Chemistry Reference
In-Depth Information
EXAMPLE 21.13
10
16
A geologist analyzes a sample of rock and finds that it contains
atoms of for every atoms of Calculate the age of the
rock, assuming that no lead was present when the rock solidified and no ura-
nium or its daughter elements escaped from the rock.
1.25
207
Pb
10
15
235
U.
4.16
Solution
235
U
The number of atoms of
originally present was
10
16
10
15
10
16
1.25
4.16
1.66
6
10
16
1
10
15
2
10
15
1.66
6
8.33
4.17
10
8
years)
10
9
years.
It took two half-lives, or
2(7.13
1.43
The rock is
1.43 billion years old.
Practice Problem 21.13
Calculate the age of a sample of rock con-
taining atoms of for every atoms of its sta-
ble daughter isotope. Assume that no argon was in the rock when it solidified
and that no argon escaped from the rock since its solidification. The half-life of
is
10
17
40
10
17
40
2.57
19
K
7.71
18
Ar,
40
10
9
19
K
1.3
years.
EXAMPLE 21.14
206
Pb
Calculate the age of a sample of rock containing 25.5 g of
for every 29.5 g
238
U.
of
Solution
Although the ratio of masses of
a given isotope
is equal to the ratio of num-
bers of atoms (because each atom of a given isotope has the same mass at time
zero as at time
t
), the ratio of the masses of different isotopes and
for example) is
not
equal to the ratio of atoms. We must change each mass to
moles of atoms. To three significant digits, the mass of a mole of each of the
isotopes involved in this problem is equal to its mass number (in grams):
(
206
Pb
238
U,
a
1 mol
206
Pb
206 g
206
Pb
25.5 g
206
Pb
0.123
8
mol
206
Pb
b
a
1 mol
238
U
238 g
238
U
29.5 g
238
U
0.123
9
mol
238
U
b
238
U
Half of the
has disintegrated, so one half-life has passed, and the rock is
years old.
10
9
4.51
Practice Problem 21.14
Calculate the age of a sample of rock con-
taining 9.11 g of and 9.11 g of its daughter isotope. Assume that no
argon was in the rock when it solidified and that no potassium or argon escaped
from the rock since its solidification. The half-life of
40
40
19
K
18
Ar,
40
10
9
19
K
is
1.3
years.
