Radioactivity - Institute for Structure and Nuclear ... · PDF file Radioactivity Lecture 4...
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Transcript of Radioactivity - Institute for Structure and Nuclear ... · PDF file Radioactivity Lecture 4...
Radioactivity
Lecture 4 The Physics of radioactive Decay
and Nuclear Reaction
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
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
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
2 1 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
β- decay n ⇒ p+e-+ν
β+ decay p ⇒ n+e++ν
_
Alpha Decay of the Nucleus
Occurs mainly for very heavy nuclei which are not stable against alpha emission
Alpha particle α = 4He
88 226
86 222
2 4Ra Rn He⇒ +
Nucleus conversion through α-decay
Determine the end-product of the ‘yellow’ a-emitter: Z A
N Z A
NX X⇒ +− −
−2 4
2 α
Z
N
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
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
Nucleus conversion through β+,--decay
Z A
N Z A
N
Z A
N Z A
N
X X X X
⇒ +
⇒ + − +
+
+ − −
1 1
1 1
β
β Determine the end-product of the β+-emitter:
Determine the end-product of the β--emitter:
Z
N
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.mas12 http://www.nndc.bnl.gov/chart/reCenter.jsp?z=42&n=53 http://amdc.impcas.ac.cn/web/masseval.html
Some unavoidable unit considerations
227
23
19
2
2
/49.9311066.11 /300000
10022.6 106022.11
11
cMeVkgamu skmc
particlesgA JeV
s mkgJ
=⋅=
= ⋅≡
⋅=
⋅ =
−
−
http://en.wikipedia.org/wiki/Electronvolt
http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt
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
Calculating the Nuclear Binding Energy
B = (Z · mp+ N · mn- M) · c2 Binding energy B of nucleus ( ) ( ) ( ) ( )
( )
( ) nucleon
J A
CB
J s mkg
s mgsmg
smggg
cmmmCB Cnp
12 12
11 2
11 2
821625
28232424
212
1017.1
10404.110404.110404.1/1091056.1
/10310992.110674.1610672.16
66 12
−
−−−−
−−−
⋅=
⋅=
⋅=
⋅=⋅⋅⋅=
=⋅⋅⋅−⋅⋅+⋅⋅=
⋅−⋅+⋅=
( ) ( ) ( ) ( )
( )
( ) nucleon
J A
UB
J s mkg
s mgsmg
smggg
cmmmUB Unp
12 238
10 2
10 2
721624
28222424
2238
10145.1
10725.210725.210725.2/1091003.3
/10310952.310674.114610672.192
14692 238
−
−−−−
−−−
⋅=
⋅=
⋅=
⋅=⋅⋅⋅=
=⋅⋅⋅−⋅⋅+⋅⋅=
⋅−⋅+⋅=
Nuclear Potential and internal forces
( ) ( )
MeVaMeVaMeVaMeVaMeVa oddNZAoddNZAaevenNZAa
A ZAaAZZaAaAaB
psymcsv
pp
symcsv
34;23;72.0;8.16;5.15
);(0);,();,(
21
3/43/4
2 3/13/2
=====
+==⋅−=⋅+=
+ −
⋅−⋅−⋅⋅−⋅−⋅=
−−
−
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#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2
Nuclear Binding Energy Components
Mass number
1 MeV = 1.602·10-13 J
Binding energy normalized to mass number B/A B /A
(M eV
/n uc
le on
)
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)
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
BBBQBBBQ cmcmmQ
U
U
ThHeUUAbBd
AbBd
127
22
104.81025.55.52
5.52128.12755296.28325.1779
234
234
2304234234
−⋅=⋅==
=−+=
−+=−+= ⋅−⋅+= JeV 19106.11 −⋅=
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
Q value of nuclear reaction process
a
A
b
B
A+a ⇒ B+b
A(a,b)B
projectile
target
product
recoil ( ) ( ) ( ) ( )
reactioncendothermi0 reactionexothermic0
22
< >
+−+= ⋅+−⋅+=
Q Q
BBBBQ cmmcmmQ
aAbB
aAbB
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
( )
JJJQ UBPdBPdBQ
QPdU
JJJQ HBHB