Transcript Nuclides composite particles of nucleons

Introduction to Nuclides
the big bang
The big bang theory www.uwaterloo.ca/~cchieh/cact/nuctek/universe.html
Einstein-Wheeler: "Matter tells space how to curve, and space tells
matter how to move."
1927 Lemaitre: The universe began with an explosion based on red shift.
Hubble observed the red shift proportional to distance of stars from us.
1964 Penzias and Wilson discovered the cosmic microwave background
(CMB) radiation, as due to remnants of big bang.
Depending on the outcome of
the observations, the big bang
theories will be abandoned,
revised or extended to
accommodate additional
observartions.
What is in the universe?
How did the universe begin?
Where did materials come from?
Can material and energy really
inter-convert
into each other?
Nuclides
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Nuclides
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The Big Bang View
All energy (and matter) in the
universe concentrates in a region
smaller than a marble 12 billions
years ago.
It started to expand and cool to a
billion K. Elementary particles roamed
free in a sea of energy.
Further expansion caused a drop in
temperature and confined quarks in
neutrons and protons.
Galaxy clusters
Galaxies began to form.
Nuclides
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Hubble’s
Observation
One method for
gauging distance is to
observe the apparent
brightness of a galaxy.
The red shift shows
that the universe is
constantly expanding
Nuclides
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Cosmologic Matters
Radiation: massless or nearly massless, photons (light) and neutrinos.
Baryonic matter (Nuclides): composed primarily of protons, neutrons
and electrons; has essentially no pressure of cosmological importance.
Dark matter: exotic non-baryonic matter that interacts only weakly with
ordinary matter; This form of matter also has no cosmologically
significant pressure.
Dark energy: a bizarre form of matter, or perhaps a property of the
vacuum itself; characterized by a large, negative pressure; a form of
matter that can cause the expansion of the universe to accelerate
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What is the history of the universe?
Nuclides
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A nuclide
Nuclides
composite particles of nucleons
Protons and neutrons are bound together into nuclei.
Atoms contain a complement of electrons.
AEZ
A-mass number
Z-atomic number eg.
238U92
A nuclide is a type of atoms whose nuclei have a specific numbers of
protons and neutrons.
Nucleons (protons and neutrons) are convenient units to consider nuclear
changes, although the standard model considers quarks as basic
components.
Like particles, nuclides are energy states, with amounts properties.
Some basic principles are seen for stability of nuclide.
Nuclides
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Stable Nuclides
Stable nuclides remain the same for an indefinite period.
Some characteristics of stable nuclides:
Atomic number Z  83, but no stable isotopes for Z = 43 and 61.
There are 81 elements with 280 stable nuclides.
Usually there are more neutrons than protons in the nuclei.
Nuclides with magic number of protons or neutrons are very stable.
Pairing of nucleons (spin coupling) contributes to nuclide stability.
Is abundance of a nuclide related to its stability?
Nuclides
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Stable Nuclides
number of neutrons and protons
Z = # of protons
Find
N / Z for
4He2
=1
16O8 =
40Ar18 =
91Zn40 =
144Nd60 =
186Re75 =
209Bi83 =
Nuclides
N = # of neutrons
9
Stable Nuclides
N/Z of some light nuclides
Z
14
13
12
11
10
9
8 <- magic # .
7
6
5
4
3
Li Li
2 . He He
1 P D .
0 1 2 3 4
.
B
Be
5
.
C
B
6
N
C
7
O
N
.
O
Si Si Si
Al
Mg Mg Mg .
Na
Ne Ne Ne
F
.
O
.
.
.
.
.
8
9
Nuclides
10 11 12 13 14 15 16 ->N
10
Stable Nuclides
N/Z of nuclides
N / A ratio increases as
A increases
More stable isotopes
for even Z than odd Z
More stable isotones
for even N than odd N
More stable isotopes
and isotones for magic
Z and N
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
Zr . . . . . . . . + . . . XXX X X
Y
X
Sr
X XXX
Rb
X X
Kr
X X XX X
Br . . . . . + . .
X X
Se
XXXX X X
As
X
Ge
X XXX X
.
Ga
X X
Zn . . . + . X XXX X
.
Cu
X X
Ni
X XXX X
.
.
Co
X
Fe
X XXX
.
.
Mn +
X
Cr
X XXX
.
.
v
XX
Ti XXXXX .
.
.
Sc X
Ca X X
2
2 3
4
5
Nuclides
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01234567890123456789012345678901
Stable Nuclides
natural occurring heavy nuclides
Natural Occurring Isotopes of Heavy Elements (abundance)
76
77
78
79
80
81
82
83
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
184 (0.018), 186 (1.59), 187 (1.64), 188 (13.3), 189 (16.1), 190 (26.4), 192 (41.0)
191 (38.5), 193 (61.5)
190 (0.0127), 192 (0.78), 194 (32.9), 195 (33.8), 196 (25.2), 198 (7.19)
197 (100)
196 (0.146), 198 (10.02), 199 (16.84), 200(23.13), 201(13.22), 202(29.8), 204(6.85)
203 (29.5), 205 (70.5)
204 (1.4), 206 (25.1), 207 (21.7), 208 (52.3)
209 (100)
90
Th
232 (100% half life 1.4x1010 y)
92
U
235 (0.720, half life 7.04x108 y), 238 (99.276, half life 4.5x109 y)
Nuclides
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Two protons or neutrons occupy a
quantum state, due to their ½ spin.
