Geoscience Reference
In-Depth Information
Proton
β
addition
Z (protons)
Neutron
initial
nucleus
addition
N (neutrons)
(electron
capture)
(positron)
α
90 Mo
91 Mo
92 Mo
93 Mo
94 Mo
95 Mo
96 Mo
Mo
95.94
14.84
9.25
15.92
16.58
+
15.5 m
ε
5.7 h
ε
3500 a
Molybdenum
β
89 Nb
90 Nb
91 Nb
92 Nb
93 Nb
94 Nb
95 Nb
Nb
92.90638
100
+
2.0 h
+
700 a
ε a
β a
β 35.0
β
β
14.6 h
ε
Niobium
86 Zr
87 Zr
88 Zr
89 Zr
90 Zr
91 Zr
92 Zr
93 Zr
94 Zr
Zr
91 224
51.5
11.2
17.2
17.4
+
β 1.5E6 a
Zirconium
ε 16.5 h
β
1.7 h
ε 83.4 d
e 3.27 d
85 Y
86 Y
87 Y
88 Y
89 Y
90 Y
91 Y
92 Y
93 Y
Y
88.90585
100
+
2.6 h
β 2.7 d
β 58.5 d
β 3.5 h
β 10.2 h
ε
14.7 h
ε
3.4 d
ε
107 d
Yttrium
β
84 Sr
85 Sr
86 Sr
87 Sr
88 Sr
89 Sr
90 Sr
91 Sr
92 Sr
Sr
87.62
0.56
9.86
7.00
82.58
β 50.5 d
β 29.1 a
β 9.5 h
β 2.7 h
64.8 d
ε
Strontium
83 Rb
84 Rb
85 Rb
86 Rb
87 Rb
88 Rb
89 Rb
90 Rb
91 Rb
Rb
85.4678
72.16
27.84
β 18.7 d
β a
β 17.7 m
β 15.4 m
β 2.6 m
ε 86.2 d
ε 32.9 d
Rubidium
Figure 12.3
Excerpt from the chart of the nuclides with the number of neutrons on the x -axis and the number
of protons on the y -axis. Stable nuclides are in gray. White on black are long-lived radioactive
nuclides. White fields are short-lived radioactive nuclides. Each square shows the mass number,
the isotopic abundance as a percentage, the decay process and the half-life. The atomic mass of
the element is shown at the start of the row. Notice the difference in dominant nuclear processes
on either side of the stability zone:
β + and electron capture
β
above the stability zone, and
ε
below it.
where
σ i 1 are coefficients with the dimension of a surface area, called neutron-
capture cross-sections, that can be determined by laboratory experiments. The reader will
recognize in this expression the neutron flux N n v n through surface areas
σ i and
σ i and
σ i 1 .As
the excess of neutrons over protons increases, the
values decrease and neutron capture
becomes less and less efficient, while the probability and the rate of
σ
β decay increase
( Fig. 12.4 ) . When the nuclide with neutron number i is radioactive, the previous equation
must be changed to:
d n i
d t =− σ i N n v n n i + σ i 1 N n v n n i 1 − λ i n i
(12.2)
β decay constant. For a given nuclide, a steady state is reached where the
input by neutron absorption on the progenitor equals the output by radioactive decay plus
where
λ i is its
 
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