Plan
We determine the value of the specific rate constant, k, from the given half-life. This value is
then used in the first-order integrated rate equation to calculate the amount of cobalt-60
remaining after the specified time.
Solution
We first determine the value of the specific rate constant.
t1/2 so k0.131 y^1This value can now be used to determine the ratio of A 0 to A after 30.0 years.
ln
A
A^0
kt0.131 y (^1) (30.0 y)3.93
Taking the inverse ln of both sides,
A
A
^0 51.
A 0 3.42 g, so
A
A
51
0
3.4
5
2
1
g
0.067 g^6027 Co remains after 30.0 years.
You should now work Exercise 54.
DISINTEGRATION SERIES
Many radionuclides cannot attain nuclear stability by only one nuclear reaction. Instead,
they decay in a series of disintegrations. A few such series are known to occur in nature.
Two begin with isotopes of uranium,^238 U and^235 U, and one begins with^232 Th. All three
of these end with a stable isotope of lead (Z82). Table 26-4 outlines in detail the^238 U,
(^235) U, and (^232) Th disintegration series, showing half-lives. For any particular decay step,
the decaying nuclide is called the parentnuclide, and the product nuclide is the daughter.
Uranium-238 decays by alpha emission to thorium-234 in the first step of one series.
Thorium-234 subsequently emits a beta particle to produce protactinium-234 in the
second step. The series can be summarized as shown in Table 26-4a. The netreaction for
the^238 U series is
238
092 U88n
206
082 Pb^8
4
2 He^6
0
1
“Branchings” are possible at various points in the chain. That is, two successive decays
may be replaced by alternative decays, but they always result in the same final product.
There are also decay series of varying lengths starting with some of the artificially produced
radionuclides (Section 26-13).
26-11
0.693
5.27 y
0.693
t1/2
0.693
k
26-11 Disintegration Series 1015
The -radiation from^60 Co is used to treat cancers near the surface of the body.