Stable Nuclides
pairing of nucleons
Pairing nucleons stabilises nuclides,
leading to a large number of stable
nuclides with even Z and N.
No stable isotopes for Z = 43 or 61.
No stable isotones with N = 19, 31,
35, 39, 61, 89
More stable isotopes for even Z than
odd Z and for even N than odd N
Elements with even Z are more
abundant than those with odd Z of
comparable mass.
Effect of Paring Nucleons
Z
even
even
odd
odd
N
# of stable
stable nuclides
even
166
odd
57
even
53
odd
*4
total
280
*They are: 2D1, 6Li3, 10B5, & 14N7
Nuclides
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Stable Nuclides
magic numbers of nucleons
Magic numbers are 2, 8, 20, 28, 50, 82, and 126.
Double-magic number nuclides: 4He2, 16O8, 40Ca20, 48Ca20, & 208Pb82.
4He2
as alpha particles, abundant in the universe,
16O8 abundant on Earth.
Six stable isotopes of Ca20, 5 stable isotopes of Ni28, high for their masses.
Large number of stable isotopes and isotones with Z & N = 50 and 82.
The heavies stable nuclide 209Bi83 has 126 neutrons.
O8, Ca20, Ni28, Sn50 and Pb82 have relative high abundance.
Nuclides
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Stable Nuclides
abundances of elements
Atomic Abundance (AA) of Elements of the Inner Solar System Excluding the Sun
Log (AA)
0
.
-1
.
-2
.
-3
.
-4
.
-5
.
-6
.
-8
.
-9
.
-10
.
.
O
. MgSi
.
Ca
.
. Al S
Na
C
.
P
Cl
.
N F
Be
.
LiB
.
.
.
.
.
.
.
.
Fe .
Ni
.
. Ti CrMCo
V
Cu SeAs
.
.
.
.
.Sc
.
.
Ga
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Sn
.
.
.
.
.
.
Sc Zr
Mn
Y.
.
Ru
Sb
.
PdCd.
Br
.
RhAgIn I
. Mo
.
Ba
W
.
.
CeNdSm
. Dy
YbHf
Pr
La . EuTbHoTu Lu
.
.
.
Pb
Pt.
Os
IrAu
.Tl
Re
.
0
1
2
3
4
5
6
7
8 Mass No.
12345678901234567890123456789012345678901234567890123456789012345678901234567890
Even Z elements are more abundant
than odd Z ones of comparable mass.
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Stable and Radioactive Nuclides
mass and stability of nuclides
Mass and energy are equivalent, E = m c2.
Relative mass is the key for stability of nuclides.
Energy drives changes.
9C
10C
11C
If a system can lower its energy, it will.
Unstable nuclides undergo decay or fission,
releasing energy stabilises the system.
Discuss the stability of carbon isotopes.
Nuclides
12C
13C
14C
15C
16C
Half life
127. ms
19.3 s
20.3 m
stable
stable
5730. y
2.45 s
0.75 s
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Stable and Radioactive Nuclides
binding energy
The binding energy (BE) of a nuclide is the energy released when the
atom is synthesized from the appropriate numbers of hydrogen atoms
and neutrons.
Z H + N n = AEZ + BE
or Z mH + N mn = mE + BE
where mH, mn, and mE are masses of H, n, and AEZ respectively.
Eg
BE = Z mH + N mn - mE
BE (3He) = (2*1.007825 + 1.008665 - 3.01603) 931.481 MeV = 7.72 MeV
BE (4He) = (2*1.007825 + 2*1.008665 - 4.00260) 931.481 MeV = 28.30 MeV
Nuclides
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Stable and Radioactive Nuclides
average binding energy
The binding energy and average
binding energy of some nuclides
Nuclide
3He2
4He2
16O8
56Fe26
54Fe26
208Pb82
238U92
BE
MeV
7.72
28.3
127.6
492.3
471.76
1636.44
1801.7
BE / A
MeV / nucleon
2.57
7.08
7.98
8.79
8.74
7.87
7.57
Variation of the Average Binding Energy
as a Function of Mass Number A
BE
BEa
A
Fe
v
U
3
A
A
He
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The Average Binding Energy Curve
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Stable and Radioactive Nuclides
mass excess (ME)
The difference between the
mass of a nuclide and its mass
number, A, is the mass excess
(ME),
ME = mass - A.
What are the MEs for the
nuclides listed here?
Masses (amu) of some entities
H
1.00782503 18O 17.99916
2D
2.014102 54Fe 54.938296
3H
3.016049 56Fe 55.934939
4He 4.002603 206Pb 205.975872
12C 12.000000
209Bi 208.9804
14C 14.003242
235U 235.043924
16O 15.994915
238U 238.055040
Which is the standard?
