the first nuclear reaction. Enrico Fermi showed the existence of neutron induced reactions, which produce artificial radioactivity.
Nuclear reactions can produce energy Q > 0 exothermic or need energy Q < 0 endothermic
A(a,b)B Q = (mA+ ma- mB- mb)·c2
Q = BB+ Bb- BA-BB
Nobel Prize 1938
Difference of masses in entrance and exit channel determines Q
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Q value of nuclear reaction process
a
A
b
B
A+a ⇒ B+b
A(a,b)B
projectile
target
product
recoil ( ) ( )( ) ( )
reactioncendothermi0reactionexothermic0
22
<>
+−+=⋅+−⋅+=
QQ
BBBBQcmmcmmQ
aAbB
aAbB
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Example: Nuclear Reaction energy budget
isotope B (J)
2H 3.34131·10-13
4He 4.53297·10-12 12C 1.47643·10-11
119Pd 1.59643·10-10
238U 2.88631·10-10
( )
JJJQUBPdBPdBQ
QPdU
JJJQHBHBHeBQ
QHeHH
111010146
2389273
1194673
11946
7311946146
23892
121213
2242
421
211
21
1006542.31059633.121088631.2
)()()(
2
108647.31053295.41034131.32)()(2)(
−−−
−−−
⋅=⋅⋅−⋅=
−+=
+⇒
⋅=⋅−⋅⋅=
+⋅−=
+⇒+
Conversion of nuclei through fusion or fission leads to release of energy!
http://www.nndc.bnl.gov/exfor/endf00.jsp http://www.nndc.bnl.gov/exfor/exfor.htm
http://www.nndc.bnl.gov/exfor/endf00.jsphttp://www.nndc.bnl.gov/exfor/endf00.jsphttp://www.nndc.bnl.gov/exfor/exfor.htmhttp://www.nndc.bnl.gov/exfor/exfor.htmhttp://www.nndc.bnl.gov/exfor/exfor.htm
RadioactivityNature of RadiationOrigin of RadiationRadiation as Energy ReleaseSlide Number 5Alpha Decay of the NucleusNucleus conversion through α-decaySlide Number 8Slide Number 9Slide Number 10Energy in NucleiSome unavoidable unit considerationsNuclear binding energyCalculating the Nuclear Binding EnergyNuclear Potential and internal forcesNuclear Binding Energy ComponentsSlide Number 17Nuclear Decay ProcessesNuclear Reactions and Energy ReleaseQ value of nuclear reaction processExample: Nuclear Reaction energy budget