Geoscience Reference
In-Depth Information
Ir187
10.5 h
Ir188
41.5 h
Ir189
13.2 d
Ir190
11.78 d
Ir191
EC
EC
EC
EC,
β
-
37.3
Os186
Os187
Os188
Os189
Os190
1.58
1.6
13.3
16.1
26.4
Re185
Re186
90.64 h
Re187
4.35E10 y
β
Re188
16.98 h
Re189
24.3 h
-
37.40
EC,
β
-
62.60
β
-
β
-
W184
3E+17 y
W185
75.1 d
W186
W187
23.72 h
W188
69.4 d
30.67
β
-
28.6
β
-
β
-
Figure 12.22
The chart of the nuclides in the W-Ir range. The solid squares represent stables nuclides or
nuclides with a long half-life.
Show that the number of nuclides at time
t
after the Big Bang, the number
N
i
of
nuclides in the Universe, is given by:
λ
i
1
e
−
λ
i
t
p
i
N
i
=
−
1.65, calculate the age of the Universe.
6. Dating the Universe II. We now use the slowly decaying
187
Re-
187
Os chronometer.
Figure 12.22
shows the portion of the chart of nuclides in the W-Ir range.
a. We neglect the contribution of the
p
process to nucleosynthesis in this range. Explain
why the
186
Os and
187
Os nuclides are pure
s
nuclides. Draw the
s
-process pathway
on
Fig. 12.22
.
b. Using the abundances shown on the figure and cross-sections of 422 (
186
Os) and 896
(
187
Os) millibarns (1 mb
d. From the ratio
p
232
Th
/
p
238
U
=
10
−
31
m
2
), find the abundance of radiogenic
187
Os due
to the decay of
187
Re since the beginning of the Universe.
c. Using the solar abundances of Re and Os (0.0517 and 0.675 atoms per 10
6
Si), cal-
culate the age of the universe. Refer to
Table 4.1
for the decay constants. You will
need to consider that
187
Re decays so slowly that its abundances are not affected by
radioactivity. Although other solutions are easily worked out (e.g. continuous pro-
duction, see previous exercise), it is easier to assume that all the
187
Re was created
in one single event just after the Big Bang.
7. We assume that core formation completely eliminated the very siderophile elements,
in particular Ir and Os, from the terrestrial mantle. The modern mantle nevertheless
contains 3.43 ppb of Os and 3.19 ppb of Ir. What is the proportion of late veneer in the
form of chondrites with 520 ppb Os and 490 ppb Ir that has contributed to the modern
mantle? Neglect the contribution of the continental crust. Assuming that the mantle is
dry and that oceans were added by the late veneer, what is the water content of the
incoming projectiles? Refer to
Appendix F
for the appropriate constants.
8. The acceleration of gravity
g
at the surface of a planet varies as
g
=
r
2
where
G
=
6.67 10
−
11
m
3
kg
−
1
s
−
2
is the universal gravitational constant, and
M
and
r
the mass
and radius of the planet, respectively. Calculate
g
at the surface of the planets listed
=
GM
/
