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
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