Which have negative MEs?
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Stable and Radioactive Nuclides
mass excess (ME) and average -BE
Comparison of mass excess and average binding energy (amu)
Nuclide
Mass
H 1.007825
n 1.008665
3He
3.01603
4He
4.00260
12C 12.000000
16O 15.994915
40Ca 39.96259
54Fe 53.939612
56Fe 55.934939
208Pb82 207.976627
238U92 238.050784
ME
-BE average BE
0.007825 0
0.008665 0
0.01603 -0.00276
0.00260 -0.0076
0
-0.00825
-0.005085 -0.00857
-0.03741 -0.00917
-0.060388 -0.00938
-0.065061 -0.00944
-0.023373 -0.00845
0.050784
-0.00813
Nuclides
0
0
0.00828
0.0304
0.09894
0.1369
0.3669
0.5065
0.52851
1.757
1.934
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Stable and Radioactive Nuclides
fission and fusion energy and ME
Variation of ME with A
for Some Stable Nuclides
ME amu
3He
0.01
n
0.005
0.0
H
4He
–0.005
U
12C
Pb
Fe
Nuclides
A
22
Stable and Radioactive Nuclides
application of mass excess (ME)
Like masses, the ME can be used to calculate energy of decay,
because the same scale is used for both.
eg:
ME’s of 40Sc21 and 40Ca20 are -20.527 and -34.847 MeV respectively.
Estimate the energy of decay for
40Sc21

40Ca20
+ b+ or
40Sc21
+ e– 
40Ca20
solution:
Edecay = -20.527 - (-34.847) = 14.32 MeV
Edecay includes 1.02 MeV for the positron-electron pair for b+ decay.
Nuclides
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Stable and Radioactive
Nuclides
Mass Excesses of Isobars
with Mass number 123
ME of isobars
-0.08ME
amu
Mass excesses (amu) of
isobars with mass
number 123:
b–
-0.09
-0.10 In
49
b+, EC
Sn Sb Te I Xe Cs Ba
50 51 52 53 54 55 56
Z
In49
Sn50
Sb51 Te52 I-53
Xe54
Cs55
Ba56
-0.0896 -0.0943 -0.0958 -0.0967 -0.0944 -0.0915 -0.0870 -0.0808
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Stable and Radioactive Nuclides
BE of isobars
Plots of BE an ME are very similar,
and either one can be used to
show the decay of isobars.
Only 57Fe26 is stable for isobars of
mass 57
.Mass
.amu
Cr24
Mn25
Fe26
Co27
Ni28
56.9434
56.9383
56.9354
56.9363
56.3980
Isobars with Mass
Number 57
-494 –
Cr
-495
-496
_
b+ Ni
EC
b–
-497
.BE
.amu
-498
0.53031
0.53462
0.53667
0.53493
0.53240
-499
-500
Nuclides
–
Mn
24
25
–
Co
–
Fe
27
28
25
Stable and Radioactive Nuclides
problem types
Evaluate the BE of a nuclide
tell nuclide with zero BE
Mass and BE of mass 57
isobars
.Mass
.amu
evaluate ME of a nuclide
tell nuclide with zero ME
evaluate decay energy
estimate decay mode
predict the stable isobar(s)
Cr24
Mn25
Fe26
Co27
Ni28
56.9434
56.9383
56.9354
56.9363
56.3980
.BE
.amu
0.53031
0.53462
0.53667
0.53493
0.53240
estimate max kinetic energy of
beta or positrons in beta decay
Nuclides
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Relative Mass Differences (MeV) for
Isobars with Mass Number 120.
Stable and Radioactive
Nuclides
Ba
22
ME of isobars
20
continue
18
Cs
16
Ag
14
Pairing of nucleons
plays a role for stability
of isobars with even
mass numbers.
12
10
8
6
4
2
0
Xe
Cd
I
There are even-even
and odd-odd type of
nuclides in isobars of
even mass numbers
In
Sb Te
Sn
47 48 49 50 51 52 53 54 55 56
Nuclides
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Stable and Radioactive Nuclides
a semi-empirical equation for BE
Proportional
to A
Instability
due to p
Pairing of
nucleon
2
2
20
(
A

2
Z
)
0
.
6
Z
BE(A,Z) = 14.1A - 13A2/3 + Ea
1/ 3
A
A
Decrease
due to
surface
tension
Nuclides
Instability
due to
neutron to
proton ratio
28
The big bang
Nuclides
Factors for stable nuclides
summary
mass and stability
Relative Mass Differences (MeV) for
Isobars with Mass Number 120.
Ba
22
20
18
Cs
16
Ag
14
6
4
2
0
3He
n
10
8
ME amu
0.01
12
Variation of ME with A
for Some Stable Nuclides
Xe
Cd
0.005
H
U
I
0.0
In
4He
–0.005
12C
Fe
Pb
Sb Te
Sn
47 48 49 50 51 52 53 54 55 56
Nuclides
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A